Melting enhancement in triplex-tube latent thermal energy storage system using nanoparticles-fins combination

International Journal of Heat and Mass Transfer 109 (2017) 417–427

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International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt

Melting enhancement in triplex-tube latent thermal energy storage system using nanoparticles-fins combination Jasim M. Mahdi a,b, Emmanuel C. Nsofor a,⇑ a b

Department of Mechanical Engineering and Energy Processes, Southern Illinois University, Carbondale, IL 62901, USA Department of Energy Engineering, University of Baghdad, Baghdad 10071, Iraq

a r t i c l e

i n f o

Article history: Received 16 August 2016 Received in revised form 15 November 2016 Accepted 5 February 2017

Keywords: Melting PCM Triplex-tube Thermal energy storage Nanoparticles Fins

a b s t r a c t Latent thermal energy storage based on Phase Change materials (PCMs) offers a promising solution for correcting the problem of availability of intermittent energy from renewable sources like solar, wind, etc. PCMs have the potential to store large amounts of energy in relatively small volumes and within nearly isothermal processes. However, a major drawback of today’s PCMs is that their low thermal conductivity values critically limit their energy storage applications. Also, this grossly reduces the melting/ solidification rates, thus making the system response time to be too long. In this study, three enhancement techniques: fins, nanoparticles and a combination of both were investigated with the aim of correcting this limitation. A numerical study based on enthalpy method was used to comparably examine the effects of these techniques on the PCM melting rate in triplex-tube latent heat storage system. A mathematical model that takes into account the natural convection and the Brownian motion of nanoparticles was formulated and successfully validated against previous experimental data. The influence of using different dimensions of fin and different nanoparticle volume fractions on evolution of the solid-liquid interfaces, distribution of isotherms, and temporal profile of liquid fraction over the whole melting process was studied and reported. The results indicate that PCM melting is improved by using these techniques studied. Also it was found that the use of fins alone is better than using either nanoparticles alone or a combination of fins and nanoparticles. The use of longer fins with smaller thicknesses is recommended so as to improve phase-change heat transfer and minimize the volume occupied in the energy storage space. Ó 2017 Elsevier Ltd. All rights reserved.

1. Introduction Increasing share of renewables like solar and wind for responding to growing global energy demand requires efficient means to correct their intermittent nature. In this regard, thermal energy storage (TES) was found to be a practical choice for broad renewable-based applications, that range from solar water heaters to building air conditioning systems [1]. By definition, TES is the storage of energy in a thermal form for later use. There are three options available for storing energy in TES systems: sensible, latent, and thermochemical. Latent option is more attractive than others due to the relatively high storage density and nearly isothermal nature of the storage process. For example, latent TES using Phase Change Materials (PCMs) can store 5–14 times higher energy than using sensible storage materials for the same volume [2]. However, low thermal conductivity of most PCMs strongly sup⇑ Corresponding author. E-mail address: [email protected] (E.C. Nsofor). http://dx.doi.org/10.1016/j.ijheatmasstransfer.2017.02.016 0017-9310/Ó 2017 Elsevier Ltd. All rights reserved.

presses the energy charging/discharging rates and makes the system response time too long to achieve the desired results. Therefore, many investigations have been conducted to enhance the thermal conductivity of PCMs and many concepts such as insertion of fins [3–9], heat pipes [10], and metal matrices [11] have been proposed. However, the major drawback associated with all those techniques is their extra added weight and/or volume limits flexibility in designing light, small-size storage systems in cases where weight and volume usage are of design concerns. Furthermore, these techniques negatively affect the PCM fluidity during the phase-change and they degrade the positive contribution of natural convection in the associated heat transfer process. A more recent way that can maintain relatively better fluid-like form during the phase-change process is to improve the thermal conductivity through dispersion of highly conductive nanoparticles having nominal sizes ranging from 1 to 100 nm [12–18]. Among the techniques mentioned above, fins come at the top of the list as the most commonly used heat transfer enhancement technique in engineering applications including PCM-based TES

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Nomenclature A Am b Cp dp g k

C L P r t T Tl Ts u v V w HTF

area mushy zone constant fin thickness (mm) specific heat (J/kg K) pore size (m) gravity acceleration (m/s2) thermal conductivity (W/m K) latent melting heat (J/kg K) triplex-tube length pressure (Pa) tube radius (m) time (s) temperature (K) liquidus temperature of the PCM (K) solidus temperature of the PCM (K) velocity component in r-direction (m/s) velocity component in h-direction (m/s) volume (mm3) fin length (mm) heat transfer fluid

applications. Also, heat transfer can be further enhanced through incorporation of highly conductive nanoparticles. As reported by a number of studies (e.g. [13,14]), successful dispersion of nanoparticles will enable the PCM to have higher thermal conductivity and exhibit better thermal storage performance. The concept of incorporating nanoparticles to enhance the thermal response of PCMs has been first introduced by Khodadadi and Hosseinizadeh [12]. The study showed through numerical simulation that phase-change heat transfer enhancement by nanoparticles is promising for utilization in TES applications. Wu et al. [13] experimentally investigated the melting/solidification characteristics of copper/paraffin as a nanoparticle-enhanced phase change material (nanoPCM). The results revealed that with copper nanoparticles of 2% by weight the thermal conductivity of paraffin can be enhanced by 14% in solid phase and 18% in liquid phase. Arasu and Mujumdar [14] numerically investigated heat transfer enhancement by dispersing alumina nanoparticles in paraffin as a PCM and found that nano-enhanced paraffin shows higher melting rate when the cavity is heated from the side rather than from below due to enhanced natural convection effect. Sciacovelli et al. [19] numerically studied the thermal behavior of a vertical shell-and-tube TES unit charged with a nano-PCM. The results indicated a melting time reduction of 15% achieved by doping nanoparticles of 4% volumetric concentration. Chieruzzi et al. [20] dispersed 1 wt.% silica, alumina, and a mixture of silica and alumina nanoparticles in potassium nitrate as a PCM and found that addition of silica nanoparticles has the best potential for enhancing the PCM specific heat and total stored heat. Recently, Mahdi and Nsofor [21] showed via numerical investigation that dispersing alumina nanoparticles of (3–8% by volume) in paraffin RT82 can reduce the discharging (solidification) period up to 20% in a horizontal triplex-tube TES unit. Due to the effectiveness, relative ease in fabrication, and low cost of construction, metal fins are being considered as one of the most practical heat transfer enhancement techniques [4]. Gharebaghi and Sezai [3] numerically studied a finned heat sink filled with RT27 as PCM in horizontal and vertical arrangements. Results showed that for high temperature differences the heat transfer rate can be increased as much as 80 times by adding fins, and a faster melting can be achieved with decreasing fin spacing.

PCM TES

phase change material thermal energy storage

Greek letters fluid density (kg/m3) ut total volume fraction uf fin volume fraction un nanoparticle volume fraction k liquid fraction b thermal expansion coefficient (K
1) l dynamic viscosity (kg/m s) f correction factor

q

Subscripts np nanoparticle npcm nanoPCM f fin i, o inner, outer tube w wall

Agyenim et al. [4] used circular-finned, longitudinal-finned and bare tubes in a double-pipe TES system to study charging and discharging of Erythritol as a PCM. The results indicated that the longitudinal fins gave the best heat transfer performance with a reduced subcooling during the discharge. Ismail and Lino [5] experimentally studied solidification of PCM in a TES system with bare tube, finned tube and finned tube with stainless steel wire as a turbulence promoter. The results revealed that the use of the turbulence promoter reduces time for complete solidification but the reductions are less pronounced than those due to the fins. AlAbidi et al. [7] experimentally studied the phase change of paraffin RT82 in finned triplex-tube TES system for different temperatures and mass flow rates of the heat transfer fluid (HTF). The results indicated that the HTF temperature has more influence on the PCM melting than the HTF mass flow rate. Rathod and Banerjee [8] presented an experimental study on melting and solidification of paraffin as a PCM in vertical shell-and-tube heat exchanger assisted by longitudinal fins. The study reported a reduction in total time of up to 25% in melting and 44% in solidification with installation of fins. Sciacovelli et al. [9] numerically studied the thermal behavior of a shell-and-tube TES system assisted by Y-shaped fins with single and double bifurcations. The results showed that the discharge efficiency increases by about 24% when optimal fins with double bifurcation are used. Darzi et al. [22] used finned-circular, circular and elliptical cylinders to numerically study the melting and solidification of a nanoPCM within a concentric cylindrical annulus. The results showed that changing shape into elliptical, adding nanoparticles or inserting fins all leads to higher phase change rates. It is worthy to state here that employing enhancement additives such as fins and nanoparticles, to alleviate the poor thermal conductivity of PCMs may lead to loss of storage capacity compared to employing only the pure PCM due to reduction in the PCM volume (or decreased mass of the storage material). This study has used the fin volume fraction (uf) along with the nanoparticle volume fraction (un) to study the volume reduction arising from using the fins and nanoparticles for the heat transfer enhancement. The study attempts to positively combine nanoparticles and fins as a compound enhancement technique to achieve better charging

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(melting) process in triplex-tube TES system. With this combination, it is expected that the nanoparticles promote better convection contribution (compared to fins alone) because they affect the melt fluidity less during PCM melting. Meanwhile, the fins provide better heat penetration through the PCM (compared to nanoparticles alone). A further emphasis in this study is to compare the melting performance of three enhancement techniques: nanoparticles alone, fins alone, and fin-nanoparticle combination based on the total volume occupied by each. Such strategy for optimizing performance has not been reported. Furthermore, the literature misses a study that compares the efficiency of using nanoparticles and fins or composite of both in a triplex-tube TES system. Selection of the triplex-tube was because it provides a larger heat-exchange area compared to the common double-pipe heat exchanger and it achieves faster phase-change process [7]. Enhancement of the melting rate and the solidification rate are important in achieving improved storage processes in latent thermal energy systems. This study is only on the nanoPCM melting with fins in the triplex-tube system. NanoPCM solidification with fins is an ongoing research for which results are expected to be published in the near future. The results from these investigations would be helpful in improving the design and operation of latent TES systems. In this study, a two-dimensional model using finitevolume discretization was developed to numerically investigate the PCM melting with nanoparticles in a finned triplex-tube TES system. In the model, the natural convection of liquid PCM, the Brownian motion of nanoparticles, and the temperaturedependent physical properties of nano-PCM were all taken in a consideration. 2. Problem Statement and formulation A schematic representation of the finned triplex-tube heat exchanger is shown in Fig. 1. The figure is a cross-section showing (a) the physical model and (b) the computational domain. Due to symmetry in the h-direction, only the right-half has been considered in the computation. The triplex-tube has been used as an energy storage medium container in a solar-powered liquiddesiccant air-conditioning system [7]. It consists of three horizontally mounted concentric copper tubes with lengths of 500 mm. The inner, middle and outer tubes have diameters of 50.8, 150 and 200 mm respectively. Both the middle and outer tubes have a thickness of 2 mm while the inner one has a thickness of

HTF

1.2 mm only. NanoPCM fills the annular space between the inner and middle tubes while the HTF flows through both the inner and outer tubes. Eight copper fins are incorporated with length (w) and thickness (b) which are varied according to the cases tabulated in Table 1. RT82 was used as PCM, alumina as a material for nanoparticles, and water as HTF. RT82 has been selected because it provides: (i) constant-temperature phase-change process, (ii) unlimited lifetime with no super cooling effect, and (iii) stable performance in repeated phase-change cycles [23]. The computational domain is an annulus representing the annular space that houses the nanoPCM with ro and ri being the radii of the middle and inner tubes respectively. Initially (at t = 0), the nanoPCM has a uniform temperature of 300 K, which sufficiently lowers the solidus temperature (Ts) to ensure that the PCM is at the solid phase. Thus, the initial condition can be defined as

at t ¼ 0; T ¼ Tint ¼ 300 K For time t > 0, both the inner and outer surfaces of the annulus are suddenly exposed to the HTF which has a constant temperature higher than the melting point of the nano-PCM (TW > Tl). So, the boundary conditions can be defined as (1) at r ¼ ri ; T ¼ Tw ¼ 363; 368 and 373 K (2) at r ¼ ro ; T ¼ Tw ¼ 363; 368 and 373 K Since Tw is greater than the liquidus temperature Tl, heat will start penetrating through both inner and outer surfaces to initiate melting in form of a melt layer adjacent to each surface. Selection of such charging temperatures was based on the minimum operation temperature ðT P 70 CÞ to power the solar-powered liquiddesiccant air conditioning systems [7]. During melting, the heat transfer occurs by only conduction in solid PCM and by both conduction and convection in liquid PCM due to the temperature gradient across the annulus. This, in turns, creates a buoyancy-driven flow in the liquid part of the PCM. In order to develop a mathematical model for nano-PCM melting, the PCM is assumed to be in the liquid phase and its flow is transient, laminar and incompressible. Furthermore, the following assumptions were made: (1) The temperature variation in the HTF is negligible, i.e. (Tw is constant), (2) Viscous dissipations are negligible, (3) No-slip conditions for velocities at the boundaries, (4) All thermo-physical properties of the PCM are

Upper symmetry line

ro NanoPCM

ri

r

w

HTF

b

T =T T =T Lower symmetry line

Fig. 1. Triplex-tube storage system configuration (a) physical domain and (b) computational domain.

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Table 1 Volume fractions of fins and nanoparticles with fin dimensions. Case #

uf

un

ut

b (mm)

w (mm)

1 2 3 4 5 6

0.00 0.02 0.01 0.00 0.01 0.02

0.00 0.00 0.01 0.02 0.01 0.00

0.00 0.02 0.02 0.02 0.02 0.02

– 2 2 – 1 1

– 19.3 9.7 – 19.3 38.6

temperature-independent except density in the momentum equations, (5) Boussinesq approximation is used to account for density variation as q ¼ qm =ðbðT
T m Þ þ 1Þ, where T m ¼ ðT s þ T l Þ=2 (6) Volume variation associated with the phase change is neglected, and (7) No heat loss or gain from the surroundings. The equations governing the fluid motion and the temperature distribution of the PCM are governed by the standard NavierStokes and energy equations:

2.1. Calculations of the fin length V f ¼ N  Af  L; where Af ¼ w  b. Here N is the no. of fins, w is fin length, b is fin thickness, and L is triplex-tube length.

V t ¼ V PCM þ V f ¼ pðr 2o
r 2i Þ  L:

rV ¼0

ð1Þ

ut ¼ uf þ un ; where uf , un is fin and nanoparticle volume fraction respectively.

 ð1
kÞ2 @u 1
þ V  ru ¼
rP þ lnpcm r2 u þ Cu 3 @t qnpcm k þe

ð2Þ

uf ¼

 @v 1

rP þ lnpcm r2 v þ ðqbÞnpcm gðT
T ref Þ þ V  rv ¼ @t qnpcm þ Cv

ð1
kÞ2

@h @ ðDHÞ knpcm rH þ þ r  ðVhÞ ¼ r  @t @t ðqC p Þnpcm

Design limitations are pre-assigned as: b ¼ 1; or 2 mm, N = 8 mm, and ut ¼ 0:02.

ð3Þ

k3 þ e

! ð4Þ

In these equations, u is the velocity component in the r - direction, v is the velocity component in the h-direction, l is dynamic viscosity, P is pressure and C is the mushy zone constant which is used to control damping as velocity approaches zero when the PCM solidifies. It is usually set at around 105–106 in most of the numerical studies [24]. In the present study, it is found that a value of C = 106 provides the best match to previous results by Al-Abidi et al. [7]. e is a small number (0.001) to prevent division by zero, h is sensible enthalpy, and DH is latent heat. The sensible enthalpy can be represented by the expression:

Z

T

h ¼ href þ

Cp dT Tref

where href is the reference enthalpy at the reference temperature (Tref = 273 K) and Cp is the specific heat at constant pressure. The latent heat can be written in terms of the melting heat, C, as:

DH ¼ kC where k is the liquid fraction during phase change in the temperature interval Ts < T < Tl. It may vary from zero (solid) to 1 (liquid) and can be defined as:

8 T 6 Ts > < 0; k ¼ ðT
Ts Þ=ðTl
Ts Þ Ts < T < Tl > : 1; T P Tl

Regarding the fins, the governing energy equation is written as:

  @ qCu C p;Cu T Cu ¼ r  ðkCu rT Cu Þ @t

pðr2o
r2i Þuf Vf N  w  b ¼ )w¼ V t pðr2o
r2i Þ Nb

ð5Þ

The subscript ‘‘Cu” refers to the fin material (copper), and qC, Cp,C, kC are its density, specific heat, and thermal conductivity respectively.

2.2. 2Thermo-physical properties The thermo-physical properties of the PCM (RT82) are listed in Table 1 [23]. The nominal thermo-physical properties of alumina (Al2O3), and copper (Cu) are listed in the same table as well. The density, specific heat capacity, latent melting heat, and thermal expansion coefficient of the nano-PCM can be evaluated based on the simple theoretical model of mixing as [12,17,25–30]:

qnpcm ¼ un qnp þ ð1
un Þqpcm

ð6Þ

ðqC p Þnpcm ¼ un ðqC p Þnp þ ð1
un ÞðqC p Þpcm

ð7Þ

ðqCÞnpcm ¼ ð1
un ÞðqCÞpcm

ð8Þ

ðqbÞnpcm ¼ un ðqbÞnp þ ð1
un ÞðqbÞpcm

ð9Þ

In equations (6)(9), un is the volume fraction of the nanoparticles, Cp is specific heat, q is the density, C is melting heat and the subscripts np, npcm, and pcm refer to nanoparticle, nano-PCM, and base PCM, respectively. The dynamic viscosity and the thermal conductivity of the nano-PCM can be written using the model developed by Vajjha et al. [31,32] as:

lnpcm ¼ 0:983eð12:959uÞ lpcm knpcm ¼

where

ð10Þ

knp þ 2kpcm
2ðkpcm
knp Þun kpcm knp þ 2kpcm þ ðkpcm
knp Þun sffiffiffiffiffiffiffiffiffiffiffiffiffiffi BT f ðT; un Þ þ 5  104 bk fun qpcm C p;pcm qnp dnp b

is

bk ¼ 8:4407ð100un Þ




Boltzmann
1:07304

constant,

ð11Þ 1.381  10
23 J/K,

, and f is a function defined as:

f ðT; un Þ ¼ 2:8217  10
2 un þ 3:917  10
3

 1 T ref


 þ
3:0669  10
2 un
3:9112  10
3

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0.8 0.7

Liquid Fraction

This model for the thermal conductivity of nano-PCM takes into account the effects of Brownian motion of nanoparticles (second term on the right hand side) and the effects of nanoparticle size, volume fraction and temperature dependence. It is to be noted that f is a correction factor that comes from the Brownian motion term, and because there is no Brownian motion in the solid phase, its value is defined as the same for liquid fraction [14]. The thermophysical properties used in the study are summarized in Table 2.

0.6 0.5 N=11230

0.4

N=14743

0.3

N=17426

0.2

3. Numerical procedure and validation

0.1

3.1. Validation The numerical model developed in this study was validated against experimental data by Al-Abidi et al. [7]. The same initial conditions, boundary conditions and physical properties in the experimental study were used to validate the present results. Fig. 3 shows a comparison of the average temperature versus time between the two studies. As can be observed, the results of both

Table 2 Thermophysical properties of the PCM, nanoparticles and fins. Property

RT82

Al2O3

Cu

qm (kg/m3)

770 2 0.2 0.03499 176 350 358 0.001

3600 0.765 36 – – – – –

8920 380 400 – – – – –

Cp (kJ/kg K) k (W/m K) l (N s/m2) L (kJ/kg) Ts (K) Tl (K) b (1/K)

0

0

10

20

30

40

50

60

Time (minutes) Fig. 2. Effects of grid size on the variation of liquid fraction versus time.

90

Average Temperature (°C)

The transient numerical simulation of nano-PCM melting was performed using the computational-fluid-dynamics package ANSYS FLUENT 17.0 which employs a mathematical formulation based on enthalpy-porosity technique. In this technique, the solution is based on a fixed grid and the governing equations are modified such that they are valid for both phases. The mushy zone where both phases coexist is modeled as a ‘‘pseudo” porous medium with porosity equal to the liquid fraction. The porosity increases from 0 (solid) to 1 (liquid) as the material melts. The PRESSURE BASED method, which is recommended in incompressible flow [33], is adopted for solving the governing equations (Equations (1)(5)) after discretizing by the finite-volume method with high-order quadratic upstream interpolation for convective kinematics (QUICK) difference scheme presented by Leonard [34]. The semi-implicit method for pressure linked equations (SIMPLE) algorithm given by Patankar [35] was used in pressure-velocity coupling with the pressure staggering option (PRESTO) scheme for pressure correction [12,14]. A set of user-defined functions (UDFs) were written in C++ to implement the properties of the nano-PCM. To ensure grid independent solution, three different grid arrangements of (N = 11,230, 14,743, and 17,426) have been tested for discretizing the computational domain. A grid size of N = 11,230 cells was selected due to its affordable computational time. Further refinement of the grid size was found to not lead to significant changes in the solution as shown in Fig. 2. Furthermore, a time step of 0.3 s was selected, and it was able to keep the solution stable in all the cases considered in the simulation. The under-relaxation factors for the velocity components, pressure correction, and thermal energy were selected as 0.5, 0.3 and 1 respectively. The convergence criteria to terminate iteration were set as 10
4 for continuity and momentum, and 10
6 for energy.

80 70 60

Al-Abidi et al Present

50 40 30

0

10

20

30

40

50

60

Time (minutes) Fig. 3. Comparison of temperature profile vs. experimental data by Al-Abidi et al. [7].

studies are agreeable with each other. This indicates that the present simulation model is reliable enough to be used for investigating the enhancement of PCM melting by fins-nanoparticles combination in triplex-tube TES system.

4. Results and discussion A series of numerical simulations were done to assess the enhanced melting of paraffin RT82 by alumina nanoparticles and copper fins in a triplex-tube TES system. The cases simulated are summarized in Table 1. The total volume fraction for the combination of fins and nanoparticles was fixed at (ut = 0.02). Higher volume fractions were not considered to avoid affecting much of the storage capacity by further reduction in the available PCM volume. Moreover, average volume fraction (ut = 0.02) was selected noting such ratio gave good results for nanoparticle dispersion in several nanoPCMs [12,13,18,20]. The results are presented here in the form of isotherms, location of solid–liquid interfaces, and transient liquid fraction profile. The simulation in all cases begins with the PCM in a fully solid state at an initial temperature (Tint = 300 K). The HTF (water) is pumped at temperatures (THTF = 363, 368 and 373 K) which are above the PCM melting point (Tl = 358 K). This allows the PCM close to the walls to initiate melting, and produce a melt layer adjacent to the walls. As time progresses, this layer gradually grows to occupy the whole space by absorbing more heat from the heating walls. At the same time, the existence of nanoparticles and fins act as a compound thermal conductivity promoter significantly expediting the PCM melting process, as we will see later on in this section.

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4.1. Evolution of solid–liquid interface To demonstrate the impact of dispersing nanoparticles on PCM melting inside the annulus between the finned inner and middle tubes of the triplex-tube, the contours of the solid-liquid interface (Fig. 4) and isotherms (Fig. 5) have been monitored over various time periods (½, 1, and 1½ h) of melting. Fig. 6 shows the temporal evolution of the two solid–liquid interfaces of the base PCM without fins (ut = 0) and nanoPCM with fins (ut = 0.02). The melting process is divided into three time stages to better analyze and discuss the results. – During the early stage (t  ½ h), cases (without fins) 1, and 5 reveal that the two solid–liquid interfaces (represented by light green) are almost similar and they take the shape of two concentric circles closely parallel to the solid walls. In addition, the increase in nanoparticle volume fraction during this period

Case 2

Case 3

Case 1

Case 2

Case 3

Case 4

Case 5

Case 6

1½hr

1½ hr

1 hr

1 hr

½ hr

½ hr

Case 1

causes no visible effect on either the shape or the location of the two interfaces because only a thin PCM melt layer was established. However, in other cases (with fins), heat transfer appears to be significantly promoted by the existence of fins as larger melting layers near and around the fins are developed, especially in cases with longer fin such as cases 2, 3 and 6 in Fig. 4. In those cases, heat transfer by conduction from the fin to the PCM gets promoted leading to expanded melting layers that occupy the spaces between the fins. In other words, higher liquid fractions of the PCM can be reached with increasing uf than by increasing un. This indicates that the fins improve the heat transfer better compared to the nanoparticles during this period of melting. – In the second stage (½ h < t  1 h), the role of natural convection is noticeable by the more deformation in shape of the solid–liquid interfaces. The hot PCM melt that originally occupied the lower half of the annulus starts to slightly move

1hr

1 hr 1½ hr Fig. 4. Contours of the liquid fraction at various volume fractions of fins and nanoparticles.

½ hr

Case 6

1½hr

Case 5

½ hr

Case 4

Fig. 5. Isotherms at various volume fractions of fins and nanoparticles.

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1.0 Case 2 Case 3 Case 4

0.9

Liquid Fraction

0.8 0.7 0.6

91

101

134

0.5 0.4 0.3 0.2 0.1 0.0

0

30

60

90

120

150

Time (Minutes) Fig. 6. Evolution of the PCM liquid fraction with nanoparticles and fins of w = 2 mm at THTF = 363 K.

upward under buoyancy effect and causes convective movement in the upper half. This movement of the PCM melt promotes higher melting rate at the top and makes the upper part of solid–liquid interface to move faster than the lower part. This is similar but more pronounced trend than in the previous period. The effect of fins remains more effective than that of the nanoparticles. As can be observed from Fig. 4 at t = 1 h, the cases with longer fins such as 2, 5 and 6 keep showing a growing melt layer size as a sign of better melting being achieved over other cases. This implies that using longer fins results in better melting propagation in the annulus by causing heat to penetrate farther distances in the solid PCM. – In the final stage (t  1½ h), the melt layer increases in size to occupy the major part of the annulus in most cases regardless of the value of the nanoparticle volume fraction or fin volume fraction. The melting is terminated early in the upper part due to the buoyancy effect that continues to increase in this part, while the melting is a little delayed in the lower half of the annulus due to the relatively heavier density of solid PCM compared to the liquid PCM. For example, in Fig. 4 at t = 1½ h, cases with fins such as case 5 (uf = 0.02) shows that there is still a portion of the solid PCM occupying the lower half that has not melted yet, whereas, it is completely melted in case 6 (uf = 0.02). Also, the results regarding the effects of nanoparticles show that the size of the melted layer increases as the nanoparticle volume fraction increases. Such behavior can be realized by comparing case 4 to case 1. This is attributed to the fact that the existence of fins, nanoparticles or combination of both, promotes higher conductive heat transfer and faster propagation of melting across the not melted PCM is originated. By comparing the cases in Fig. 4, it can be concluded that increasing the height of fins (i.e. higher uf) under the condition of same total volume fraction (ut) leads to faster development of solid-liquid interfaces than increasing the nanoparticle concentration (un). Such outcomes can be realized when either case 2 or case 6 is compared to case 4. 4.1.1. Analysis of isotherms Fig. 5 shows the distributions of isotherms at every ½ h of melting for the ten cases reported. The results are grouped in time stages as follows: – At the beginning (t  ½ h), the isotherms in the cases without fins show a series of uniform concentric circles parallel to the annulus walls. This is because the heat transfer process is dom-

423

inated by pure conduction. The change in the nanoparticle volume fraction shows no noticeable influence on the distribution of the isotherms through the annulus. This indicates that the existence of nanoparticles at this time period is only to further enhance the heat transfer by conduction between the liquid PCM and the solid walls. For the cases with fins, the isotherms look closer near and around the fin surfaces. Some rotating cells in the spaces between fins start to appear in cases such as case 2 and case 6, meaning that they have higher heat transfer rates than other cases. This is because the fins enhance heat conduction in the solid phase zone, and further contribute to its dominancy over convection in the liquid phase zone. – In the second period (1 h  t  1½ h), the isotherms slightly start to depart from the uniformity in shape in the cases without fins which is a sign for initiating a role for natural convection in the heat transfer process. In some cases with fins such as case 5 and 6, convection rotating cells appear at the upper half of the annulus. This is when the relatively cold PCM melt at the top moves downward under the gravity effect along the surface of the solid PCM to be replaced by a fresh mass of PCM melt moving upward under the effect of buoyancy. In fact, the melt movement across the annulus is governed by the difference between the buoyancy developed as a result of temperature gradients across the annulus and the gravity. The convection movement is mainly limited to the upper part of the annulus where the buoyancy force exceeds the gravity force. This explains why the liquid PCM at the top melted earlier than that at the bottom. At this time, the temperature of PCM is affected by both natural convection and heat conduction, but the dominant role remains that from conduction as long as the isotherms keep a unified color, especially in the cases with fins such as cases 5 and 6. This originates from the fact that the existence of fins suppresses the buoyancy effects and consequently weakens the natural convection role. Existence of nanoparticles in cases 3, 4 and 5 further supports the dominating role of conduction. This is attributed to the fact that nanoparticles enhance the heat conduction by two aspects. First, their high thermal conductivity results in higher conductive heat transfer according to Newton’s law of cooling, and second, their relatively high viscosity limits functionality of natural convection. – In the last stage (t  1½ h), the isotherms look more uniform in shape and unified in color compared to those in earlier melting stages especially in the lower half of the annulus due to the greater role of conduction in this zone. This makes the natural convection to lose its strength as an additional supply of heat transfer in the liquid PCM, as we have noted in the previous period. Furthermore, complete termination of the melting process in most or all parts of the annulus as in cases 5 and 6 is the prevailing trend throughout this period. This means that the entire heat transfer process continues to be conduction dominated and that convection may exert only a little influence. The dominancy is due to the relatively high thermal conductivities of the nanoparticles and the fins. Also, the flow resistance generated due to the presence of the fins severely suppresses the convection contribution. In summary, it is seen that the nanoparticles and the fins enhance the thermal conduction contribution at the expense of the natural convection contribution.

4.2. Characteristics of nanoPCM melting with fins In order to analyze the effect of adding nanoparticles, fins, or combination of both on the duration of the charging (melting) process, histories of the PCM liquid fraction were tracked and analyzed based on total enhancement volume fraction (ut ¼ 0:02). Liquid

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fraction (k) is defined as the ratio of the liquid PCM volume to the whole PCM (liquid + solid) volume. It indicates the rate of melting or solidification of the PCMs and contributes to evaluating the performance of latent TES systems. Fig. 6 compares the temporal evolution of liquid fraction during the PCM melting with nanoparticles and fins for total volume fraction ut ¼ 0:02. The dimensions of the fins are prearranged in a way to have fin volume fraction or composite volume fraction combined with nanoparticles of up to 0.02. Fig. 6 suggests that the configuration of fins with fin length of 19.3 mm and no nanoparticles (case 2) gives the best performance of melting for the cases of ut ¼ 0:02 and w = 2 mm. Fig. 7 shows a comparison for the temporal evolution of the PCM liquid fraction for the cases of ut ¼ 0:02 and w = 1 mm. As can be seen from the figure, case 6 with no nanoparticles and fins of fin length 38.6 mm gives the best enhanced melting rate. Results from Figs. 6 and 7 imply that under the same PCM volume reduction the fins alone achieve more favorable heat transfer to the PCM than either the nanoparticles alone or the combination of fins and nanoparticles. In other words, the existence of nanoparticles leads in both cases to attenuate the heat transfer enhancement and consequently prolong the phase change process compared to the case of fins alone. It can also be seen from Figs. 6 and 7 that all the cases show a steeper slope in the liquid fraction curve after about 30 min of melting as a sign of the starting of an improved thermal performance in the system. As indicated earlier, the role of natural convection in the heat transfer process starts to show in the melting period after about 30 min. So, it can be concluded that improvement in the melting progress is achieved after the natural convection is well established. This is confirmed in all the cases, but in case 2 and case 6, it is more obvious due to the substantial heat transfer enhancement achieved by longer fins used in those cases. This is further clarified by considering the time to complete the melting which corresponds to the state when there is no solid remaining in the annulus. From the times shown in Figs. 6 and 7, it can be seen that the trend for the total melting time varies depending on the fin/nanoparticle volume fraction. For instance, in Fig. 6 it is seen that increasing the fin volume fraction from 0.01(case 3) to 0.02 (case 2) while decreasing nanoparticle volume fraction from 0.01(case 3) to 0.00 (case 2) reduces the melting time from 101 min to 91 min, i.e. about 10% time reduction. A similar trend is seen in Fig. 7 that increasing the fin volume fraction from 0.01(case 5) to 0.02 (case 6) while decreasing nanoparticle volume fraction from 0.01(case 5) to 0.00 (case 6) decreases the melting time from 75 min to 66 min, i.e. about 12% time reduction. Thus,

the melting rate of the PCM is faster with increasing fin volume fraction and lower nanoparticle volume fraction. Table 3 summarizes the values of the total time required to reach complete melting along with the percentages of possible time saving at THTF = 363 K. Results from the table show that all the three enhancement techniques considered: (fins alone: cases 2, and 6), (nanoparticles alone: case 4) and (combination of fins and nanoparticles: cases 3, and 5) show significant improvement in the storage process compared to the base case (case 1). Compared to the base case, the time needed to completely melt the PCM is reduced by up to about 59% using fins alone (case 6), 17% using nanoparticles alone (case 4) and 44% using the combination of fins and nanoparticles (case 5). It is clear that employing fins as heat transfer promoter without nanoparticles is the best option compared to using either the nanoparticles alone or the combination of both. However, by comparing cases with fins alone, it can be concluded that using longer fins with smaller thickness (i.e. case 6) is better than using shorter fins with larger thickness (i.e. case 2). This leads to a deduction that larger fins inhibit the contribution of natural convection but they provide better heat transfer in the PCM which in turn assists the role of thermal conduction. Finally, the use of the combination (fins + nanoparticles) is more efficient than using nanoparticles alone for the same volume reduction limit. For example, this can be realized from comparison of the melting time in case 5 to that of case 4. This infers that the potential of enhancement is increased with the existence of fins more than the existence of nanoparticles alone. It should be noted here that this study considers three enhancement techniques: nanoparticles alone, fins alone, and nanoparticlefin combination. Since, each technique causes its own PCM volume reduction, there is the need to use the volume reduction that each technique causes so that the technique that gives the best performance for the volume requirement can be determined. The volume reduction for each technique was realized using un, uf, and ut, where: (ut = un) is the volume fraction for the case of nanoparticles alone, (ut = uf) is the volume fraction for the case of fins alone, and (ut = uf + un) is the volume fraction for the case of nanoparticle-fin combination. For example, for the case of (ut = 0.02), we can use the variations (0.00  uf  0.02) and (0.00  un  0.02), but (uf + un = 0.02) should be kept for comparing for the cases of (ut = 0.02). Thus, volume occupied by fins is kept constant in the case of fins alone (uf = 0.02), but has to be varied in the case of nanoparticle-fin combination within the range (0.00  uf  0.02) to give (ut = 0.02).

4.3. Effect of the HTF temperature 1.0 Case 4 Case 5 Case 6

0.9

Liquid Fraction

0.8 0.7 0.6

75

134

0.5 66

0.4 0.3 0.2 0.1 0.0

0

15

30

45

60

75

90

105

120

135

Time (Minutes) Fig. 7. Evolution of the PCM liquid fraction with nanoparticles and fins of w = 1 mm at THTF = 363 K.

The temperature of the HTF is a significant parameter that also needs to be considered in the design of TES systems with PCMs as the storage media. Increasing the charging temperature of the HTF remarkably improves the phase change rate and shortens the duration of the PCM phase transition. In this section, the case of fin thickness (w = 0.02) is reported for the investigation on the effect of the HTF temperature on the PCM melting evolution. Fig. 8 shows the instantaneous liquid fraction during a complete charging of the triplex-tube system with the HTF at three different temperatures: THTF = 363, 368, and 373 K. As can be seen from Fig. 8(a)–(c), the melting period becomes shorter as the HTF temperature increases. The reason for this is that at a higher HTF temperature a greater temperature gradient at the heating walls occurs, consequently leading to a higher heat transfer into the PCM. This gives rise to accelerated phase change rate. Data from Fig. 8 indicate that with the HTF temperature of 363 K, the PCM takes a maximum of 134 minutes to complete the melting process, while it takes only 90 and 66 minutes respectively in the cases of THTF = 368 and 373 K.

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J.M. Mahdi, E.C. Nsofor / International Journal of Heat and Mass Transfer 109 (2017) 417–427 Table 3 The possible saving in the time required to reach the complete melting status at THTF = 363 K. Case #

uf

un

ut

T (min)

% Time saving

1 2 3 4 5 6

0.00 0.02 0.01 0.00 0.01 0.02

0.00 0.00 0.01 0.02 0.01 0.00

0.00 0.02 0.02 0.02 0.02 0.02

162 91 101 134 91 66

0 43.8 37.7 17.3 43.8 59.2

1.0 1.0

Case 4 Case 5 Case 6

0.9

Case 4 Case 5 Case 6

0.9 0.8

0.8 0.7 Liquid Fraction

Liquid Fraction

0.7 0.6 134

75

0.5 66

0.4

46

0.6 52

0.5

90

0.4

0.3

0.3

0.2

0.2

0.1

0.1 0.0

0.0 0

15

30

45

60

75

90

0

105 120 135 150

10

20

30

40

50

60

Time (Minutes)

Time (Minutes)

(a)

(b)

1.0

70

80

90 100

Case 4 Case 5 Case 6

0.9

Liquid Fraction

0.8 0.7

34

0.6 0.5

66

39

0.4 0.3 0.2 0.1 0.0 0

10

20

30

40

50

60

70

80

Time (Minutes)

(c) Fig. 8. Evolution of the PCM liquid fraction with nanoparticles and fins at: (a) THTF = 363 K, (b) THTF = 368 K and (c) THTF = 373 K.

Table 4 The possible saving in the complete melting time for various HTF temperatures. Time to reach a complete melting in (min)

% Time saving

Case #

T HTF ¼ 363 K

T HTF ¼ 368 K

T HTF ¼ 373 K

T HTF ¼ 363 K

T HTF ¼ 368 K

T HTF ¼ 373 K

1 2 3 4 5 6

162 91 101 134 75 66

114 63 69 90 52 46

86 47 51 66 39 34

00.0 43.8 37.7 17.3 53.7 59.2

00.0 44.7 39.5 21.1 54.4 59.6

0.00 45.3 40.7 23.2 54.7 60.5

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The effects of varying the HTF temperature on the complete melting time for all the six cases studied are summarized in Table 4. Regarding the influence of the HTF temperature on the potential of fins/nanoparticles for phase-change enhancement, data from Table 4 show that in general, the percentage reduction in the melting time is better as the HTF temperature increases. For example, melting time can be saved by 44% in case 2 compared to the base case (case 1) for the HTF temperature of 363 K, while time saving goes up to 45% for the case of THTF = 368 K for the same comparison. This is due to the fact that conduction heat transfer increases as the HTF temperature gradient at the heating walls increases. As indicated earlier, the presence of fins/nanoparticles increases conduction dominancy over convection in this thermal energy storage heat transfer process. Thus, the heat transfer enhancement potential of fins/nanoparticles increases as conduction further dominates, which arises as the HTF temperature increases. This was seen in all the cases considered as seen in Table 4. The case of THTF = 373 K shows the largest percentage time saving compared to others. This suggests that the HTF temperature is a parameter that should also play a part in optimizing the design of a fin/nanoparticle combination for triplex tube latent heat thermal energy storage system.

5. Conclusions and recommendations A numerical study has been performed to investigate the effect of utilizing fins and nanoparticles in the PCM melting enhancement in a triplex-tube TES storage system. Three different techniques: fins alone, nanoparticles alone, and fin-nanoparticle combination were investigated with each of these occupying the same percentage volume of the system. The problem was restricted to a 2D finned annulus containing a nanoPCM, isothermally heated at both walls of the triplex-tube by a HTF at temperatures of 363, 368 and 373 K. Graphical results in the form of isotherms, solid-liquid interface positions, and transient liquid fraction profile over various periods of melting have been presented and discussed. The conclusions that can be drawn from the present study are as follows: (1) The melting process in a triplex-tube TES system is significantly improved by introduction of nanoparticles or a combination of fins and nanoparticles. However, a much better improvement is achieved by employing fins alone for the same volume usage. (2) Longer fins support better propagation of melting in the solid PCM by achieving deeper heat penetration leading to shorter melting duration. (3) There should be proper selection of the fin dimensions to ensure good performance within minimal PCM volume reduction. Generally, use of longer fins with smaller thickness is recommended based on outcomes of the present study. (4) Use of the combination (fins + nanoparticles) is more efficient than using nanoparticles alone within the same volume usage. This implies that the potential of enhancement is increased by the application of the fins more than the application of the nanoparticles alone. (5) Melting of the PCM is affected by natural convection and heat conduction but the dominant role remains that of conduction for the entire process. This is due to the flow resistant forces generated by the fin structure and the extra viscosity created by presence of the nanoparticles. (6) Increasing the HTF temperature not only contributes to reducing the PCM melting time it also improves the enhancement potential of the nanoparticle-fin combination..

Thus the HTF temperature is a parameter that should also play a part in optimizing the design of a fin/nanoparticle combination for the triplex tube latent heat thermal energy storage system. Due to the both-sides heating approach of the triplex-tube configuration, the heat exchanger performs better than the doublepipe heat exchanger for PCM-related storage applications. However, only a limited related research exists at this time. More studies are thus needed to further elucidate the TES performance in PCM triplex-tube heat exchangers for both horizontal and vertical positions.

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