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Melting enhancement of a phase change material with presence of a metallic mesh
Accepted Manuscript Melting enhancement of a phase change material with presence of a metallic mesh Shahzada Zaman Shuja, Bekir Sami Yilbas, Main Mobeen Shaukat PII:
S1359-4311(15)00038-1
DOI:
10.1016/j.applthermaleng.2015.01.033
Reference:
ATE 6302
To appear in:
Applied Thermal Engineering
Received Date: 4 September 2014 Revised Date:
10 January 2015
Accepted Date: 12 January 2015
Please cite this article as: S.Z. Shuja, B.S. Yilbas, M.M. Shaukat, Melting enhancement of a phase change material with presence of a metallic mesh, Applied Thermal Engineering (2015), doi: 10.1016/ j.applthermaleng.2015.01.033. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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MELTING ENHANCEMENT OF A PHASE CHANGE MATERIAL WITH PRESENCE OF A METALLIC MESH
Bekir Sami Yilbas*
Main Mobeen Shaukat
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Shahzada Zaman Shuja
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ME Department, King Fahd University of Petroleum & Minerals, Dhahran 31261, Saudi Arabia: Email: [email protected]: Tel: +966 3 860 4481
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ABSTRACT
The thermal characteristics of phase change material (n-octadecane) with presence of metallic meshes are investigated in relation to thermal energy storage.
The influence of the mesh
geometry on the phase change duration is predicted for two cases of the metallic mesh arrangements. In the first case, the constant area of the mesh with different geometries, namely triangular, rectangular, and hexagonal, is considered; in which case, the amount of phase change
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material accommodated in each mesh remains the same for all the meshes incorporated. In the second case, the perimeter of the three meshes is considered to be the same. This arrangement results in variation of the mesh area for different mesh geometric configurations. An experiment
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is carried out to validate the predictions of melt isotherms. Since the mesh size used in the experiments is in the order of 50 micrometers, an optical microscope is used to monitor the melting process under the controlled environment. It is found that the predictions of the melt
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isotherm are in good agreement with that of the experimental data. Triangular mesh geometry resulted in the early initiation of the phase change in the mesh. In addition, the total melting time becomes less for the triangular mesh as compared to those of square and hexagonal mesh geometries.
Keywords: Phase Change, Latent Heat, Energy Storage, Metallic Mesh
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INTRODUCTION
Phase change materials (PCM) are widely used in thermal management of heat transferring devices [1 - 2]. This is due to a high thermal storage capacity of the PCM. during the phase
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change process; however, low thermal conductivity of most of PCM limits the practical applications of the phase change materials in thermal storage systems. In this case, the time required for storing the waste heat released from the heat transferring device becomes long and thermal management becomes inefficient at the slow phase change rates. Thermal storage time of
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the phase change materials can be improved through enhancement of the thermal properties such as thermal conductivity. Inclusion of high conductivity nano particles, such as carbon nanotubes
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(CNT) or graphene platelets, in the phase change material enhances the thermal conductivity; provided that the orientation and local concentration of the high conductive particles changes in the phase change material due to the convection current and charged forces generated during the phase change process. Therefore, thermal properties of the mixture of nano particle and phase change material change during the melting process while influencing the heat transfer rates towards the mixture. On the other hand metallic meshes consisting of regular geometric patterns,
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such as polygons, can improve the heat conduction in the phase change material while shortening the thermal storage duration. The metallic meshes are geometrically fixed in the phase change material and mesh positions do not alter locally during the phase change process unlike those of the nano particles. Although different geometric patterns alter the heat conduction rates in the
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phase change material, it is not explicit to assess intuitively or analytically which pattern can result the highest heat conduction rates while shorting the phase change duration. Consequently,
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investigation into influence of mesh patterns on the thermal characteristics of the phase change material becomes necessary.
Considerably research studies were carried out to examine thermal characteristics of the phase change materials. Thermal energy storage utilizing phase change materials was studied by Chukwu et al. [3]. They demonstrated that the use of a copper increased the thermal conductivity of the system while reducing the thermal storage time. A numerical study for the melting of nano-enhanced phase change material in a square cavity was carried out by Sebti et al. [4]. They showed that the nano-fluid heat transfer rate increased and the melting time decreased as the 2
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volume fraction of nanoparticles increased in the phase change material. Thermal performance of a wire-mesh/hollow-glass-sphere composite structure was investigated by Kim et al. [5]. They indicated that the wire-screen-mesh insulation with air in the interstices led to improved insulation, but the use of hollow-glass microspheres did not improve the insulation capabilities.
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A numerical study for melting in an enclosure with discrete protruding heat sources was carried out by Faraji and El Qarnia [6]. They demonstrated that the heat generated in the system was dissipated via melting of PCM (n-eicosane) in the rectangular enclosure. A spiral coil phasechange thermal energy storage tank with cooling agent, as cyclic material, was studied by Hu et
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al. [7]. They showed that thermal energy storage tanks had good storage performance at the beginning, but the thermal energy storage rate became steady over the time and remained very
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low as the time progressed further, indicating that the thermal energy storage ability of the PCM thermal energy storage tank deteriorated over the time. Thermal performance of organic/inorganic nano-composite phase change materials for thermal energy storage in buildings was studied by Chang et al. [8]. They demonstrated that a nano-composite PCM had a good potential for heating and cooling in buildings and it overcame weaknesses and deficiencies of pure P.C.Ms. A numerical analysis to estimate the thermal performance in a finned cylinder
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due to latent heat thermal system was carried out by Ahmadpour et al. [9]. They showed that the thermal performance of the system improved significantly when the fins were incorporated. The performance of a cement-based composite thermal storage system consisting of phase change materials and carbon nanotubes was examined by Han et al. [10]. They showed that the modified
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cement mortar incorporating the carbon nanotubes could effectively enhance the thermal storage property of cement-based building materials. Solidification behavior of a water based nano-fluid
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phase change material with presence of a nucleating agent for cool thermal storage system was studied by Chandrasekaran et al. [11]. The findings revealed that the enhanced heat transport properties of the nano-fluid phase change material along with the elimination of subcooling and accelerating charging would be very useful for designing an energy efficient cool thermal energy storage system. Thermal conductivity enhancement of nanostructure-based colloidal suspensions utilized as phase change materials for thermal energy storage was examined by Khodadadi et al. [12]. They demonstrated that carbon-based nanostructures and carbon nanotubes exhibited far greater enhancement of thermal conductivity in comparison to metallic/metal oxide nanoparticles, which was due to the high aspect-ratio of these nano-fillers. Effects of various 3
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carbon nano-fillers on the thermal conductivity and energy storage properties of paraffin-based nano-composite phase change materials were investigated by Fan et al. [13]. They indicated that graphene nano-platelets resulted in greatest relative enhancement in thermal conductivity due to their two-dimensional planar structure, which led to reduced filler/matrix thermal interface
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resistance. Heat transfer enhancement for thermal energy storage system incorporating stearic acid nano-composite consisting of multi-walled carbon nanotubes was examined by Li et al. [14]. They showed that the addition of multiwall carbon nanotubes could improve the thermal conductivity of stearic acid effectively; however, it also weakened the natural convection of
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stearic acid in the liquid state. Use of highly conducting core–shell phase change materials for thermal regulation was studied by Vitorino et al. [15]. They demonstrated that the microstructure
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of the graphite shell remained stable upon repeated cycling above and below the melting temperature of the paraffin, and shape stabilization was also retained, even without external encapsulation. The melting of phase change material in a cylinder shell with hierarchical heat sink array was investigated by Liu et al. [16].They analyzed the phase change parameters in terms of paraffin melting time, water heating speed and exergy efficiency, in both dimensional and dimensionless forms. The charging and discharging performance of a thermal energy storage
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system with encapsulated phase change was examined by Sellan et al. [17]. They demonstrated that increasing the capsule size, fluid flow rate, or decreasing the Stefan number, resulted in an increase in the thermocline region which finally decreased the effective discharge time and the total utilization. Thermal conductivity enhancement of the phase change materials with ultrathin-
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graphite foams for thermal energy storage was investigated by Ji et al. [18]. They demonstrated that embedding continuous ultrathin-graphite foams with low volume fractions (0.8-1.2 vol%) in
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a phase change material could increase thermal conductivity by up to 18 times, with negligible change in the melting temperature or specific heat of fusion of the phase change materials. The performance assessment of heat storage by phase change materials containing multiwall carbon nanotubes and graphite were carried out by Teng et al. [19]. They indicated that adding multiwall carbon nanotubes reduced the melting temperature and increased the solidification temperature of the phase change material.
Although thermal conductivity enhancement of the phase change material was studied earlier [18, 19], the main focus was to use carbon nanotubes or graphene platelets in the phase change 4
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material and the use of metallic meshes is not incorporated in the storage systems. Therefore, in the present study, melting and storage characteristics of phase change material incorporating types of meshes are investigated. Three different mesh geometries, namely, triangle, square, and hexagonal are incorporated in the analysis. The geometric configurations of the meshes are
phase change material.
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arranged to have either the same area or the same perimeter while keeping constant amount of The geometric configuration of the metallic mesh resulting in the
shortest melting duration is identified. The numerical predictions are validated with the
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experimental data.
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THERMAL ANALYSIS
In the analysis, phase change material (n-octadecane) and aluminum mesh are considered to be present simultaneously in the solution domain. The mesh geometry is varied to include triangular, rectangular, and hexagonal geometric configurations. Two cases are considered in the simulations. In the first case, the area of the meshes with different configurations is set to be the
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same. In the second case, triangular, rectangular, and hexagonal meshes have the same perimeter. In order to estimate the total melting time of the phase change material for both cases, constant temperature heat source is allocated at the edges of the mesh. The study is extended to include the simulation of same kind of the multi mesh system incorporating the same amount of phase
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change material. The simulations are repeated for three different mesh geometries, namely, triangular, rectangular, and hexagonal. In this case, constant temperature heat source is allocated
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at one edge of the multi mesh thermal storage system and the other edges are kept insulated.
The transient heat equation for the phase change material and aluminum substrate can be written as:
∂ ( ρ c pT ) ∂t
= ∇. ( k∇T )
(1)
where k, cp and ρ denote thermal conductivity, specific heat, and density respectively. 5
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For the solid and liquid phases, the specific heat capacity of the phase change material (PCM) does not alter considerably for the temperature range considered in the present study (293 K – 308 K). However, the specific heat capacity cp , changes considerably during the phase change
∆cp =
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process. The change can be approximated by: ∆h T
(2)
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switching from 0 to 1 over the transition interval.
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where ∆h is the variation of enthalpy, represented by using a normalized Gaussian function θ
As the PCM heats up, it melts and, during the phase transition, a significant amount of latent heat is absorbed. The total amount of heat absorbed per unit mass of PCM during the transition is given by ∆h . The PCM undergoes a temperature transition zone of 3 K (Tliquidus - Tsolidus, where Tliquidus is the liquidus temperature and Tsolidus is the solidus temperature of the PCM), during which a mixture of both solid and molten material co-exist in a mushy zone. To account for the
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∆h latent heat related to the phase transition, cp in the heat equation is replaced with cp + δ , ∆T where ∆h is the latent heat of the transition and δ is a distribution that satisfy the relation related to specific heat-temperature behavior during the phase change. In this case, the latent heat
Tm +∆T
Tm −∆T
(δ
∆h )dT = ∆h ∆T
(3)
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∫
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of melting can be written as:
where the left side is the total amount of heat absorbed per unit mass during the melting, Tm is the melting point and ∆T denotes the half-width of the curve, here set to 3K, representing half the transition temperature span. For the present study the normalized Gaussian function is used. The volume fraction of the liquid phase B, is given by:
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T > Tm + ∆T 1 B = (T − Tm + ∆T ) / 2∆T Tm − ∆T ≤ T ≤ Tm + ∆T 0 T < Tm − ∆T
(4)
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In order to solve Eq. 1 numerically, the boundary and initial conditions need to be introduced. The solution domain covers the frame of the optical images taken under the microscope. This enables to simulate the actual process at microscopic level. Since the scale of the solution
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domain is in the order of hundred micrometers, the Fourier heating law is applicable.
Initial condition:
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Initially, it is assumed that the solution domain is at an initial equilibrium temperature (Tin), i.e.:
T ( x , y ,0 ) = Tin = 293K
The boundary conditions are presented according to the considerations incorporated in the simulations.:
Boundary conditions:
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Triangular, rectangular, and hexagonal mesh with the same areas or same perimeters:
) is introduced in the mesh. In this case, the rate of input
, where A is the area of the mesh) to each mesh becomes the same for the same
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heat flux (
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A constant rate of total heat (
area meshes; however, it changes as the area changes for the constant perimeter meshes. In addition, the edges of the mesh are considered to be insulated. Figure (1) shows the boundary conditions for different meshes.
Thermal storage system consisting of phase change material and one type of a meshes:
A schematic view of the thermal storage system and the boundary conditions are shown in figure (2). The number of meshes incorporated in the solution domain is 10×10. The top edge of the 7
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storage system is considered to be at a fixed temperature (T = 308 K). Insulated boundary condition is considered for the all other boundaries, i.e.:
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∂T ∂T ∂T ( xmax , y ,t ) = ( x ,0,t ) = ( x , ymax ,t ) = 0 ∂x ∂y ∂y
NUMERICAL SOLUTION
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In order to solve the transient heat conduction equation (Eq. 1) for a stationary medium, the finite element method is utilized. This method provides a means of spatial and temporal discretization
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of the governing equation. As a first step the application of the Galerkin method for the transient equation subjected to appropriate boundary and initial conditions is addressed. The temperature is discretized over space as follows:
n
T ( x , y ,t ) = ∑ Ni ( x , y ) Ti ( t )
(5)
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i =1
where Ni are the shape functions, n is the number of nodes in an element, and Ti(t) are the timedependent nodal temperatures. Triangular elements are used, which defines the shape functions
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for the present study.
The Galerkin representation of the energy equation is:
∫
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∂ ( ρ cpT ) Ni ∇. ( k∇T ) − dΩ = 0 ∂t Ω
(6)
Ω is the solution domain. Employing the gauss-divergence theorem for the conduction term and
on substituting the spatial approximation from Eq.1, the spatially discretized finite element equation becomes:
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∂T + [K ]{T} = {f} ∂t
[C ]
(7)
[C] = ∫
Ω
[K ] = ∫ [B] [D][B]dΩ;
ρ cp [N] [N] dΩ; T
T
Ω
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where
{f} = ∫ q [N]
T
Γq
d Γq
(8)
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Γ q is the boundary where q the heat flux is prescribed. [B] = ∇N is the derivative matrix, which
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relates the gradient of the field variable to the nodal values, and [D] is the property matrix.
Since the thermal conductivity k(T), density ρ(T) and cp(T) are functions of temperature in general, the resulting equation is non-linear and requires an iterative solution.
Time discretization using the Finite Difference Method (FDM)
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It can be seen from the semi-discrete form of Eq. 7 that the differential operator involving the time-dependent term still remains to be discretized; in this case, a numerical approximation using the backward Euler finite difference method is considered.
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For temperature variation in the time domain between the n and n + 1 time levels, using the first
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term of the Taylor series, we can write the temperature gradient as: ∂T T n+1 − T n = ∂t ∆t
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which when substituted in Eq. 7 gives for the backward Euler scheme:
T n +1 − T n n +1 n +1 C [ ] + [K ]{T} = {f} ∆t
(10)
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Re-arrangement gives: n +1
= [ C]{T} + ∆t {f} n
n +1
(11)
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([C] + ∆t [K ]){T}
This equation gives the nodal values of temperature at the n + 1 time level. These temperature values are calculated using the n time level values.
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Stability
The implicit scheme with a backward difference approximation (BDF) for the time used in the study is unconditionally stable; however, the accuracy of the scheme is governed by the size of
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the time step.
In the simulations, three different geometric meshes are considered and the amount of PCM is kept the constants for all the cases in the thermal storage system. In addition, the amount of aluminum in the solution domain is kept the same for the aluminum meshes cases. Therefore,
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aluminum mass remains constant in the solution domain consists of PCM and aluminum mesh.
The grid independent tests were conducted; in which case, the number of elements used in the solution domain is doubled. It is observed that the differences in time to reach of the melting
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temperature due to both element sizes are significantly small, which is in the order of 0.1%.
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Table 1 gives the data used for PCM and aluminum in the simulations.
EXPERIMENTAL
The experiment was carried out to examine the melting stages of n-octadecene phase change material in the square aluminum mesh. Since the cells were small in size ( ∼ 55 µm×55 µm), the experimental tests were carried out under the optical microscope. The aluminum meshes were prepared as shown in figure (3). The meshes were filled totally with n-octadecene. The samples
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were, then, kept in the refrigerator at 285 K for one hour to ensure the complete solidification of n-octadecene in the aluminum meshes. The samples consisting of complete solidified phase change material and aluminum meshes were kept in the laboratory environment to reach temperature of 293 K prior to the phase change tests. A small test rig was developed and the
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workpiece was heated from one end at a constant temperature heat source at 308 K. Temperature variation across the workpiece was monitored and the stages of the phase change during the heating cycle was recorded under the optical microscope. The experiment was repeated five times to ensure the repeatability of the temperature measurement and the stages of the phase
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change during the heating process. The experimental error was determined as 6% based on the repeatability of the temperature data during the tests. The experimental conditions were
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incorporated in the simulations to predict the various stages of the molten distribution in the aluminum meshes.
Figure (4) shows micrograph of aluminum mesh and molten PCM obtained from the optical microscope and its counterpart corresponding to the simulations for the same heating period. It can be observed that the melted regions corresponding to the experiment and predictions agree
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well. The small differences between the both results are associated with the experimental error and the consideration of homogeneous properties of the PCM in the simulations. In addition, the total melting time of PCM in the aluminum mesh is measured and the finding is compared with that of predicted from the numerical simulations. It is found that the time required for the total
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melting of PCM in the aluminum mesh is 1.3 s and the predicted time for the total melting is 1.35 s, which are very close. It should be noted that the PCM used in the experiments is
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technical grade with the purity in the order of 99%.
RESULTS AND DISCUSSION
Thermal characteristics of the phase change material are examined for different geometric configurations of the metallic meshes. The duration of the complete melting is predicted for different mesh configurations while keeping the amount of phase change material constant in the thermal storage system. A numerical method is introduced to obtain the temperature field and liquid fraction distribution in the solution domain. 11
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Figure (5) shows temperature contours for different geometric configurations of the metallic meshes while figure (6) shows liquid fraction contours. The contours are prepared for two cases: i) the area covered by the mesh remains the same for all the geometric configurations of the
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mesh, and ii) the perimeter of the mesh remains the same for all the mesh configurations. A uniform heat input (5 W) is introduced in the mesh and initially the mesh and the phase change material are assumed to be at the uniform temperature of 293 K. In the first case (constant area mesh), amount of phase change material in the mesh remains constant and the heat flux (W/m2)
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is the same for each geometric configuration of the mesh. In the second configuration, the perimeter of the different meshes remains the same while amount of the phase change material
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accommodated in each mesh varies. In this case, the total heat inputted (5 W) remains the same for all different configurations of the mesh; however, heat flux changes from one mesh type to another because of the different mesh area. Since the best edges are considered to be insulated, temperature remains high in the vicinity of the edges. Since the heating duration is kept the same for all the configurations of the mesh, partially melting of phase change material is observed for some mesh configurations, which is more pronounced for the constant area mesh arrangement
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(first case). It should be noted that the amount of heat inputted is the same for all the geometric configurations of the meshes. However, small changes in temperature are associated with the heat diffusion in the mesh, which alters because of the length scale change towards the mesh edges. This situation is also seen from the liquid fraction contours. However, thermal
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conductivity of the phase change material is low (0.358 W/mK [20]), the rate of heat diffusion is low while resulting in slow temperature increase and melting in the solution domain. In the case
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of the constant perimeter arrangements (case 2), heat flux varies because of the coverage area of the mesh. Since the rectangular and hexagonal meshes have larger area than that of the triangular mesh, heat flux in the triangular mesh becomes larger than those corresponding to the rectangular and hexagonal meshes. Consequently, heat inputted to the mesh becomes less for the square and the hexagon meshes as compared to that of the triangle mesh. This in turn increases the amount of melt in the phase change material within the triangular mesh. Nevertheless, the constant area and constant perimeter arrangements of the different configurations of the meshes provide useful information on the local effect during the melting process. The triangular mesh
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results in larger melted region in the mesh corners than that of the other geometric mesh configurations.
Figure (7) shows temporal variation of ratio of the amount of liquid phase over the total phase
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change material in a single mesh for different mesh geometric configurations with the constant area (the first case). The phase change initiates around 0.4 ms of the heating duration. However, it initiates earlier for the triangular mesh as compared to other mesh geometries. This behavior is attributed to the melting initiation in the corner region of the triangular mesh; in which case,
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small corner angle (≤ 90o) enhances the heat diffusion in between the edges. However, as the heating period progresses, the rate of melting in the cell becomes almost the same regardless of
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the mesh shape. As the heating progresses further, the completion of the melting becomes earlier for the hexagonal mesh. This is associated with the large area of the hexagonal mesh as compared to the square and triangle meshes, i.e, heat inputted per unit area becomes small for the triangular mesh, which enhances the heat diffusion towards the phase change material in the triangular mesh. Moreover, the time required for melting initiation is almost the half of the total time required for the complete melting when mlig/mtot = 1. Figure (8) shows temporal variation of
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the ratio of the amount of liquid phase over the total mass of the phase change material in the mesh for three geometric configurations due to constant perimeter of the meshes (case 2). It should be noted that keeping the same mesh perimeter results in variation of the mesh areas for different mesh geometries. In this case, triangular mesh results in the smaller area, then follows
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rectangular and the hexagonal mesh. Melting initiates earlier for the rectangular mesh as similar to that observed for the case 1 (constant area meshes). As the heating period progresses, the rate
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of melting differs for different meshes unlike the behavior observed for the case 1. This is attributed to the amount of phase change material in each mesh; in which case, the triangular mesh accommodates smaller amount of the phase change material as compared to those of the rectangular and the hexagon meshes. This alters the ratio of melted phase change material to the total phase change material in the mesh, since the area of each mesh is different. Although the melting starts from the neighborhood of the edges of each mesh and propagates towards the phase change material in the mesh regardless of the cases considered, alteration of the total amount of the phase change material in the mesh changes the values of the ratio of mlid/mtot. This results in different rise of the melting rate for the case 2. Moreover, the completion of melting in 13
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the mesh takes place earlier in the triangular mesh, and then follows the rectangular and the hexagonal meshes. This is due to the amount of phase change material in the hexagonal mesh, which is larger than those of the triangular and rectangular mesh.
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Figure (9) shows temperature variation at the centroidal point of the mesh for three different mesh geometries corresponding to the same area (case 1). The rise of temperature is steady at the centroidal point for all the mesh geometries considered. The slight change of the slope is associated with the phase change at this location. Since the phase change process is fast in the
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mesh, this behavior only occurs during the short time period. However, temporal rise of temperature is almost the same for all the mesh geometries considered in the simulations. This
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behavior is attributed to the same area of the each mesh geometry (case 1). Consequently, the distance away from the controidal point to the mesh edge remains almost the same for all the mesh geometries considered. However, in the case of the same perimeter of the mesh geometries (case 2), the rise of temperature alters at the centroidal point. This can be observed from figure (10), in which temporal variation of temperature is shown for three geometries with the same perimeter (case 2). Temperature behavior indicates that melting initiation, completion, and
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sensible heating takes place at different times in each mesh having different geometries. The time taken for the heat diffusion at the centroidal point of the mesh becomes different for each mesh having the same perimeter. Therefore, the distance between the centroidal point to the mesh edge changes for different mesh geometries having the same perimeter. In this case, the use
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of triangular mesh results in sharp increase in temperature at the centroidal point then follows rectangular and hexagonal meshes. Since the melting temperature of n-octadecane is in between
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301.15K and 303.15 K [20] (Tsolidus = 301.15K and Tliquidus = 303.15 K [17]), sensible heating almost dominates at the centroidal point of the mesh, which is more pronounced for the triangular mesh due to early completion of melting at the centroidal point. This indicates that although phase change material initiates melting earlier for the triangular mesh, energy input enhances the sensible heating of the phase change material in the mesh. Consequently, altering the mesh geometry, energy storage due to phase change and sensible heating of the phase change material takes place at different rates, which is particularly true for the constant perimeter of mesh arrangement (case 2).
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The study is extended to include incorporating the multi meshes in the phase change material. In this case, the total number of meshes and their total area remain the same in the solution domain. However, the heating situation is changed such that constant temperature heat source is introduced at one edge of the solution domain and the other edges of the solution domain are
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considered to be insulated (figure (2)). The resulting temperature contours and temporal variation of the ratio of liquid mass over the total mass of the phase change material are shown in figures (11) and (12), respectively. The temperature contours in figure (11) are plotted at the location of the centroidal point. All the mesh geometries incorporated in the simulations result in almost
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similar temperature contours in the solution domain. However, the close examination of figure (12) reveals that temporal behavior of the ratio of amount of melted phase change material over
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the total amount of phase change material differs for each mesh geometry considered. In this case, triangle mesh results in highest rate of the ratio then follows the square and the hexagonal meshes. Since the amount of phase change material is the same in the solution domain for all the mesh geometries, triangle mesh geometry causes early completion of the melting of the phase change material. Consequently, triangular mesh results in improved conduction tree while increasing the melting rate in the solution domain, i.e. heat carried by the metallic mesh is
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distributed in the solution domain in such a way that the rate of melting increases. However, the rate of melting remains almost similar for the square and hexagonal meshes. This is attributed to the conduction tree formed in the phase change material, which results in similar heat carrying performance in the solution domain. Therefore, using the rectangular mesh improves the melting
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rate and shortens the time taken for the latent heat thermal storage in the phase change material. Consequently, the present study provides a starting framework for future studies of high rate of
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melting of phase change material for latent heat thermal storage applications incorporating the metallic meshes with different geometric configurations.
Although the use of meshes and fins [9, 17] were demonstrated to improve thermal performance of phase change material in terms of duration of thermal storage, the effect of mesh geometry on the storage time were not considered in the previous study [17]. Therefore, the present study provides useful information about the effects of mesh geometry on the storage capacity and melting duration (charging time). However, using the metallic meshes improve significantly the
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charging time of the phase change thermal storage system as consistent with the findings of the early work [17].
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CONCLUSION
Thermal storage characteristics of the phase change material are investigated after incorporating the metallic meshes with different geometric configurations in the phase change material. The
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effect of the mesh geometry on the melting duration is examined for two metallic mesh arrangements. In the first case, the area of the meshes with different geometries, namely
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triangular, rectangular, and hexagonal, is considered to be constant; in which case, the amount of phase change material accommodated in each mesh remains the same for all the meshes considered. In the second case, the perimeter of all meshes is assumed to be the same. This arrangement results in different mesh areas for different mesh geometric configurations. In this case, triangular mesh gives rise to the smallest area then follows rectangular and hexagonal meshes. A uniform heat source is introduced in the mesh to assess the temporal behavior of the
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phase change process and the total melting duration due to mesh geometric configurations. In addition, in the simulations, a uniform temperature is assumed initially in the phase change material. The experiment is carried out to validate the predictions of melt isotherms. Since the mesh size used is in the order of 50 micrometers, a microscope is used to monitor the melting
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process under the controlled environment during the experiments. It is found that melt isotherm predicted agrees well with its counterpart obtained from the experiment. Time taken for complete
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melting of the phase change material is the shortest for the triangular mesh geometry then follows the rectangular and hexagonal mesh. This is more pronounced for the meshes having the same perimeter. In this case, the area covered by triangular mesh becomes smaller than those of the rectangular and the hexagonal meshes. On the other hand, keeping the mesh area same for three mesh geometries, the melting duration becomes almost the same for all the mesh geometries; provided that melting initiates earlier in the corner region of the triangular mesh. Therefore, the melting initiation delays as the corner angle of the mesh increases, i.e. melting in the phase change material starts earlier for the square mesh as compared to that of the hexagonal mesh. In general, the triangular mesh forms better conduction tree in the phase change material 16
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while carrying and distributing the heat effectively in the phase change material. In this case, the total melting duration of the phase change material becomes small. Therefore, the present study provides useful information for the designing and management of the latent heat storage systems incorporating the metallic meshes.
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REFERENCES
[1] R Baby and C Balaji, Thermal management of electronics using phase change material based
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pin fin heat sinks, J. Phys.: Conf. Ser. Vol. 395, doi:10.1088/1742-6596/395/1/012134, 2012.
[2] H. Ge and J. Liu, Cooling capacity of metal phase change material for thermal management
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of mobile phone subject to long time communication, ASME 2013 International Mechanical Engineering Congress and Exposition, Volume 8B: Heat Transfer and Thermal Engineering, doi:10.1115/IMECE2013-66240, San Diego, California, USA, November 15–21, 2013.
[3] S. Chukwu, E. Ogbonnaya, L. Weiss, Fabrication, testing, and enhancement of a thermal energy storage device utilizing phase change materials. ASME 2012 Heat Transfer Summer
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Conf. Collocated with the ASME 2012 Fluids Engineering Div. Summer Meeting and the ASME 2012 10th Int. Conf. on Nanochannels, Microchannels and Minichannels, HT 2012, DOI: 10.1115/HT2012-58309, Vol. 1, p 279-285, 2012.
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[4] S.S. Sebti, M. Mastiani, H. Mirzaei, A. Dadvand, S. Kashani, S.A. Hosseini, Numerical study of the melting of nano-enhanced phase change material in a square cavity, J. of Zhejiang
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University: Science A, Vol. 14, n 5, pp. 307-316, 2013.
[5] D.K. Kim and E.E. Marotta, L.S. Fletcher, Thermal performance of a wire-mesh/hollowglass-sphere composite structure, J. of Thermophysics and Heat Transfer, Vol. 25, n 2, pp. 254261, 2011.
[6] M. Faraji and H. El Qarnia, Numerical study of melting in an enclosure with discrete protruding heat sources, Applied Mathematical Modelling, Vol. 34, n 5, pp. 1258-1275, 2010.
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[7] W-J. Hu, Y-Q. Jiang, Y. Yao, Z-L. Ma, Modeling a spiral coil phase-change thermal energy storage tank with cooling agent as cyclic material, J. of Harbin Engineering University, Vol. 29, n 10, pp. 1135-1140, 2008.
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[8] J. Chang, W. Duan, B.Liu, S. Fu, Preparation and properties of organic/inorganic nanocomposite phase change materials for heat energy storage in building energy conservation, Advanced Materials Research, Vol. 374-377, pp. 346-351, 2012.
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[9] V. Ahmadpour, N. Ahmadi, S. Rezazadeh, M. Sadeghiazad, Numerical analysis of thermal performance in a finned cylinder for latent heat thermal system (LHTS) applications, Int. J. of
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Heat and Technology, Vol. 31, n 1, pp. 155-162, 2013.
[10] B. Han, K. Zhang, X. Yu, Enhance the thermal storage of cement-based composites with phase change materials and carbon nanotubes, J. of Solar Energy Engineering, Transactions of the ASME, Vol. 135, n 2, DOI: 10.1115/1.4023181, 2013.
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[11] P. Chandrasekaran, M. Cheralathan, V. Kumaresan, R. Velraj, Solidification behavior of water based nanofluid phase change material with a nucleating agent for cool thermal storage system, Int. J. of Refrigeration, Vol. 41, pp. 157-163, 2014.
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[12] J.M. Khodadadi, L. Fan, H. Babaei, Thermal conductivity enhancement of nanostructurebased colloidal suspensions utilized as phase change materials for thermal energy storage: A
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review, Renewable and Sustainable Energy Reviews, Vol. 24, pp. 418-444, 2013.
[13] L-W. Fan, X. Fang, X. Wang, Y. Zeng, Y-Q. Xiao, Z-T. Yu, X.Xu, Y-C. Hu, K-F. Cen, Effects of various carbon nanofillers on the thermal conductivity and energy storage properties of paraffin-based nanocomposite phase change materials, Applied Energy, Vol. 110, pp. 163172, 2013.
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[14] X-T. Li, J-H. Lee, R-Z. Wang, Y.T. Kang, Enhancement of heat transfer for thermal energy storage application using stearic acid nanocomposite with multi-walled carbon nanotubes, Energy, Vol. 55, pp. 752-761, 2013.
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[15] N. Vitorino, J.C.C. Abrantes, J.R. Frade, Highly conducting core–shell phase change materials for thermal regulation, Applied Thermal Engineering, Vol. 66, Issues 1–2, pp. 131-139, 2014.
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[16] H. Liu, S. Li, Y. Chen, Z. Sun, The melting of phase change material in a cylinder shell with
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hierarchical heat sink array, Applied Thermal Engineering, Vol. 73, Issue 1, pp. 975-983, 2014.
[17] S. Bellan, J. Gonzalez-Aguilar, M. Romero, M.M. Rahman, D.Y. Goswami, E.K. Stefanakos, D. Couling,
Numerical analysis of charging and discharging performance of a
thermal energy storage system with encapsulated phase change material, Applied Thermal Engineering, Vol. 71, Issue 1, pp. 481-500, 2014.
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[18] H. Ji, D.P. Sellan, M.T. Pettes, T. Michael, X. Kong, J. Ji, L. Shi, R.S. Ruoff, Enhanced thermal conductivity of phase change materials with ultrathin-graphite foams for thermal energy storage, Energy and Environmental Science, Vol. 7, n 3, pp. 1185-1192, 2014.
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[19] T-P. Teng, C-M. Cheng, C-P. Cheng, Performance assessment of heat storage by phase change materials containing MWCNTs and graphite, Applied Thermal Engineering, Vol. 50, n 1,
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pp. 637-644, 2013.
[20] American Society of Heating, Refrigerating and Air Conditioning Engineers, ASHRAE, Handbook of Fundamentals, ASHRAE, New York, NY, 2001.
[21] F.P. Incorpera, D.P. Dewitt, T.L. Bergman, A.S. Lavine, Fundamentals of Heat and Mass Transfer, 6th Ed., John Wiley and Sons, NJ, 2007.
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Acknowledgments:
The authors acknowledge the funded project RG 1204 via support of Thermoelectric Group formed by the Deanship of Scientific Research at King Fahd University of Petroleum and
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Minerals, Dhahran, Saudi Arabia for this work.
Cp(T) Temperature dependent heat capacity (J/kgK)
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NOMENCLATURE
Thermal capacitance matrix
H
Enthalpy (J/kg)
{f}
Source term
k(T)
Temperature dependent thermal conductivity (W/mK)
[k]
Thermal conductivity matrix
n
Time level of iteration
Ni
Shape factor
T
Temperature (K)
t
Time (s)
∆t
Time increment
Tm
Averaged melting temperature (K)
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[C]
Tliquidus Liquid phase temperature during phase change (K)
∆T q x xmax
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Tsolidus Solid phase temperature during phase change (K) Temperature increment
Heat flux (W/m2)
Distance along x-axis (m) Location along x-axis where liquid phase terminates (m)
y
Distance along y-axis (m)
ymax
Location along y-axis where liquid phase terminates (m)
Greek Symbols 20
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Distribution function of latent heat of melting
ρ
Density (kg/m3)
Γq
Heat flux boundary
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δ
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List of Table Captions
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Table 1. Properties of n-octadecane and aluminum used in the simulations [20, 21].
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List of Figure Captions
Figure 1. Geometric configurations of the meshes used in the simulations and the boundary conditions.
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Figure 2. A schematic view of the thermal storage system consisting of aluminum meshes and the phase change material, and boundary conditions used in the simulations. It should be noted that square mesh is shown; however, the boundary conditions are applicable for the triangular and hexagonal meshes. In addition, number of meshes and the total area remain the constant for the triangular and the hexagonal meshes.
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Figure 3. Optical images of aluminum meshes: a) without PCM filled and ii) with PCM filled. Figure 4. Optical Image captured under microscope and simulation results for the liquid fraction.
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Figure 5. Simulation results of temperature contours in the different meshes for constant area (case 1) and constant perimeter consideration. Heating duration is 0.8 s. Figure 6. Simulation results of liquid fraction contours in the different meshes for constant area (case 1) and constant perimeter consideration. Heating duration is 0.8 s.
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Figure 7. Simulation results of temporal variation of the ratio of liquid mass over the total mass of PCM in different meshes. Simulations correspond to the consideration of constant area meshes. Figure 8. Simulation results of temporal variation of the ratio of liquid mass over the total mass of PCM in different meshes. Simulations correspond to the consideration of constant perimeters of meshes.
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Figure 9. Simulation results of temporal variation of temperature at the centroidal point of the solution domain for different mesh arrangements. It should be noted that mesh area remains constant for all the meshes considered (case 1).
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Figure 10. Simulation results of temporal variation of temperature at the centroidal point of the solution domain (thermal storage system) for different mesh arrangements. It should be noted that mesh perimeter remains constant for all the meshes considered (case 2). Figure 11. Simulation results of temperature contours in the thermal storage system for different meshes. The heating period is 0.01 s. Figure 12. Simulation results of temporal variation of the ratio of liquid mass over the total mass of PCM in the thermal storage system incorporating different meshes.
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Table 1. Properties of n-octadecane and aluminum used in the simulations [20, 21]. Specific Heat
Thermal
Latent Heat of Tsolidus
kg/m3
J/kgK
conductivity
Melting
Tliquidus
W/mK
J/kg
K
Solid Phase
814
2150
0.358
236624
301.15
Liquid
774
2180
0.152
-
303.15
2702
903
237
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Density
321000
933
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Aluminum
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Phase
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and
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5
5
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Insulated Edges
Figure 1. Geometric configurations of the meshes used in the simulations and the boundary
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conditions.
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Insulated Edges
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Insulated Edges
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T = 308 K
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Insulated Edges
Figure 2. A schematic view of the thermal storage system consisting of aluminum meshes and the phase change material (), and boundary conditions used in the simulations. It should be noted that square mesh is shown; however, the boundary conditions are applicable for the triangular and hexagonal meshes. In addition, number of meshes and the total area remain the constant for the triangular and the hexagonal meshes.
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a)
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Aluminum Meshes
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b)
200 µm
PCM in Solid Phase
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Aluminum Meshes with PCM
Figure 3. Optical images of aluminum meshes: a) without PCM filled and ii) with PCM filled.
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Liquid Phase Solid Phase
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Mushy Zone
Mushy Zone Solid Phase
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Liquid Phase
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200 µm
Figure 4. Optical Image captured under microscope and simulation results for the liquid fraction.
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Figure 5. Simulation results of temperature contours in the different meshes for constant area (case 1) and constant perimeter consideration. Heating duration is 0.8 s. 29
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Figure 6. Simulation results of liquid fraction contours in the different meshes for constant area (case 1) and constant perimeter consideration. Heating duration is 0.8 s. 30
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Figure 7. Simulation results of temporal variation of the ratio of liquid mass over the total mass of PCM in different meshes. Simulations correspond to the consideration of constant area meshes.
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Figure 8. Simulation results of temporal variation of the ratio of liquid mass over the total mass of PCM in different meshes. Simulations correspond to the consideration of constant perimeters of meshes. 32
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Figure 9. Simulation results of temporal variation of temperature at the centroidal point of the solution domain for different mesh arrangements. It should be noted that mesh area remains constant for all the meshes considered (case 1).
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Figure 10. Simulation results of temporal variation of temperature at the centroidal point of the solution domain (thermal storage system) for different mesh arrangements. It should be noted that mesh perimeter remains constant for all the meshes considered (case 2).
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Figure 11. Simulation results of temperature contours in the thermal storage system for different meshes. The heating period is 0.01 s. 35
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Figure 12. Simulation results of temporal variation of the ratio of liquid mass over the total mass of PCM in the thermal storage system incorporating different meshes.
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Research Highlights
Time taken for complete melting of PCM is shortest for triangular aluminum mesh.
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Melting duration is almost same for different mesh geometries of same area.
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Melting initiates earlier in corner region of meshes.
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Triangular mesh forms better conduction tree in phase change material.
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S1359-4311(15)00038-1
DOI:
10.1016/j.applthermaleng.2015.01.033
Reference:
ATE 6302
To appear in:
Applied Thermal Engineering
Received Date: 4 September 2014 Revised Date:
10 January 2015
Accepted Date: 12 January 2015
Please cite this article as: S.Z. Shuja, B.S. Yilbas, M.M. Shaukat, Melting enhancement of a phase change material with presence of a metallic mesh, Applied Thermal Engineering (2015), doi: 10.1016/ j.applthermaleng.2015.01.033. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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MELTING ENHANCEMENT OF A PHASE CHANGE MATERIAL WITH PRESENCE OF A METALLIC MESH
Bekir Sami Yilbas*
Main Mobeen Shaukat
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Shahzada Zaman Shuja
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ME Department, King Fahd University of Petroleum & Minerals, Dhahran 31261, Saudi Arabia: Email: [email protected]: Tel: +966 3 860 4481
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ABSTRACT
The thermal characteristics of phase change material (n-octadecane) with presence of metallic meshes are investigated in relation to thermal energy storage.
The influence of the mesh
geometry on the phase change duration is predicted for two cases of the metallic mesh arrangements. In the first case, the constant area of the mesh with different geometries, namely triangular, rectangular, and hexagonal, is considered; in which case, the amount of phase change
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material accommodated in each mesh remains the same for all the meshes incorporated. In the second case, the perimeter of the three meshes is considered to be the same. This arrangement results in variation of the mesh area for different mesh geometric configurations. An experiment
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is carried out to validate the predictions of melt isotherms. Since the mesh size used in the experiments is in the order of 50 micrometers, an optical microscope is used to monitor the melting process under the controlled environment. It is found that the predictions of the melt
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isotherm are in good agreement with that of the experimental data. Triangular mesh geometry resulted in the early initiation of the phase change in the mesh. In addition, the total melting time becomes less for the triangular mesh as compared to those of square and hexagonal mesh geometries.
Keywords: Phase Change, Latent Heat, Energy Storage, Metallic Mesh
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INTRODUCTION
Phase change materials (PCM) are widely used in thermal management of heat transferring devices [1 - 2]. This is due to a high thermal storage capacity of the PCM. during the phase
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change process; however, low thermal conductivity of most of PCM limits the practical applications of the phase change materials in thermal storage systems. In this case, the time required for storing the waste heat released from the heat transferring device becomes long and thermal management becomes inefficient at the slow phase change rates. Thermal storage time of
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the phase change materials can be improved through enhancement of the thermal properties such as thermal conductivity. Inclusion of high conductivity nano particles, such as carbon nanotubes
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(CNT) or graphene platelets, in the phase change material enhances the thermal conductivity; provided that the orientation and local concentration of the high conductive particles changes in the phase change material due to the convection current and charged forces generated during the phase change process. Therefore, thermal properties of the mixture of nano particle and phase change material change during the melting process while influencing the heat transfer rates towards the mixture. On the other hand metallic meshes consisting of regular geometric patterns,
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such as polygons, can improve the heat conduction in the phase change material while shortening the thermal storage duration. The metallic meshes are geometrically fixed in the phase change material and mesh positions do not alter locally during the phase change process unlike those of the nano particles. Although different geometric patterns alter the heat conduction rates in the
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phase change material, it is not explicit to assess intuitively or analytically which pattern can result the highest heat conduction rates while shorting the phase change duration. Consequently,
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investigation into influence of mesh patterns on the thermal characteristics of the phase change material becomes necessary.
Considerably research studies were carried out to examine thermal characteristics of the phase change materials. Thermal energy storage utilizing phase change materials was studied by Chukwu et al. [3]. They demonstrated that the use of a copper increased the thermal conductivity of the system while reducing the thermal storage time. A numerical study for the melting of nano-enhanced phase change material in a square cavity was carried out by Sebti et al. [4]. They showed that the nano-fluid heat transfer rate increased and the melting time decreased as the 2
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volume fraction of nanoparticles increased in the phase change material. Thermal performance of a wire-mesh/hollow-glass-sphere composite structure was investigated by Kim et al. [5]. They indicated that the wire-screen-mesh insulation with air in the interstices led to improved insulation, but the use of hollow-glass microspheres did not improve the insulation capabilities.
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A numerical study for melting in an enclosure with discrete protruding heat sources was carried out by Faraji and El Qarnia [6]. They demonstrated that the heat generated in the system was dissipated via melting of PCM (n-eicosane) in the rectangular enclosure. A spiral coil phasechange thermal energy storage tank with cooling agent, as cyclic material, was studied by Hu et
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al. [7]. They showed that thermal energy storage tanks had good storage performance at the beginning, but the thermal energy storage rate became steady over the time and remained very
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low as the time progressed further, indicating that the thermal energy storage ability of the PCM thermal energy storage tank deteriorated over the time. Thermal performance of organic/inorganic nano-composite phase change materials for thermal energy storage in buildings was studied by Chang et al. [8]. They demonstrated that a nano-composite PCM had a good potential for heating and cooling in buildings and it overcame weaknesses and deficiencies of pure P.C.Ms. A numerical analysis to estimate the thermal performance in a finned cylinder
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due to latent heat thermal system was carried out by Ahmadpour et al. [9]. They showed that the thermal performance of the system improved significantly when the fins were incorporated. The performance of a cement-based composite thermal storage system consisting of phase change materials and carbon nanotubes was examined by Han et al. [10]. They showed that the modified
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cement mortar incorporating the carbon nanotubes could effectively enhance the thermal storage property of cement-based building materials. Solidification behavior of a water based nano-fluid
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phase change material with presence of a nucleating agent for cool thermal storage system was studied by Chandrasekaran et al. [11]. The findings revealed that the enhanced heat transport properties of the nano-fluid phase change material along with the elimination of subcooling and accelerating charging would be very useful for designing an energy efficient cool thermal energy storage system. Thermal conductivity enhancement of nanostructure-based colloidal suspensions utilized as phase change materials for thermal energy storage was examined by Khodadadi et al. [12]. They demonstrated that carbon-based nanostructures and carbon nanotubes exhibited far greater enhancement of thermal conductivity in comparison to metallic/metal oxide nanoparticles, which was due to the high aspect-ratio of these nano-fillers. Effects of various 3
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carbon nano-fillers on the thermal conductivity and energy storage properties of paraffin-based nano-composite phase change materials were investigated by Fan et al. [13]. They indicated that graphene nano-platelets resulted in greatest relative enhancement in thermal conductivity due to their two-dimensional planar structure, which led to reduced filler/matrix thermal interface
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resistance. Heat transfer enhancement for thermal energy storage system incorporating stearic acid nano-composite consisting of multi-walled carbon nanotubes was examined by Li et al. [14]. They showed that the addition of multiwall carbon nanotubes could improve the thermal conductivity of stearic acid effectively; however, it also weakened the natural convection of
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stearic acid in the liquid state. Use of highly conducting core–shell phase change materials for thermal regulation was studied by Vitorino et al. [15]. They demonstrated that the microstructure
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of the graphite shell remained stable upon repeated cycling above and below the melting temperature of the paraffin, and shape stabilization was also retained, even without external encapsulation. The melting of phase change material in a cylinder shell with hierarchical heat sink array was investigated by Liu et al. [16].They analyzed the phase change parameters in terms of paraffin melting time, water heating speed and exergy efficiency, in both dimensional and dimensionless forms. The charging and discharging performance of a thermal energy storage
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system with encapsulated phase change was examined by Sellan et al. [17]. They demonstrated that increasing the capsule size, fluid flow rate, or decreasing the Stefan number, resulted in an increase in the thermocline region which finally decreased the effective discharge time and the total utilization. Thermal conductivity enhancement of the phase change materials with ultrathin-
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graphite foams for thermal energy storage was investigated by Ji et al. [18]. They demonstrated that embedding continuous ultrathin-graphite foams with low volume fractions (0.8-1.2 vol%) in
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a phase change material could increase thermal conductivity by up to 18 times, with negligible change in the melting temperature or specific heat of fusion of the phase change materials. The performance assessment of heat storage by phase change materials containing multiwall carbon nanotubes and graphite were carried out by Teng et al. [19]. They indicated that adding multiwall carbon nanotubes reduced the melting temperature and increased the solidification temperature of the phase change material.
Although thermal conductivity enhancement of the phase change material was studied earlier [18, 19], the main focus was to use carbon nanotubes or graphene platelets in the phase change 4
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material and the use of metallic meshes is not incorporated in the storage systems. Therefore, in the present study, melting and storage characteristics of phase change material incorporating types of meshes are investigated. Three different mesh geometries, namely, triangle, square, and hexagonal are incorporated in the analysis. The geometric configurations of the meshes are
phase change material.
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arranged to have either the same area or the same perimeter while keeping constant amount of The geometric configuration of the metallic mesh resulting in the
shortest melting duration is identified. The numerical predictions are validated with the
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experimental data.
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THERMAL ANALYSIS
In the analysis, phase change material (n-octadecane) and aluminum mesh are considered to be present simultaneously in the solution domain. The mesh geometry is varied to include triangular, rectangular, and hexagonal geometric configurations. Two cases are considered in the simulations. In the first case, the area of the meshes with different configurations is set to be the
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same. In the second case, triangular, rectangular, and hexagonal meshes have the same perimeter. In order to estimate the total melting time of the phase change material for both cases, constant temperature heat source is allocated at the edges of the mesh. The study is extended to include the simulation of same kind of the multi mesh system incorporating the same amount of phase
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change material. The simulations are repeated for three different mesh geometries, namely, triangular, rectangular, and hexagonal. In this case, constant temperature heat source is allocated
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at one edge of the multi mesh thermal storage system and the other edges are kept insulated.
The transient heat equation for the phase change material and aluminum substrate can be written as:
∂ ( ρ c pT ) ∂t
= ∇. ( k∇T )
(1)
where k, cp and ρ denote thermal conductivity, specific heat, and density respectively. 5
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For the solid and liquid phases, the specific heat capacity of the phase change material (PCM) does not alter considerably for the temperature range considered in the present study (293 K – 308 K). However, the specific heat capacity cp , changes considerably during the phase change
∆cp =
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process. The change can be approximated by: ∆h T
(2)
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switching from 0 to 1 over the transition interval.
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where ∆h is the variation of enthalpy, represented by using a normalized Gaussian function θ
As the PCM heats up, it melts and, during the phase transition, a significant amount of latent heat is absorbed. The total amount of heat absorbed per unit mass of PCM during the transition is given by ∆h . The PCM undergoes a temperature transition zone of 3 K (Tliquidus - Tsolidus, where Tliquidus is the liquidus temperature and Tsolidus is the solidus temperature of the PCM), during which a mixture of both solid and molten material co-exist in a mushy zone. To account for the
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∆h latent heat related to the phase transition, cp in the heat equation is replaced with cp + δ , ∆T where ∆h is the latent heat of the transition and δ is a distribution that satisfy the relation related to specific heat-temperature behavior during the phase change. In this case, the latent heat
Tm +∆T
Tm −∆T
(δ
∆h )dT = ∆h ∆T
(3)
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∫
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of melting can be written as:
where the left side is the total amount of heat absorbed per unit mass during the melting, Tm is the melting point and ∆T denotes the half-width of the curve, here set to 3K, representing half the transition temperature span. For the present study the normalized Gaussian function is used. The volume fraction of the liquid phase B, is given by:
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T > Tm + ∆T 1 B = (T − Tm + ∆T ) / 2∆T Tm − ∆T ≤ T ≤ Tm + ∆T 0 T < Tm − ∆T
(4)
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In order to solve Eq. 1 numerically, the boundary and initial conditions need to be introduced. The solution domain covers the frame of the optical images taken under the microscope. This enables to simulate the actual process at microscopic level. Since the scale of the solution
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domain is in the order of hundred micrometers, the Fourier heating law is applicable.
Initial condition:
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Initially, it is assumed that the solution domain is at an initial equilibrium temperature (Tin), i.e.:
T ( x , y ,0 ) = Tin = 293K
The boundary conditions are presented according to the considerations incorporated in the simulations.:
Boundary conditions:
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Triangular, rectangular, and hexagonal mesh with the same areas or same perimeters:
) is introduced in the mesh. In this case, the rate of input
, where A is the area of the mesh) to each mesh becomes the same for the same
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heat flux (
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A constant rate of total heat (
area meshes; however, it changes as the area changes for the constant perimeter meshes. In addition, the edges of the mesh are considered to be insulated. Figure (1) shows the boundary conditions for different meshes.
Thermal storage system consisting of phase change material and one type of a meshes:
A schematic view of the thermal storage system and the boundary conditions are shown in figure (2). The number of meshes incorporated in the solution domain is 10×10. The top edge of the 7
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storage system is considered to be at a fixed temperature (T = 308 K). Insulated boundary condition is considered for the all other boundaries, i.e.:
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∂T ∂T ∂T ( xmax , y ,t ) = ( x ,0,t ) = ( x , ymax ,t ) = 0 ∂x ∂y ∂y
NUMERICAL SOLUTION
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In order to solve the transient heat conduction equation (Eq. 1) for a stationary medium, the finite element method is utilized. This method provides a means of spatial and temporal discretization
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of the governing equation. As a first step the application of the Galerkin method for the transient equation subjected to appropriate boundary and initial conditions is addressed. The temperature is discretized over space as follows:
n
T ( x , y ,t ) = ∑ Ni ( x , y ) Ti ( t )
(5)
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i =1
where Ni are the shape functions, n is the number of nodes in an element, and Ti(t) are the timedependent nodal temperatures. Triangular elements are used, which defines the shape functions
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for the present study.
The Galerkin representation of the energy equation is:
∫
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∂ ( ρ cpT ) Ni ∇. ( k∇T ) − dΩ = 0 ∂t Ω
(6)
Ω is the solution domain. Employing the gauss-divergence theorem for the conduction term and
on substituting the spatial approximation from Eq.1, the spatially discretized finite element equation becomes:
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∂T + [K ]{T} = {f} ∂t
[C ]
(7)
[C] = ∫
Ω
[K ] = ∫ [B] [D][B]dΩ;
ρ cp [N] [N] dΩ; T
T
Ω
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where
{f} = ∫ q [N]
T
Γq
d Γq
(8)
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Γ q is the boundary where q the heat flux is prescribed. [B] = ∇N is the derivative matrix, which
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relates the gradient of the field variable to the nodal values, and [D] is the property matrix.
Since the thermal conductivity k(T), density ρ(T) and cp(T) are functions of temperature in general, the resulting equation is non-linear and requires an iterative solution.
Time discretization using the Finite Difference Method (FDM)
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It can be seen from the semi-discrete form of Eq. 7 that the differential operator involving the time-dependent term still remains to be discretized; in this case, a numerical approximation using the backward Euler finite difference method is considered.
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For temperature variation in the time domain between the n and n + 1 time levels, using the first
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term of the Taylor series, we can write the temperature gradient as: ∂T T n+1 − T n = ∂t ∆t
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which when substituted in Eq. 7 gives for the backward Euler scheme:
T n +1 − T n n +1 n +1 C [ ] + [K ]{T} = {f} ∆t
(10)
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Re-arrangement gives: n +1
= [ C]{T} + ∆t {f} n
n +1
(11)
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([C] + ∆t [K ]){T}
This equation gives the nodal values of temperature at the n + 1 time level. These temperature values are calculated using the n time level values.
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Stability
The implicit scheme with a backward difference approximation (BDF) for the time used in the study is unconditionally stable; however, the accuracy of the scheme is governed by the size of
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the time step.
In the simulations, three different geometric meshes are considered and the amount of PCM is kept the constants for all the cases in the thermal storage system. In addition, the amount of aluminum in the solution domain is kept the same for the aluminum meshes cases. Therefore,
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aluminum mass remains constant in the solution domain consists of PCM and aluminum mesh.
The grid independent tests were conducted; in which case, the number of elements used in the solution domain is doubled. It is observed that the differences in time to reach of the melting
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temperature due to both element sizes are significantly small, which is in the order of 0.1%.
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Table 1 gives the data used for PCM and aluminum in the simulations.
EXPERIMENTAL
The experiment was carried out to examine the melting stages of n-octadecene phase change material in the square aluminum mesh. Since the cells were small in size ( ∼ 55 µm×55 µm), the experimental tests were carried out under the optical microscope. The aluminum meshes were prepared as shown in figure (3). The meshes were filled totally with n-octadecene. The samples
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were, then, kept in the refrigerator at 285 K for one hour to ensure the complete solidification of n-octadecene in the aluminum meshes. The samples consisting of complete solidified phase change material and aluminum meshes were kept in the laboratory environment to reach temperature of 293 K prior to the phase change tests. A small test rig was developed and the
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workpiece was heated from one end at a constant temperature heat source at 308 K. Temperature variation across the workpiece was monitored and the stages of the phase change during the heating cycle was recorded under the optical microscope. The experiment was repeated five times to ensure the repeatability of the temperature measurement and the stages of the phase
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change during the heating process. The experimental error was determined as 6% based on the repeatability of the temperature data during the tests. The experimental conditions were
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incorporated in the simulations to predict the various stages of the molten distribution in the aluminum meshes.
Figure (4) shows micrograph of aluminum mesh and molten PCM obtained from the optical microscope and its counterpart corresponding to the simulations for the same heating period. It can be observed that the melted regions corresponding to the experiment and predictions agree
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well. The small differences between the both results are associated with the experimental error and the consideration of homogeneous properties of the PCM in the simulations. In addition, the total melting time of PCM in the aluminum mesh is measured and the finding is compared with that of predicted from the numerical simulations. It is found that the time required for the total
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melting of PCM in the aluminum mesh is 1.3 s and the predicted time for the total melting is 1.35 s, which are very close. It should be noted that the PCM used in the experiments is
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technical grade with the purity in the order of 99%.
RESULTS AND DISCUSSION
Thermal characteristics of the phase change material are examined for different geometric configurations of the metallic meshes. The duration of the complete melting is predicted for different mesh configurations while keeping the amount of phase change material constant in the thermal storage system. A numerical method is introduced to obtain the temperature field and liquid fraction distribution in the solution domain. 11
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Figure (5) shows temperature contours for different geometric configurations of the metallic meshes while figure (6) shows liquid fraction contours. The contours are prepared for two cases: i) the area covered by the mesh remains the same for all the geometric configurations of the
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mesh, and ii) the perimeter of the mesh remains the same for all the mesh configurations. A uniform heat input (5 W) is introduced in the mesh and initially the mesh and the phase change material are assumed to be at the uniform temperature of 293 K. In the first case (constant area mesh), amount of phase change material in the mesh remains constant and the heat flux (W/m2)
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is the same for each geometric configuration of the mesh. In the second configuration, the perimeter of the different meshes remains the same while amount of the phase change material
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accommodated in each mesh varies. In this case, the total heat inputted (5 W) remains the same for all different configurations of the mesh; however, heat flux changes from one mesh type to another because of the different mesh area. Since the best edges are considered to be insulated, temperature remains high in the vicinity of the edges. Since the heating duration is kept the same for all the configurations of the mesh, partially melting of phase change material is observed for some mesh configurations, which is more pronounced for the constant area mesh arrangement
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(first case). It should be noted that the amount of heat inputted is the same for all the geometric configurations of the meshes. However, small changes in temperature are associated with the heat diffusion in the mesh, which alters because of the length scale change towards the mesh edges. This situation is also seen from the liquid fraction contours. However, thermal
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conductivity of the phase change material is low (0.358 W/mK [20]), the rate of heat diffusion is low while resulting in slow temperature increase and melting in the solution domain. In the case
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of the constant perimeter arrangements (case 2), heat flux varies because of the coverage area of the mesh. Since the rectangular and hexagonal meshes have larger area than that of the triangular mesh, heat flux in the triangular mesh becomes larger than those corresponding to the rectangular and hexagonal meshes. Consequently, heat inputted to the mesh becomes less for the square and the hexagon meshes as compared to that of the triangle mesh. This in turn increases the amount of melt in the phase change material within the triangular mesh. Nevertheless, the constant area and constant perimeter arrangements of the different configurations of the meshes provide useful information on the local effect during the melting process. The triangular mesh
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results in larger melted region in the mesh corners than that of the other geometric mesh configurations.
Figure (7) shows temporal variation of ratio of the amount of liquid phase over the total phase
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change material in a single mesh for different mesh geometric configurations with the constant area (the first case). The phase change initiates around 0.4 ms of the heating duration. However, it initiates earlier for the triangular mesh as compared to other mesh geometries. This behavior is attributed to the melting initiation in the corner region of the triangular mesh; in which case,
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small corner angle (≤ 90o) enhances the heat diffusion in between the edges. However, as the heating period progresses, the rate of melting in the cell becomes almost the same regardless of
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the mesh shape. As the heating progresses further, the completion of the melting becomes earlier for the hexagonal mesh. This is associated with the large area of the hexagonal mesh as compared to the square and triangle meshes, i.e, heat inputted per unit area becomes small for the triangular mesh, which enhances the heat diffusion towards the phase change material in the triangular mesh. Moreover, the time required for melting initiation is almost the half of the total time required for the complete melting when mlig/mtot = 1. Figure (8) shows temporal variation of
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the ratio of the amount of liquid phase over the total mass of the phase change material in the mesh for three geometric configurations due to constant perimeter of the meshes (case 2). It should be noted that keeping the same mesh perimeter results in variation of the mesh areas for different mesh geometries. In this case, triangular mesh results in the smaller area, then follows
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rectangular and the hexagonal mesh. Melting initiates earlier for the rectangular mesh as similar to that observed for the case 1 (constant area meshes). As the heating period progresses, the rate
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of melting differs for different meshes unlike the behavior observed for the case 1. This is attributed to the amount of phase change material in each mesh; in which case, the triangular mesh accommodates smaller amount of the phase change material as compared to those of the rectangular and the hexagon meshes. This alters the ratio of melted phase change material to the total phase change material in the mesh, since the area of each mesh is different. Although the melting starts from the neighborhood of the edges of each mesh and propagates towards the phase change material in the mesh regardless of the cases considered, alteration of the total amount of the phase change material in the mesh changes the values of the ratio of mlid/mtot. This results in different rise of the melting rate for the case 2. Moreover, the completion of melting in 13
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the mesh takes place earlier in the triangular mesh, and then follows the rectangular and the hexagonal meshes. This is due to the amount of phase change material in the hexagonal mesh, which is larger than those of the triangular and rectangular mesh.
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Figure (9) shows temperature variation at the centroidal point of the mesh for three different mesh geometries corresponding to the same area (case 1). The rise of temperature is steady at the centroidal point for all the mesh geometries considered. The slight change of the slope is associated with the phase change at this location. Since the phase change process is fast in the
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mesh, this behavior only occurs during the short time period. However, temporal rise of temperature is almost the same for all the mesh geometries considered in the simulations. This
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behavior is attributed to the same area of the each mesh geometry (case 1). Consequently, the distance away from the controidal point to the mesh edge remains almost the same for all the mesh geometries considered. However, in the case of the same perimeter of the mesh geometries (case 2), the rise of temperature alters at the centroidal point. This can be observed from figure (10), in which temporal variation of temperature is shown for three geometries with the same perimeter (case 2). Temperature behavior indicates that melting initiation, completion, and
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sensible heating takes place at different times in each mesh having different geometries. The time taken for the heat diffusion at the centroidal point of the mesh becomes different for each mesh having the same perimeter. Therefore, the distance between the centroidal point to the mesh edge changes for different mesh geometries having the same perimeter. In this case, the use
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of triangular mesh results in sharp increase in temperature at the centroidal point then follows rectangular and hexagonal meshes. Since the melting temperature of n-octadecane is in between
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301.15K and 303.15 K [20] (Tsolidus = 301.15K and Tliquidus = 303.15 K [17]), sensible heating almost dominates at the centroidal point of the mesh, which is more pronounced for the triangular mesh due to early completion of melting at the centroidal point. This indicates that although phase change material initiates melting earlier for the triangular mesh, energy input enhances the sensible heating of the phase change material in the mesh. Consequently, altering the mesh geometry, energy storage due to phase change and sensible heating of the phase change material takes place at different rates, which is particularly true for the constant perimeter of mesh arrangement (case 2).
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The study is extended to include incorporating the multi meshes in the phase change material. In this case, the total number of meshes and their total area remain the same in the solution domain. However, the heating situation is changed such that constant temperature heat source is introduced at one edge of the solution domain and the other edges of the solution domain are
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considered to be insulated (figure (2)). The resulting temperature contours and temporal variation of the ratio of liquid mass over the total mass of the phase change material are shown in figures (11) and (12), respectively. The temperature contours in figure (11) are plotted at the location of the centroidal point. All the mesh geometries incorporated in the simulations result in almost
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similar temperature contours in the solution domain. However, the close examination of figure (12) reveals that temporal behavior of the ratio of amount of melted phase change material over
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the total amount of phase change material differs for each mesh geometry considered. In this case, triangle mesh results in highest rate of the ratio then follows the square and the hexagonal meshes. Since the amount of phase change material is the same in the solution domain for all the mesh geometries, triangle mesh geometry causes early completion of the melting of the phase change material. Consequently, triangular mesh results in improved conduction tree while increasing the melting rate in the solution domain, i.e. heat carried by the metallic mesh is
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distributed in the solution domain in such a way that the rate of melting increases. However, the rate of melting remains almost similar for the square and hexagonal meshes. This is attributed to the conduction tree formed in the phase change material, which results in similar heat carrying performance in the solution domain. Therefore, using the rectangular mesh improves the melting
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rate and shortens the time taken for the latent heat thermal storage in the phase change material. Consequently, the present study provides a starting framework for future studies of high rate of
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melting of phase change material for latent heat thermal storage applications incorporating the metallic meshes with different geometric configurations.
Although the use of meshes and fins [9, 17] were demonstrated to improve thermal performance of phase change material in terms of duration of thermal storage, the effect of mesh geometry on the storage time were not considered in the previous study [17]. Therefore, the present study provides useful information about the effects of mesh geometry on the storage capacity and melting duration (charging time). However, using the metallic meshes improve significantly the
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charging time of the phase change thermal storage system as consistent with the findings of the early work [17].
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CONCLUSION
Thermal storage characteristics of the phase change material are investigated after incorporating the metallic meshes with different geometric configurations in the phase change material. The
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effect of the mesh geometry on the melting duration is examined for two metallic mesh arrangements. In the first case, the area of the meshes with different geometries, namely
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triangular, rectangular, and hexagonal, is considered to be constant; in which case, the amount of phase change material accommodated in each mesh remains the same for all the meshes considered. In the second case, the perimeter of all meshes is assumed to be the same. This arrangement results in different mesh areas for different mesh geometric configurations. In this case, triangular mesh gives rise to the smallest area then follows rectangular and hexagonal meshes. A uniform heat source is introduced in the mesh to assess the temporal behavior of the
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phase change process and the total melting duration due to mesh geometric configurations. In addition, in the simulations, a uniform temperature is assumed initially in the phase change material. The experiment is carried out to validate the predictions of melt isotherms. Since the mesh size used is in the order of 50 micrometers, a microscope is used to monitor the melting
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process under the controlled environment during the experiments. It is found that melt isotherm predicted agrees well with its counterpart obtained from the experiment. Time taken for complete
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melting of the phase change material is the shortest for the triangular mesh geometry then follows the rectangular and hexagonal mesh. This is more pronounced for the meshes having the same perimeter. In this case, the area covered by triangular mesh becomes smaller than those of the rectangular and the hexagonal meshes. On the other hand, keeping the mesh area same for three mesh geometries, the melting duration becomes almost the same for all the mesh geometries; provided that melting initiates earlier in the corner region of the triangular mesh. Therefore, the melting initiation delays as the corner angle of the mesh increases, i.e. melting in the phase change material starts earlier for the square mesh as compared to that of the hexagonal mesh. In general, the triangular mesh forms better conduction tree in the phase change material 16
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while carrying and distributing the heat effectively in the phase change material. In this case, the total melting duration of the phase change material becomes small. Therefore, the present study provides useful information for the designing and management of the latent heat storage systems incorporating the metallic meshes.
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REFERENCES
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pin fin heat sinks, J. Phys.: Conf. Ser. Vol. 395, doi:10.1088/1742-6596/395/1/012134, 2012.
[2] H. Ge and J. Liu, Cooling capacity of metal phase change material for thermal management
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of mobile phone subject to long time communication, ASME 2013 International Mechanical Engineering Congress and Exposition, Volume 8B: Heat Transfer and Thermal Engineering, doi:10.1115/IMECE2013-66240, San Diego, California, USA, November 15–21, 2013.
[3] S. Chukwu, E. Ogbonnaya, L. Weiss, Fabrication, testing, and enhancement of a thermal energy storage device utilizing phase change materials. ASME 2012 Heat Transfer Summer
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Conf. Collocated with the ASME 2012 Fluids Engineering Div. Summer Meeting and the ASME 2012 10th Int. Conf. on Nanochannels, Microchannels and Minichannels, HT 2012, DOI: 10.1115/HT2012-58309, Vol. 1, p 279-285, 2012.
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[4] S.S. Sebti, M. Mastiani, H. Mirzaei, A. Dadvand, S. Kashani, S.A. Hosseini, Numerical study of the melting of nano-enhanced phase change material in a square cavity, J. of Zhejiang
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University: Science A, Vol. 14, n 5, pp. 307-316, 2013.
[5] D.K. Kim and E.E. Marotta, L.S. Fletcher, Thermal performance of a wire-mesh/hollowglass-sphere composite structure, J. of Thermophysics and Heat Transfer, Vol. 25, n 2, pp. 254261, 2011.
[6] M. Faraji and H. El Qarnia, Numerical study of melting in an enclosure with discrete protruding heat sources, Applied Mathematical Modelling, Vol. 34, n 5, pp. 1258-1275, 2010.
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[7] W-J. Hu, Y-Q. Jiang, Y. Yao, Z-L. Ma, Modeling a spiral coil phase-change thermal energy storage tank with cooling agent as cyclic material, J. of Harbin Engineering University, Vol. 29, n 10, pp. 1135-1140, 2008.
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[8] J. Chang, W. Duan, B.Liu, S. Fu, Preparation and properties of organic/inorganic nanocomposite phase change materials for heat energy storage in building energy conservation, Advanced Materials Research, Vol. 374-377, pp. 346-351, 2012.
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[9] V. Ahmadpour, N. Ahmadi, S. Rezazadeh, M. Sadeghiazad, Numerical analysis of thermal performance in a finned cylinder for latent heat thermal system (LHTS) applications, Int. J. of
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Heat and Technology, Vol. 31, n 1, pp. 155-162, 2013.
[10] B. Han, K. Zhang, X. Yu, Enhance the thermal storage of cement-based composites with phase change materials and carbon nanotubes, J. of Solar Energy Engineering, Transactions of the ASME, Vol. 135, n 2, DOI: 10.1115/1.4023181, 2013.
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[11] P. Chandrasekaran, M. Cheralathan, V. Kumaresan, R. Velraj, Solidification behavior of water based nanofluid phase change material with a nucleating agent for cool thermal storage system, Int. J. of Refrigeration, Vol. 41, pp. 157-163, 2014.
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[12] J.M. Khodadadi, L. Fan, H. Babaei, Thermal conductivity enhancement of nanostructurebased colloidal suspensions utilized as phase change materials for thermal energy storage: A
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review, Renewable and Sustainable Energy Reviews, Vol. 24, pp. 418-444, 2013.
[13] L-W. Fan, X. Fang, X. Wang, Y. Zeng, Y-Q. Xiao, Z-T. Yu, X.Xu, Y-C. Hu, K-F. Cen, Effects of various carbon nanofillers on the thermal conductivity and energy storage properties of paraffin-based nanocomposite phase change materials, Applied Energy, Vol. 110, pp. 163172, 2013.
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[14] X-T. Li, J-H. Lee, R-Z. Wang, Y.T. Kang, Enhancement of heat transfer for thermal energy storage application using stearic acid nanocomposite with multi-walled carbon nanotubes, Energy, Vol. 55, pp. 752-761, 2013.
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[15] N. Vitorino, J.C.C. Abrantes, J.R. Frade, Highly conducting core–shell phase change materials for thermal regulation, Applied Thermal Engineering, Vol. 66, Issues 1–2, pp. 131-139, 2014.
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[16] H. Liu, S. Li, Y. Chen, Z. Sun, The melting of phase change material in a cylinder shell with
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hierarchical heat sink array, Applied Thermal Engineering, Vol. 73, Issue 1, pp. 975-983, 2014.
[17] S. Bellan, J. Gonzalez-Aguilar, M. Romero, M.M. Rahman, D.Y. Goswami, E.K. Stefanakos, D. Couling,
Numerical analysis of charging and discharging performance of a
thermal energy storage system with encapsulated phase change material, Applied Thermal Engineering, Vol. 71, Issue 1, pp. 481-500, 2014.
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[18] H. Ji, D.P. Sellan, M.T. Pettes, T. Michael, X. Kong, J. Ji, L. Shi, R.S. Ruoff, Enhanced thermal conductivity of phase change materials with ultrathin-graphite foams for thermal energy storage, Energy and Environmental Science, Vol. 7, n 3, pp. 1185-1192, 2014.
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[19] T-P. Teng, C-M. Cheng, C-P. Cheng, Performance assessment of heat storage by phase change materials containing MWCNTs and graphite, Applied Thermal Engineering, Vol. 50, n 1,
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pp. 637-644, 2013.
[20] American Society of Heating, Refrigerating and Air Conditioning Engineers, ASHRAE, Handbook of Fundamentals, ASHRAE, New York, NY, 2001.
[21] F.P. Incorpera, D.P. Dewitt, T.L. Bergman, A.S. Lavine, Fundamentals of Heat and Mass Transfer, 6th Ed., John Wiley and Sons, NJ, 2007.
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Acknowledgments:
The authors acknowledge the funded project RG 1204 via support of Thermoelectric Group formed by the Deanship of Scientific Research at King Fahd University of Petroleum and
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Minerals, Dhahran, Saudi Arabia for this work.
Cp(T) Temperature dependent heat capacity (J/kgK)
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NOMENCLATURE
Thermal capacitance matrix
H
Enthalpy (J/kg)
{f}
Source term
k(T)
Temperature dependent thermal conductivity (W/mK)
[k]
Thermal conductivity matrix
n
Time level of iteration
Ni
Shape factor
T
Temperature (K)
t
Time (s)
∆t
Time increment
Tm
Averaged melting temperature (K)
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[C]
Tliquidus Liquid phase temperature during phase change (K)
∆T q x xmax
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Tsolidus Solid phase temperature during phase change (K) Temperature increment
Heat flux (W/m2)
Distance along x-axis (m) Location along x-axis where liquid phase terminates (m)
y
Distance along y-axis (m)
ymax
Location along y-axis where liquid phase terminates (m)
Greek Symbols 20
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Distribution function of latent heat of melting
ρ
Density (kg/m3)
Γq
Heat flux boundary
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δ
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List of Table Captions
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Table 1. Properties of n-octadecane and aluminum used in the simulations [20, 21].
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List of Figure Captions
Figure 1. Geometric configurations of the meshes used in the simulations and the boundary conditions.
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Figure 2. A schematic view of the thermal storage system consisting of aluminum meshes and the phase change material, and boundary conditions used in the simulations. It should be noted that square mesh is shown; however, the boundary conditions are applicable for the triangular and hexagonal meshes. In addition, number of meshes and the total area remain the constant for the triangular and the hexagonal meshes.
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Figure 3. Optical images of aluminum meshes: a) without PCM filled and ii) with PCM filled. Figure 4. Optical Image captured under microscope and simulation results for the liquid fraction.
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Figure 5. Simulation results of temperature contours in the different meshes for constant area (case 1) and constant perimeter consideration. Heating duration is 0.8 s. Figure 6. Simulation results of liquid fraction contours in the different meshes for constant area (case 1) and constant perimeter consideration. Heating duration is 0.8 s.
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Figure 7. Simulation results of temporal variation of the ratio of liquid mass over the total mass of PCM in different meshes. Simulations correspond to the consideration of constant area meshes. Figure 8. Simulation results of temporal variation of the ratio of liquid mass over the total mass of PCM in different meshes. Simulations correspond to the consideration of constant perimeters of meshes.
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Figure 9. Simulation results of temporal variation of temperature at the centroidal point of the solution domain for different mesh arrangements. It should be noted that mesh area remains constant for all the meshes considered (case 1).
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Figure 10. Simulation results of temporal variation of temperature at the centroidal point of the solution domain (thermal storage system) for different mesh arrangements. It should be noted that mesh perimeter remains constant for all the meshes considered (case 2). Figure 11. Simulation results of temperature contours in the thermal storage system for different meshes. The heating period is 0.01 s. Figure 12. Simulation results of temporal variation of the ratio of liquid mass over the total mass of PCM in the thermal storage system incorporating different meshes.
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Table 1. Properties of n-octadecane and aluminum used in the simulations [20, 21]. Specific Heat
Thermal
Latent Heat of Tsolidus
kg/m3
J/kgK
conductivity
Melting
Tliquidus
W/mK
J/kg
K
Solid Phase
814
2150
0.358
236624
301.15
Liquid
774
2180
0.152
-
303.15
2702
903
237
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Density
321000
933
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Aluminum
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Phase
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and
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5
5
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5
Insulated Edges
Figure 1. Geometric configurations of the meshes used in the simulations and the boundary
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conditions.
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Insulated Edges
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Insulated Edges
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T = 308 K
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Insulated Edges
Figure 2. A schematic view of the thermal storage system consisting of aluminum meshes and the phase change material (), and boundary conditions used in the simulations. It should be noted that square mesh is shown; however, the boundary conditions are applicable for the triangular and hexagonal meshes. In addition, number of meshes and the total area remain the constant for the triangular and the hexagonal meshes.
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a)
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Aluminum Meshes
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b)
200 µm
PCM in Solid Phase
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Aluminum Meshes with PCM
Figure 3. Optical images of aluminum meshes: a) without PCM filled and ii) with PCM filled.
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Liquid Phase Solid Phase
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Mushy Zone
Mushy Zone Solid Phase
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Liquid Phase
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200 µm
Figure 4. Optical Image captured under microscope and simulation results for the liquid fraction.
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Figure 5. Simulation results of temperature contours in the different meshes for constant area (case 1) and constant perimeter consideration. Heating duration is 0.8 s. 29
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Figure 6. Simulation results of liquid fraction contours in the different meshes for constant area (case 1) and constant perimeter consideration. Heating duration is 0.8 s. 30
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Figure 7. Simulation results of temporal variation of the ratio of liquid mass over the total mass of PCM in different meshes. Simulations correspond to the consideration of constant area meshes.
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Figure 8. Simulation results of temporal variation of the ratio of liquid mass over the total mass of PCM in different meshes. Simulations correspond to the consideration of constant perimeters of meshes. 32
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Figure 9. Simulation results of temporal variation of temperature at the centroidal point of the solution domain for different mesh arrangements. It should be noted that mesh area remains constant for all the meshes considered (case 1).
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Figure 10. Simulation results of temporal variation of temperature at the centroidal point of the solution domain (thermal storage system) for different mesh arrangements. It should be noted that mesh perimeter remains constant for all the meshes considered (case 2).
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Figure 11. Simulation results of temperature contours in the thermal storage system for different meshes. The heating period is 0.01 s. 35
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Figure 12. Simulation results of temporal variation of the ratio of liquid mass over the total mass of PCM in the thermal storage system incorporating different meshes.
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Research Highlights
Time taken for complete melting of PCM is shortest for triangular aluminum mesh.
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Melting duration is almost same for different mesh geometries of same area.
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Melting initiates earlier in corner region of meshes.
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Triangular mesh forms better conduction tree in phase change material.
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