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Numerical and experimental investigation of heat transfer in liquid cooling serpentine mini-channel heat sink with different new configuration models
Thermal Science and Engineering Progress 6 (2018) 128–139
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Numerical and experimental investigation of heat transfer in liquid cooling serpentine mini-channel heat sink with different new configuration models
T
⁎
Ahmed Abdulnabi Imrana, , Nabeel Sameer Mahmouda, Hayder Mohammad Jaffalb a b
Mechanical Engineering Department, University of Technology, Baghdad, Iraq Mechanical Engineering Department, Al-Mustansiriayah University, Baghdad, Iraq
A R T I C LE I N FO
A B S T R A C T
Keywords: Serpentine channel Pressure drop Heat sink Thermal resistance CFD Experimental
Cooling of electronic chips has become a basic viewpoint in the advancement of electronic devices. Overheating may cause glitch or harm to hardware. A water-cooled mini-channel is a successful cooling innovation for cooling of heat sinks. In this work, geometric optimisation of a 3D serpentine mini-channel heat sink (SMCHS) was investigated. Four configurations of SMCHS were proposed. These configurations were then simulated numerically and tested experimentally. Finite volume method computational fluid dynamics technique is used to model single-phase forced convection for water-cooling laminar flow in a 3D mini-channel heat sink with various channel configurations. Experiments were conducted to analyse the effect of water mass flow rate and heat load on thermal and hydraulic performances of the SMCHS. Experimental results agree well with numerical results. Results indicate that the performance of the proposed device effectively improves when serpentines with two inlets and two outlets are used compared with conventional serpentine with one inlet and one outlet.
1. Introduction A basic serpentine mini-channel heat sink (SMCHS) has received considerable attention given the high heat transfer coefficient and success of this device in high heat flux applications for electronic devices. Many studies have developed various aspects of engineering applications, including theoretical viewpoints which involve different patterns of investigations and outline strategies, and the practical aspects of these applications. Many recent studies have concentrated on hydrodynamic analysis and enhancement of straight minichannel heat sinks. Several of these studies have focused on the effects of heat flux, Reynolds number, channel dimensions and electric field on enhancing the cooling performances of electronic devices. Xie et al. [1] examined the effects of channel dimensions, fin thickness, bottom thickness and inlet velocity; Kumar and Sehgal [2] considered the effect of channel hydraulic diameter; Naphon and Nakharintr [3] studied the effects of heat flux, fin height and coolant flow rate; Moghanlou et al. [4] tested the effect of an electric field on the laminar flow of a square channel. Ghasemiet et al. [5] studied the effect of the channel diameter of a circular-shaped minichannel heat sink. The other part of studies has focused on the effects of using obstacles, grooves and surface roughness on minichannels. Bi et al. [6] contemplated the effects of dimples and cylindrical grooves; Xiaoqin and Jianlin [7] investigated the effects of
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non-uniform inlet cross sections; Attalla et al. [8] studied the influences of different degrees of surface roughness; Shen et al. [9] examined the effect of internal vertical bifurcation. Different unconventional flow field configurations have been widely used to enhance heat sink performance. Gongnan and Shian [10] explored two types of chip arrangements, namely, diagonal and parallel; Tang et al. [11] presented a mini-channel heat sink with a double-layer structure that consists of a minichannel and holes; Banda et al. [12] proposed non-conventional patterns for liquid-cooled heat sinks; Kim et al. [13] designed a multistage minichannel heat sink. Numerous studies have handled heat transfer enhancement using nanofluids. Various formulations of nanofluids are used as coolants in serpentine and straight channels that are incorporated in a minichannel and microchannel heat sinks. Ijam et al. [14] tested Al2O3–water and TiO2–water nanofluids for a copper minichannel heat sink; Ho and Chen [15,16] investigated the heat transfer characteristic of Al2O3–water nanofluid in a rectangular forced and natural circulation loop; Naphon and Nakharintr [17] tested a mixture of deionised water and nanoscale TiO2 particles with three different channel heights; Moraveji and Ardehali [18] and Ho et al. [19] investigated the effect of Al2O3–water nanofluid in a rectangular minichannel; Mashaei et al. [20] explored the effects of Al2O3–water nanofluid in a serpentine microchannel; Sivakumar et al. [21,22] examined the use of water–CuO and Al2O3–water that flows through a
Corresponding author. E-mail addresses: [email protected] (A.A. Imran), [email protected] (N.S. Mahmoud), jaff[email protected] (H.M. Jaffal). URL: https://orcid.org/0000-0002-3048-9623 (H.M. Jaffal).
https://doi.org/10.1016/j.tsep.2018.03.011 Received 29 December 2017; Received in revised form 22 March 2018; Accepted 25 March 2018 2451-9049/ © 2018 Published by Elsevier Ltd.
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Nomenclature A As Cp Dh Hch Hb hav ks kf L Lch LMTD ṁ n nt Nu p q Q Rt Rcond
Rconv Rfluid Rch t T Tin Tout Tbase Tmax Tmin Tmf U u v V w W Wch x, y, z ρ μ ν
heat transfer area of heat sink (m2) surface heat transfer area of channel (m2) specific heat at constant pressure (J/kg oC) hydraulic diameter (m) height of channel (m) plate thickness (m) average convection heat transfer coefficient (W/m2 oC) thermal conductivity of heat sink (W/m oC) thermal conductivity of fluid (W/m oC) length of heat sink (m) length of one channel (m) Logarithmic arithmetic mean temperature difference (oC) mass flow rate (kg/s) number of channel number of turn bend Nusselt number pressure (N/m2) Heat flux (W/m2) heat load (W) thermal resistance (oC/W) conduction thermal resistance (oC/W)
serpentine microchannel; Sohel et al. [23] studied the use of Al2O3–H2O nanofluid instead of pure water in a minichannel heat sink; Ghasemi et al. [24] tested the effect of using alumina–water (Al2O3–H2O) nanofluid as a coolant on the performance of a triangle-shaped minichannel heat sink; Saeed and Kim [25] tested the Al2O3–H2O nanofluid as a coolant in minichannel heat sinks with three channel configurations. Kazuhisa and Koichi [26] experimentally investigated the heat transfer characteristics of the mini-channel heat sink. Copper minichannel-finned heat sinks are examined under constant heat flux conditions of over 200 W/cm2 to elucidate their relevance as a single-phase flow cooling device for next-generation power devices. The effects of fin thickness and channel width are assessed in detail. Xuekang et al. [27] investigated the significance and advancement of the channel geometry of a serpentine channel heat sink that utilises a multi-objective genetic algorithm. A straightforward network model for thermal resistance is created to explore the total thermal characteristics performance of the serpentine channel heat sink. Inlet velocity, channel height, channel width, and fin width are parameters that must be enhanced in accordance with the requirements of fixed width and length of the heat sink. The investigation shows that a decrease in pressure drop and thermal resistance can be efficient by streamlining channel design and inlet velocity. The issue of a uniform flow distribution has received an increasing consideration for heat sink outline. Chen et al. [28] exhibited a multi-objective basic plan of a serpentine channel heat sink. The effects of channel height, channel width, inlet velocity, and number of channels are studied as the outline factors. The structural modelling of a serpentine channel heat sink with one inlet and one outlet is the 3D model of this heat sink. In this demonstration, the two variables are considered to represent the performance of the heat sink, that is, total thermal resistance and pressure drop of a serpentine channel. Numerical outcomes and experimental data have determined that the deterioration in thermal resistance and pressure drop can be accomplished by ensuring channel configuration and inlet velocity, thereby resulting in the desired thermal performance of the heat sink. Xiaohong et al. [29] developed an orthogonal trial plane technique that uses a multiobjective improvement design to enhance the heat transfer capacity and flow consistency of a U-type heat sink. Thus, a computational fluid dynamics (CFD) model is established, and then the temperature and flow fields are explored. The results demonstrate that the dispersion of liquid in each parallel channel is not only a component of the flow
convection thermal resistance (oC/W) fluid thermal resistance (oC/W) radius of channel (m) thickness (m) temperature (oC) fluid temperature at inlet (oC) fluid temperature at outlet (oC) base temperature of heat sink (oC) maximum base temperature of heat sink (oC) minimum temperature of fluid (oC) mean fluid temperature (oC) overall heat transfer coefficient (W/m2 oC) velocity component in the x-direction (m/s) velocity component in the y-direction (m/s) Average velocity (m/s) velocity component in the y-direction (m/s) width of heat sink (m) width of channel (m) Cartesian coordinate (m) density (kg/m3) dynamic viscosity (N s/m2) kinematic viscosity (m2/s)
conditions in the header but also affected by the geometric size of the header and parallel channels; moreover, the optimum U-sort heat sink through orthogonal experiment outline technique can provide a uniform distribution flow. Saad et al. [30] explored tentatively a watercooled mini-channel heat sink that is used to simulate a high heatgenerating microchip. The effect of sink geometry on water is investigated along with five heat sinks. The five heat sinks have a fin spacing of 0.2, 0.5, 1.0 and 1.5 mm with a flat plate heat sink. The base temperature and thermal resistance of the heat sinks are reduced by decreasing the fin spacing and expanding a volumetric flow rate of water that circulates through the heat sink. Xiao et al. [31] proposed a straightforward thermal resistance model to simulate the thermal characteristics of serpentine channel heat sinks. The model involves an advancement of thermal resistance units associated with stream systems which show the pressure and temperature distribution among the units. The fluid Reynolds number, pressure and temperature results of a 10channel serpentine heat sink are acquired by fluctuating the channel aspect ratio and thus contrasted with a full 3D CFD modelling. The results exhibit that the model can anticipate characteristics of the heat transfer for serpentine channels with high precision and in a general senseless enlisting time. Hao et al. [32] proposed an analytical model to research the pressure drop and thermal resistance in heat sinks with serpentine channels of 180° bends. The aggregate thermal resistance is obtained by utilizing a network model for thermal resistance given an equivalent thermal circuit strategy. Pressure drop is determined considering a straight channel by bend loss because the bends disrupt the hydrodynamic boundary occasionally. The model is experimentally approved by measuring the pressure and temperature characteristics of heat sinks with geometric parameters of a diver and various Reynolds numbers. Tong et al. [33] numerically examined the temperature uniformity in a water-cooled mini-channel heat sink under high-heating flux with various flow field configurations. A network model for thermal resistance is established, and the channels of variable height were proposed to enhance the uniformity of temperature on the heating surface. The effect of flow field configurations on uniformity flow distribution is firstly examined, and a circular turning constructal distributor is selected because of its optimal uniformity flow distribution and cooling performance. Waleed et al. [34] conducted experimental and numerical studies of the attributes of fluid flow and heat transfer in a square cross section wavy serpentine microchannel with insulated 129
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is the same, and the number of meanders varies. The first configuration is conventional SMCHS with one inlet and one outlet. The second configuration contains two serpentines with two inlets and two outlets in parallel and arranged lengthwise. The third configuration has two serpentines with two inlets and two outlets in parallel and in a Ushaped path. The fourth configuration contains two serpentines with two inlets and two outlets in the diagonal direction. The bottom plate thickness is Hb, and the top cover is bonded, glued or clamped to provide closed channels for liquid flow. The coolant flow velocity Vin is the parameter of interest in designing a SMCHS. The effects of this parameter on hydrothermal performance are examined in this work. The maximum allowable temperature of the bottom surface and the acceptable pressure drop are the constraints.
upper wall and other sidewalls held at constant temperature. Moderate pressure drop and convective heat transfer to a straight microchannel were evaluated by using mixtures of glycerine–water as working fluids inside the serpentine microchannel. Ashrafi and Shams [35] developed a numerical scheme for the effect of flow field orientation on water management in a proton exchange membrane fuel cell with a single serpentine channel. Diverse configurations were used for legitimate water management, and the optimal configuration must be selected for the most effective and stable operation of fuel cells. Ahmed et al. [36] numerically and experimentally studied the impact of the secondary flow produced by chevron fins on the hydrothermal performance of a SMCHS. To improve convective heat transfer and decrease thermal resistance of a SMCHS, a new design of serpentine channel using chevron fins was optimized in terms of the chevron oblique angle, channel width and number of channels. In the present work, novel SMCHSs with several configurations are considered to establish the flow of the optimised thermal performance of a cooling system. The utilisation of water as the coolant in the heat sink and forced convection heat transfer were comparatively investigated by using a 3D CFD simulation. Furthermore, experimental studies were conducted to validate the numerical results.
3. Numerical methodology 3.1. Simulation method The CFD problem discussed in this work is the comparison of flow parameters and temperature properties of a serpentine mini-channel with its modifications and configurations. To analyse the thermal and hydraulic characteristics of the SMCHSs, a 3D solid–fluid conjugate model is used to predict the flow and heat transfer performance of heat sinks through a finite volume CFD-based method by using commercial solver. In Fig. 1, all configurations of the SMCHSs have the same channel total length of 900 mm with a channel of rectangular square cross-section Wch × Hch = 4 mm × 5 mm. The preprocessor Design Modeler is used to build the computational domain. The 3D computational domain of the heat sink is depicted in Fig. 2, and its structure dimensions are L × W × Hb = 150 mm × 100 mm × 10 mm. The SMCHS comprises the base and cover plates. The top surface is insulated, whilst the bottom surface is uniformly heated. Water passes through the channel of heat sink and deflects heat from a heat
2. Proposed serpentine channel heat sink configurations The heat transfer enhancement techniques are widely used in many applications in the heating process to enhance the performance of heat sinks or reduce their weight and size. In this work, the geometric optimisation for channel configurations of the SMCHS is proposed. The objective is to reduce the peak temperature from the walls to the coolant fluid. Fig. 1 displays a pictorial view of the suggested models. The unvaried total area that is cooled is W × L with individual minichannel flow passage dimensions of Wch × Hch. The hydraulic diameter is fixed for all configurations. The length of the total serpentine channel
Fig. 1. Schematic of SMCHS configurations (a) configuration A (b) configuration B (c) configuration C (d) configuration D. 130
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Exit water
Inlet water
Fig. 2. Computational domain and mesh distribution of the modelling.
temperature and velocity gradients Fig. 2, whilst unstructured meshes are utilised in the solid zone. For accuracy of results, examinations of grid independence were performed in each model. These examinations are verified by the difference in the outlet coolant temperature which is within 1%, and the final count of mesh for each configuration is listed in Table 1. In order to solve the governing integral equations for the continuity, Navier–Stokes, and energy equations, the solver utilises the CFD finite volume strategy as a solution technique for solving the governing integral equations for continuity, Navier–Stokes and energy equations. The technique comprises the following steps:
dissipating component that is attached to the bottom of the heat sink base. The following suppositions are formulated to build the heat transfer and fluid flow model: - A single-phase fluid flow is laminar, incompressible and a steadystate transport process. - For fluid flow, the effect of radiation heat transfer is negligible. - The influence of gravity and other body forces are neglected. - The thermophysical properties of heat sink and fluid are constant. The finite volume CFD method is used in this work to compute the flow fields and heat transfer through solid and fluid regions. The flow distribution across the channel is solving continuity, Navier–Stokes, and energy equations along the length from the input to output for solid and fluid domains. Thus, solid–fluid interface condition must be imposed between the domains for a conservative interface flux. The properties of the materials used in this analysis are default values presented in the package database. For the mini-channels, structured meshes are utilised in the inlet, outlet and channels. The mesh is concentrated in the boundary layer zone near the channel wall to accurately predict
• A grid is generated on the domain, as previously presented. • Sets of algebraic equations are established for pressure, velocity and •
conserved scalars by integrating the governing equations on each control volume. Discretised equations are linearised and solved iteratively.
A pressure-based segregated solution algorithm is used as a solver. The governing equations are solved sequentially and iteratively (i.e. separated from one another), as illustrated in the flowchart in Fig. 3.
Table 1 Shows the mesh size and the skewness mesh quality criteria of each configuration. Configuration A
Configuration B
Configuration C
Configuration D
Mesh parameters
Mesh size
Mesh skewness
Mesh size
Mesh skewness
Mesh size
Mesh skewness
Mesh size
Mesh skewness
Channel domain Sink solid base
994,194 2,114,814
0.24 0.81
3,368,000 6,252,314
0.306 0.87
1,166,778 2,900,824
0.24 0.87
2,481,600 4,042,865
0.28 0.86
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u
∂ 2w ∂ 2w ∂ 2w ⎞ ∂w ∂w ∂w 1 ∂p + ν⎛ 2 + + +v +w =− 2 ∂y ∂z 2 ⎠ ∂x ∂y ∂z ρ ∂z ⎝ ∂x ⎜
⎟
(2c)
where p, ρ and ν are the pressure drop, density and kinematic viscosity of the coolant, respectively. Energy equation for the fluid:
u
kf ∂T ∂T ∂T ∂ 2T ∂ 2T ∂ 2T ⎞ +v +w = +⎛ 2 + + 2 ∂x ∂y ∂z ρCp ∂ x ∂ y ∂z 2 ⎠ ⎝ ⎜
⎟
(3)
where ρ, T, kf and Cp are the density, temperature, thermal conductivity and specific heat at a constant pressure of the coolant, correspondingly. Energy equation for the solid:
∂ 2T ∂ 2T ∂ 2T ⎞ ks ⎛ 2 + + =0 2 ∂ x ∂ y ∂z 2 ⎠ ⎝ ⎜
⎟
(4)
where ks is the thermal conductivity of the solid. 3.3. Boundary conditions The boundary conditions defined in the processor serve as inputs for the model. The fluid and solid domains and boundary conditions are presented in Fig. 2. For the computational zone, boundary conditions are provided as follows: - The inlet water temperature (5)
T = Tin = constant Fig. 3. Flow chart for pressure-based segregated algorithm.
- The bottom wall surface is subjected to a constant heat flux and adiabatic conditions at the others walls
SIMPLE algorithm is used in pressure–velocity coupling for pressure correction. A point implicit (Gauss–Seidel) linear equation solver is used to solve the resultant set of equations for the dependent variable in each cell. The energy and momentum conservation equations are discretised by a second-order upwind interpolation scheme is utilised to calculate cell-face pressure. For the energy equation, the solutions are considered converged when the normalised residual values are less than 10−7 but 10−4 for the other variables. The governing equations for this conjugated heat transfer issue with the above mentioned suppositions can be depicted as follows:
−ks
(7)
- No slip boundary in all channel walls (8)
u = v = w = 0,
- The conjugate boundary condition at the internal surfaces (liquid/ solid interface)
−kf
∂Tf ∂n
= −ks
∂Ts ∂n
(9)
(1) - Zero gauge pressure is assigned at the outlet of the mini-channel heat sink
Momentum equation:
u
(6)
- The uniform inlet is velocity and is assumed
The flow is based on continuity, momentum and energy equations. Continuity equation:
u
∂T ∂T = =0 ∂x ∂z
u = uin = constant
3.2. Governing equations
∂u ∂v ∂w + + =0 ∂x ∂y ∂z
∂T = q, ∂y
∂ 2u ∂ 2u ∂ 2u ∂u ∂u ∂u 1 ∂p + ν⎛ 2 + 2 + 2 ⎞ +v +w =− ∂y ∂z ⎠ ∂x ∂y ∂z ρ ∂x ⎝ ∂x ⎜
p = pout = atmosphere pressure
⎟
∂ 2u
∂ 2u
(2a)
The inlet and outlet of heat sinks are defined as velocity-inlet and pressure-outlet boundaries. The inlet velocity for configuration (A) ranges from 0.0833 m/s to 0.5 m/s, and the corresponding volume flow rate is 0.1–0.6 L/min. The inlet velocity for other configurations is
∂ 2u
∂u ∂u ∂u 1 ∂p + ν⎛ 2 + 2 + 2 ⎞ +v +w =− ∂y ∂z ⎠ ∂x ∂y ∂z ρ ∂x ⎝ ∂x ⎜
(10)
⎟
(2b)
Table 2 Shows the boundary condition type of each configuration. Configurations
Working fluid inlet
Working fluid outlet
Heat sink bottom surface
Heat sink surfaces
A B C D
Velocity-inlet (0.0833–0.5 m/s) Velocity-inlet (0.0416–0.2083 m/s)
Pressure-outlet (P = 0)
Wall with q = 10,000–100,000 W/m2
Insulated wall q = 0 W/m2
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calculated based on that the flow rate is divided equally in the two new channels. The fluid temperature of the inlet is 293 K, and the pressure at the outlet is 0 Pa (gauge pressure). On the bottom wall of the computational domain, a constant heat flux is imposed whilst adiabatic conditions for all other walls are specified. Heat flux density of chip is 10,000–100,000 W/m2. All variables are initiated from the inlet boundary condition. The boundary conditions types for the proposed configurations used in the solver are listed in Table 2.
SMCHS base were drilled, and then thermocouples were installed in the holes to measure the base temperatures. The holes are located at a distance of 4 mm depth from the surfaces of the mini-channel base with equal longitudinal distance. The average bulk wall temperature is measured using K-type thermocouples with 1 mm diameter beads. The temperature measurements of the liquid coolant are made using two additional thermocouples with a space of 1.5 cm near the inlet and outlet of the channel. The pressure drop across the SMCHS is measured using a digital differential manometer. A flow meter is used to measure the water flow rate between 1 and 10 Lpm. A thermal block-based compound is applied to the heater and channel sink to avoid air gaps and ensure an effective heat transfer. The channel with heater assembly is insulated using a glass wool to minimise heat losses. The power provided by a variac was increased by a fixed value, and the flow rate was adjusted using a control valve at a fixed value. The experimental test steady conditions were maintained for 30 min. The volume flow rates in the experiments were observed at 1–6 Lpm with an uncertainty of ± 4%. The heat load is in the range of 40–400 W with an uncertainty of 1%. The inlet temperature of the fluid was kept up at approximately 27 °C, and the maximum temperature of the overall heat sink was maintained at less than 90 °C. The pressure drop accuracy of measurement is within ± 1%.
4. Experimental methodology 4.1. 1Experimental setup and procedure An experimental test rig was manufactured and installed at the Heat Transfer Laboratory of the Mechanical Engineering Department of the University of Technology. The general arrangement of the equipment is indicated schematically in Fig. 4 and photographically in Fig. 5. The test rig was designed for the various operating parameters to be varied and tried. The main components of this apparatus are test modules, cooling fluid, measuring equipment, reservoir, power supply and cooling system. Fig. 6 demonstrates the modules of all SMCHSs. The cooling fluid was distilled water which enters the system from a reservoir through a filter and then passes through the heat sink, where the coolant becomes hot by absorbing heat from the heat source. The coolant must be cooled down before the liquid enters the heat sink again for recirculation. This process was realised using a radiator cooler. Therefore, the hot coolant became cool at the radiator cooler and then went back to the storage tank to continuously recirculate through the system by a pump. The power produced by the pump creates sufficient pressure to push the cooling fluid to pass through the module. The flow rates of coolant are varied during a set of experiments controlled by using a globe valve. A flowmeter is used to measure the volume flow rate inside the loop system. The source of heat is provided at the bottom surface of the SMCHS. The plate-type heater has a maximum heat input of 500 W/230 V and is used as a source of input heat to the SMCHS which can be changed through a variac. The instruments used for measuring the electrical power are voltmeter and ammeter. The AC voltage from the main power supply is reduced using a stepdown transformer; thus, the heat input to the bottom surface of the SMCHS is constant for each test. Five holes through the centreline of the
4.2. Experimental data reduction The heat rejected from the heat sink by the liquid that circulates through the SMCHS was calculated by applying the principle of preservation of energy to control volume, with one input and one output, with no work interactions, and assuming that no changes occurred in the potential kinetic energy and kinetic energy. This is demonstrated by Eq. (11)
̇ p (Tout −Tin ) Q = mC
(11)
The input and output of water temperatures are measured by two Ktype thermocouple probes, placed in the insulated pipes and connected to the heat sink. The thermophysical properties of cooling water at mean fluid temperature, Tmf, Eq. (12) were used in all calculations.
Tmf =
Tout + Tin 2
(12)
The mean -log- temperature-difference (LMTD) through the heat
Fig. 4. Schematic diagram for experimental setup. 133
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Data logger of temperature Ammeter
Digital manometer
Flow meter
Variac Heat sink
Fig. 5. Photographic picture for the experimental test rig.
Configuration A
Configuration B
Configuration C
Configuration D
Fig. 6. The configurations of all SMCHSs.
five reading of thermocouple that measured SMCHS temperatures as
sink was calculated by Eq. (13). Tbase was measured by using five K-type thermocouple wires that were placed at the copper heat sink, in accordance with Saad et al. [30].
LMTD =
(Tbase−Tin )−(Tbase−Tout ) ln
(
(Tbase − Tin) (Tbase − Tout )
)
(17)
Equation (11) disregards the spread of thermal resistance considering the different temperatures among input and output or given the interface thermal resistance between the heat sink and the heater. The conductive thermal resistance was defined by
(13)
For each flow rate, the overall heat transfer coefficient for each heat sink was ascertained by applying Eq. (14) and then reduces to provide Eq. (15).
̇ p (Tout −Tin ) = UAs (LMTD) Q = mC
T1 + T2 + T3 + T4 + T5 5
Tbase =
R cond =
(14)
t ks A
(18)
The total convection thermal resistance is formulated as
U=
̇ p (Tout −Tin ) mC UAs (LMTD)
R conv =
(15)
The SMCHS is different from parallel channel heat sink given several sharp bends. The total thermal resistance of the heat sink by ignoring the effect of heat transfer coefficient at bends is given by
T −T Rt = max min = R cond + R conv + Rfluid Q
1 hav As
(19)
The average heat transfer coefficient is defined by
hav =
(16)
̇ p (Tout −Tin ) mC As (Tbase−Tmf )
(20)
Furthermore, the surface area available for heat transfer (As) for SMCHS configuration A can be written as
The maximum base plate temperature can be calculated from the 134
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the SMCHS (XZ plane) are depicted in Fig. 10. The mass flow rate was set to 0.01 kg/s with the heat flux of 40,000 W/m2 for each case. In all channel configurations, the largest velocity magnitudes are observed after channel meanders because the fluid recirculation results from a flow path from the inlet to the outlet through the channels, hence slightly increasing the velocity and heat transfer coefficient within these channels. For a single-phase flow inside a mini-channel, the heat transfer coefficient is nearly constant when the flow velocity of the coolant is fixed. A flow misdistribution along the flow direction becomes slightly apparent because the conventional serpentine channel is divided into two serpentines with two inlets and two outlets. Configuration (B) offers the optimal uniform distribution of fluid velocity inside the heat sink compared with channel configurations (C) and (D); this phenomenon is the significant effect on heat transfer enhancement. The variation of the Nusselt number with mass flow rate and all SMCHS configurations are illustrated in Fig. 11. The Nusselt number remarkably increases for each configuration whilst the mass flow rate increases. The increases in the Nusselt number is due to the increase in heat transfer caused by an increase in mass flow rate. From these two figures, the largest Nusselt number can be achieved in configuration (B) given a higher heat dissipation than in other types. Fig. 12 exhibits the impact of heat flux on the Nusselt number for all SMCHS configurations. From this figure, The Nusselt number for all configurations slightly increases whilst the heat flux increases. The increase in the Nusselt number is due to the increase in the amount of heat transfer, this behaviour was determined by Ahmed et al. [36].
As = (Hch × Lch × 2) n + (Wch × Lch) n + (πR ch × Hch × 2) nt + (πR ch × Wch) nt
(21)
The capacitive thermal resistance is defined by
Rfluid =
1 1 = ̇ p mC ρWch Hch VCP
(22)
This thermal resistance presents the temperature rise from inlet to outlet in bulk fluid. The Nusselt number, Nu is defined as
Nu =
hav Dh kf
(23)
where Dh represents the hydraulic diameter and is calculated as follows:
Dh =
2Wch Hch Wch + Hch
(24)
5. Results and discussion 5.1. Validation of SMCHS The validation of the numerical results was performed by using the experimental results to verify the capability of the solver to predict accurate and reliable results. The comparison was performed with the base plate temperature and pressure drop, as presented in Figs. 7 and 8, respectively, for SMCHS configuration A. In these figures, the theoretical base plate temperatures and the pressure drop of the fluid agreed well with the experiment results. The deviation between the numerical and the experimental results was observed to be 11% and 8%, correspondingly, with the above parameters. The difference between the valuable of the numerical and the experimental results is because of the assumptions of the numerical simulation and uncertainty of measurements. Moreover, the deviation of the experimental pressure from the theoretical values is high with the increase in mass flow rate. This result may be due to the entrance pressure losses in the channel increase whilst the flow rate increases.
5.3. Experimental results Figs. 13 and 14 demonstrate the effects of mass flow rates and heat loads on the heat transfer coefficient for all SMCHS configurations. The heat transfer coefficient that corresponds to the various mass flow rates for different SMCHS configurations is illustrated in Fig. 13. For each configuration, the heat transfer coefficient increases with the increase in mass flow rate. The most important reason for the increase in the amount of water is the increase in heat transfer coefficient with mass flow rate. The flow potential of the removed heat will increase and cause an increase in the heat transfer coefficient. The largest heat transfer coefficient is achieved in SMCHS configuration (B) given the change in the flow direction and additional recirculation of water that achieved extra heat exchange with the water. Fig. 14 displays the variation of heat transfer coefficient with the heat load with various SMCHS configurations. This figure also demonstrates that the heat transfer coefficient slightly increases when heat load increases for all configurations. Furthermore, the largest heat transfer coefficient can be achieved in SMCHS configuration (B) given a higher heat dissipation than other configurations. Figs. 15 and 16 depict the impacts of mass flow rates and heat loads on the overall thermal resistance for all
5.2. Numerical simulation Fig. 9 displays the contours of temperature in the fluid and solid domains of the SMCHS (XZ plane) at a heat flux of 40,000 W/m2 and water mass flow rate of 0.01 kg/s in a channel for different configurations of serpentine channel. The inlet of the channel is marked in blue. For each case, a low-temperature zone for the plate can be identified near the inlet water because the intensity of heat transfer between copper and water is at its peak at the channel inlet. The temperature difference demonstrates the trend of the heat transfer in the channel to be outward from the inside and upward from the bottom because the heating element is in contact with the copper base plate. The temperature difference between copper plate and water decreases from the inlet to the exit which is affected by flow mixing and acceleration towards the exit. The results show that the bottom surface of the SMCHS with various channel configurations exhibits various temperature distributions. In general, temperature distribution patterns are significantly affected by channel configuration. The temperature of the copper plate is at the maximum in configuration (A) compared with the other three cases as a result of using a single channel, this confirms the numerical results of Ahmed et al. [36]. A suitable channel configuration can achieve a favourable cooling performance; thus, the performance of configuration (B) heat sink model is better than configurations (C) and (D) due to quick heat dissipation to water (the lowest base temperature that corresponds to the lightest shade of green) as an after-effect of the increment in the number of bends for water flow. Velocity contours for various configurations of the serpentine channel in the fluid domain of
Fig. 7. Comparison of numerical and experimental results for base temperature. 135
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configurations, this behaviour is determined by different experiments of authors such as Xiaohong et al. [32] and Ahmed et al. [36]. The effect of heat load on the overall thermal resistance for constant mass flow rate is presented in Fig. 16. The overall thermal resistance diminishes with the expansion of the heat load for all configurations. The maximum overall thermal resistance is achieved for conventional SMCHS (configuration A) compared with all the SMCHS configurations. A comparison of the total pressure drop and the rising mass flow rates for all SMCHS configurations is depicted in Fig. 17. The total pressure drop of water is low over the SMCHS, an increase in the water mass flow rates for all SMCHS configurations increases the pressure drop. Thus, the obtained high volume flow rate requires pumping power with minimal cost considering the low-pressure drop through the SMCHS. The conventional SMCHS (configuration A) achieved a higher pressure drop than the other three configurations. Fig. 8. Comparison of numerical and experimental results for pressure drop.
6. Uncertainty analysis
SMCHS configurations. The relationship between the overall thermal resistance and mass flow rate is illustrated in Fig. 15. The overall thermal resistance is inversely proportional to the mass flow rate for all
The quantities are measured to calculate the heat load is subjected to certain uncertainties due to error in the measurement tools. The
Configuration A
Configuration B
Configuration C
Configuration D
Fig. 9. Temperature contour of the solid and liquid region of the SMCHSs. 136
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Configuration A
Configuration B
Configuration C
Configuration D
Fig. 10. Velocity contour of the solid and liquid region of the SMCHSs.
Fig. 11. Variation of Nusselt number with mass flow rates for all SMCHS configurations.
Fig. 12. Variation of Nusselt number with heat fluxes for all SMCHS configurations.
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Fig. 13. Variation of heat transfer coefficient with mass flow rates for all SMCHS configurations.
Fig. 17. Variation of pressure drop with mass flow rates for all SMCHS configurations.
analysis is suggested by Kline and McClintock [37].
Q = m∘Cp (Tout −Tin )
(25) 2
UQ =
2
2
∘ ⎛ Tout . ∂Q . UT ⎞ + ⎛ Tin . ∂Q . UT ⎞ + ⎛ m . ∂Q . Um∘⎞ out in ∘ ⎝ Q ∂m ⎠ ⎝ Q ∂Tin ⎠ ⎝ Q ∂Tout ⎠ ⎜
⎟
⎜
⎟
⎜
⎟
(26) The uncertainty in the heat load 6%. 7. Conclusions In the present work, numerical and experimental analyses of heat transfer and fluid flow characteristics of a laminar single-phase flow were conducted through the SMCHS. Four configurations of the SMCHS were designed and fabricated. The following conclusions are drawn according to the obtained results:
Fig. 14. Variation of heat transfer coefficient with loads for all SMCHS configurations.
1. The performance comparison of the four configurations of an SMCHS indicated that performance can be significantly improved in serpentines with two inlets and two outlets compared with that in a conventional serpentine with one inlet and one outlet. 2. The conventional serpentine (Configuration A) exhibited the worst uniform temperature distribution with a maximum pressure drop. The percentage enhancements in heat transfer and pressure drop of the new SMCHS to the conventional SMCHS were 136%, 104% and 91% for Configurations B, C and D, respectively. 3. The conventional SMCHS (Configuration A) achieved a higher pressure drop than the other three configurations. The pressure drop enhancements were −28%, −50% and −47% for Configurations B, C and D, correspondingly. 4. Among the three new channel configurations, Configuration B exhibited the maximum enhancement in heat transfer with the minimum thermal resistance. 5. The numerical results agreed well with the experimental results. The deviations between the numerical and experimental results for baseplate temperature and pressure drop of the fluid were 11% and 8%, respectively.
Fig. 15. Variation of thermal resistance with mass flow rates for all SMCHS configurations.
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Thermal Science and Engineering Progress journal homepage: www.elsevier.com/locate/tsep
Numerical and experimental investigation of heat transfer in liquid cooling serpentine mini-channel heat sink with different new configuration models
T
⁎
Ahmed Abdulnabi Imrana, , Nabeel Sameer Mahmouda, Hayder Mohammad Jaffalb a b
Mechanical Engineering Department, University of Technology, Baghdad, Iraq Mechanical Engineering Department, Al-Mustansiriayah University, Baghdad, Iraq
A R T I C LE I N FO
A B S T R A C T
Keywords: Serpentine channel Pressure drop Heat sink Thermal resistance CFD Experimental
Cooling of electronic chips has become a basic viewpoint in the advancement of electronic devices. Overheating may cause glitch or harm to hardware. A water-cooled mini-channel is a successful cooling innovation for cooling of heat sinks. In this work, geometric optimisation of a 3D serpentine mini-channel heat sink (SMCHS) was investigated. Four configurations of SMCHS were proposed. These configurations were then simulated numerically and tested experimentally. Finite volume method computational fluid dynamics technique is used to model single-phase forced convection for water-cooling laminar flow in a 3D mini-channel heat sink with various channel configurations. Experiments were conducted to analyse the effect of water mass flow rate and heat load on thermal and hydraulic performances of the SMCHS. Experimental results agree well with numerical results. Results indicate that the performance of the proposed device effectively improves when serpentines with two inlets and two outlets are used compared with conventional serpentine with one inlet and one outlet.
1. Introduction A basic serpentine mini-channel heat sink (SMCHS) has received considerable attention given the high heat transfer coefficient and success of this device in high heat flux applications for electronic devices. Many studies have developed various aspects of engineering applications, including theoretical viewpoints which involve different patterns of investigations and outline strategies, and the practical aspects of these applications. Many recent studies have concentrated on hydrodynamic analysis and enhancement of straight minichannel heat sinks. Several of these studies have focused on the effects of heat flux, Reynolds number, channel dimensions and electric field on enhancing the cooling performances of electronic devices. Xie et al. [1] examined the effects of channel dimensions, fin thickness, bottom thickness and inlet velocity; Kumar and Sehgal [2] considered the effect of channel hydraulic diameter; Naphon and Nakharintr [3] studied the effects of heat flux, fin height and coolant flow rate; Moghanlou et al. [4] tested the effect of an electric field on the laminar flow of a square channel. Ghasemiet et al. [5] studied the effect of the channel diameter of a circular-shaped minichannel heat sink. The other part of studies has focused on the effects of using obstacles, grooves and surface roughness on minichannels. Bi et al. [6] contemplated the effects of dimples and cylindrical grooves; Xiaoqin and Jianlin [7] investigated the effects of
⁎
non-uniform inlet cross sections; Attalla et al. [8] studied the influences of different degrees of surface roughness; Shen et al. [9] examined the effect of internal vertical bifurcation. Different unconventional flow field configurations have been widely used to enhance heat sink performance. Gongnan and Shian [10] explored two types of chip arrangements, namely, diagonal and parallel; Tang et al. [11] presented a mini-channel heat sink with a double-layer structure that consists of a minichannel and holes; Banda et al. [12] proposed non-conventional patterns for liquid-cooled heat sinks; Kim et al. [13] designed a multistage minichannel heat sink. Numerous studies have handled heat transfer enhancement using nanofluids. Various formulations of nanofluids are used as coolants in serpentine and straight channels that are incorporated in a minichannel and microchannel heat sinks. Ijam et al. [14] tested Al2O3–water and TiO2–water nanofluids for a copper minichannel heat sink; Ho and Chen [15,16] investigated the heat transfer characteristic of Al2O3–water nanofluid in a rectangular forced and natural circulation loop; Naphon and Nakharintr [17] tested a mixture of deionised water and nanoscale TiO2 particles with three different channel heights; Moraveji and Ardehali [18] and Ho et al. [19] investigated the effect of Al2O3–water nanofluid in a rectangular minichannel; Mashaei et al. [20] explored the effects of Al2O3–water nanofluid in a serpentine microchannel; Sivakumar et al. [21,22] examined the use of water–CuO and Al2O3–water that flows through a
Corresponding author. E-mail addresses: [email protected] (A.A. Imran), [email protected] (N.S. Mahmoud), jaff[email protected] (H.M. Jaffal). URL: https://orcid.org/0000-0002-3048-9623 (H.M. Jaffal).
https://doi.org/10.1016/j.tsep.2018.03.011 Received 29 December 2017; Received in revised form 22 March 2018; Accepted 25 March 2018 2451-9049/ © 2018 Published by Elsevier Ltd.
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Nomenclature A As Cp Dh Hch Hb hav ks kf L Lch LMTD ṁ n nt Nu p q Q Rt Rcond
Rconv Rfluid Rch t T Tin Tout Tbase Tmax Tmin Tmf U u v V w W Wch x, y, z ρ μ ν
heat transfer area of heat sink (m2) surface heat transfer area of channel (m2) specific heat at constant pressure (J/kg oC) hydraulic diameter (m) height of channel (m) plate thickness (m) average convection heat transfer coefficient (W/m2 oC) thermal conductivity of heat sink (W/m oC) thermal conductivity of fluid (W/m oC) length of heat sink (m) length of one channel (m) Logarithmic arithmetic mean temperature difference (oC) mass flow rate (kg/s) number of channel number of turn bend Nusselt number pressure (N/m2) Heat flux (W/m2) heat load (W) thermal resistance (oC/W) conduction thermal resistance (oC/W)
serpentine microchannel; Sohel et al. [23] studied the use of Al2O3–H2O nanofluid instead of pure water in a minichannel heat sink; Ghasemi et al. [24] tested the effect of using alumina–water (Al2O3–H2O) nanofluid as a coolant on the performance of a triangle-shaped minichannel heat sink; Saeed and Kim [25] tested the Al2O3–H2O nanofluid as a coolant in minichannel heat sinks with three channel configurations. Kazuhisa and Koichi [26] experimentally investigated the heat transfer characteristics of the mini-channel heat sink. Copper minichannel-finned heat sinks are examined under constant heat flux conditions of over 200 W/cm2 to elucidate their relevance as a single-phase flow cooling device for next-generation power devices. The effects of fin thickness and channel width are assessed in detail. Xuekang et al. [27] investigated the significance and advancement of the channel geometry of a serpentine channel heat sink that utilises a multi-objective genetic algorithm. A straightforward network model for thermal resistance is created to explore the total thermal characteristics performance of the serpentine channel heat sink. Inlet velocity, channel height, channel width, and fin width are parameters that must be enhanced in accordance with the requirements of fixed width and length of the heat sink. The investigation shows that a decrease in pressure drop and thermal resistance can be efficient by streamlining channel design and inlet velocity. The issue of a uniform flow distribution has received an increasing consideration for heat sink outline. Chen et al. [28] exhibited a multi-objective basic plan of a serpentine channel heat sink. The effects of channel height, channel width, inlet velocity, and number of channels are studied as the outline factors. The structural modelling of a serpentine channel heat sink with one inlet and one outlet is the 3D model of this heat sink. In this demonstration, the two variables are considered to represent the performance of the heat sink, that is, total thermal resistance and pressure drop of a serpentine channel. Numerical outcomes and experimental data have determined that the deterioration in thermal resistance and pressure drop can be accomplished by ensuring channel configuration and inlet velocity, thereby resulting in the desired thermal performance of the heat sink. Xiaohong et al. [29] developed an orthogonal trial plane technique that uses a multiobjective improvement design to enhance the heat transfer capacity and flow consistency of a U-type heat sink. Thus, a computational fluid dynamics (CFD) model is established, and then the temperature and flow fields are explored. The results demonstrate that the dispersion of liquid in each parallel channel is not only a component of the flow
convection thermal resistance (oC/W) fluid thermal resistance (oC/W) radius of channel (m) thickness (m) temperature (oC) fluid temperature at inlet (oC) fluid temperature at outlet (oC) base temperature of heat sink (oC) maximum base temperature of heat sink (oC) minimum temperature of fluid (oC) mean fluid temperature (oC) overall heat transfer coefficient (W/m2 oC) velocity component in the x-direction (m/s) velocity component in the y-direction (m/s) Average velocity (m/s) velocity component in the y-direction (m/s) width of heat sink (m) width of channel (m) Cartesian coordinate (m) density (kg/m3) dynamic viscosity (N s/m2) kinematic viscosity (m2/s)
conditions in the header but also affected by the geometric size of the header and parallel channels; moreover, the optimum U-sort heat sink through orthogonal experiment outline technique can provide a uniform distribution flow. Saad et al. [30] explored tentatively a watercooled mini-channel heat sink that is used to simulate a high heatgenerating microchip. The effect of sink geometry on water is investigated along with five heat sinks. The five heat sinks have a fin spacing of 0.2, 0.5, 1.0 and 1.5 mm with a flat plate heat sink. The base temperature and thermal resistance of the heat sinks are reduced by decreasing the fin spacing and expanding a volumetric flow rate of water that circulates through the heat sink. Xiao et al. [31] proposed a straightforward thermal resistance model to simulate the thermal characteristics of serpentine channel heat sinks. The model involves an advancement of thermal resistance units associated with stream systems which show the pressure and temperature distribution among the units. The fluid Reynolds number, pressure and temperature results of a 10channel serpentine heat sink are acquired by fluctuating the channel aspect ratio and thus contrasted with a full 3D CFD modelling. The results exhibit that the model can anticipate characteristics of the heat transfer for serpentine channels with high precision and in a general senseless enlisting time. Hao et al. [32] proposed an analytical model to research the pressure drop and thermal resistance in heat sinks with serpentine channels of 180° bends. The aggregate thermal resistance is obtained by utilizing a network model for thermal resistance given an equivalent thermal circuit strategy. Pressure drop is determined considering a straight channel by bend loss because the bends disrupt the hydrodynamic boundary occasionally. The model is experimentally approved by measuring the pressure and temperature characteristics of heat sinks with geometric parameters of a diver and various Reynolds numbers. Tong et al. [33] numerically examined the temperature uniformity in a water-cooled mini-channel heat sink under high-heating flux with various flow field configurations. A network model for thermal resistance is established, and the channels of variable height were proposed to enhance the uniformity of temperature on the heating surface. The effect of flow field configurations on uniformity flow distribution is firstly examined, and a circular turning constructal distributor is selected because of its optimal uniformity flow distribution and cooling performance. Waleed et al. [34] conducted experimental and numerical studies of the attributes of fluid flow and heat transfer in a square cross section wavy serpentine microchannel with insulated 129
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is the same, and the number of meanders varies. The first configuration is conventional SMCHS with one inlet and one outlet. The second configuration contains two serpentines with two inlets and two outlets in parallel and arranged lengthwise. The third configuration has two serpentines with two inlets and two outlets in parallel and in a Ushaped path. The fourth configuration contains two serpentines with two inlets and two outlets in the diagonal direction. The bottom plate thickness is Hb, and the top cover is bonded, glued or clamped to provide closed channels for liquid flow. The coolant flow velocity Vin is the parameter of interest in designing a SMCHS. The effects of this parameter on hydrothermal performance are examined in this work. The maximum allowable temperature of the bottom surface and the acceptable pressure drop are the constraints.
upper wall and other sidewalls held at constant temperature. Moderate pressure drop and convective heat transfer to a straight microchannel were evaluated by using mixtures of glycerine–water as working fluids inside the serpentine microchannel. Ashrafi and Shams [35] developed a numerical scheme for the effect of flow field orientation on water management in a proton exchange membrane fuel cell with a single serpentine channel. Diverse configurations were used for legitimate water management, and the optimal configuration must be selected for the most effective and stable operation of fuel cells. Ahmed et al. [36] numerically and experimentally studied the impact of the secondary flow produced by chevron fins on the hydrothermal performance of a SMCHS. To improve convective heat transfer and decrease thermal resistance of a SMCHS, a new design of serpentine channel using chevron fins was optimized in terms of the chevron oblique angle, channel width and number of channels. In the present work, novel SMCHSs with several configurations are considered to establish the flow of the optimised thermal performance of a cooling system. The utilisation of water as the coolant in the heat sink and forced convection heat transfer were comparatively investigated by using a 3D CFD simulation. Furthermore, experimental studies were conducted to validate the numerical results.
3. Numerical methodology 3.1. Simulation method The CFD problem discussed in this work is the comparison of flow parameters and temperature properties of a serpentine mini-channel with its modifications and configurations. To analyse the thermal and hydraulic characteristics of the SMCHSs, a 3D solid–fluid conjugate model is used to predict the flow and heat transfer performance of heat sinks through a finite volume CFD-based method by using commercial solver. In Fig. 1, all configurations of the SMCHSs have the same channel total length of 900 mm with a channel of rectangular square cross-section Wch × Hch = 4 mm × 5 mm. The preprocessor Design Modeler is used to build the computational domain. The 3D computational domain of the heat sink is depicted in Fig. 2, and its structure dimensions are L × W × Hb = 150 mm × 100 mm × 10 mm. The SMCHS comprises the base and cover plates. The top surface is insulated, whilst the bottom surface is uniformly heated. Water passes through the channel of heat sink and deflects heat from a heat
2. Proposed serpentine channel heat sink configurations The heat transfer enhancement techniques are widely used in many applications in the heating process to enhance the performance of heat sinks or reduce their weight and size. In this work, the geometric optimisation for channel configurations of the SMCHS is proposed. The objective is to reduce the peak temperature from the walls to the coolant fluid. Fig. 1 displays a pictorial view of the suggested models. The unvaried total area that is cooled is W × L with individual minichannel flow passage dimensions of Wch × Hch. The hydraulic diameter is fixed for all configurations. The length of the total serpentine channel
Fig. 1. Schematic of SMCHS configurations (a) configuration A (b) configuration B (c) configuration C (d) configuration D. 130
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Exit water
Inlet water
Fig. 2. Computational domain and mesh distribution of the modelling.
temperature and velocity gradients Fig. 2, whilst unstructured meshes are utilised in the solid zone. For accuracy of results, examinations of grid independence were performed in each model. These examinations are verified by the difference in the outlet coolant temperature which is within 1%, and the final count of mesh for each configuration is listed in Table 1. In order to solve the governing integral equations for the continuity, Navier–Stokes, and energy equations, the solver utilises the CFD finite volume strategy as a solution technique for solving the governing integral equations for continuity, Navier–Stokes and energy equations. The technique comprises the following steps:
dissipating component that is attached to the bottom of the heat sink base. The following suppositions are formulated to build the heat transfer and fluid flow model: - A single-phase fluid flow is laminar, incompressible and a steadystate transport process. - For fluid flow, the effect of radiation heat transfer is negligible. - The influence of gravity and other body forces are neglected. - The thermophysical properties of heat sink and fluid are constant. The finite volume CFD method is used in this work to compute the flow fields and heat transfer through solid and fluid regions. The flow distribution across the channel is solving continuity, Navier–Stokes, and energy equations along the length from the input to output for solid and fluid domains. Thus, solid–fluid interface condition must be imposed between the domains for a conservative interface flux. The properties of the materials used in this analysis are default values presented in the package database. For the mini-channels, structured meshes are utilised in the inlet, outlet and channels. The mesh is concentrated in the boundary layer zone near the channel wall to accurately predict
• A grid is generated on the domain, as previously presented. • Sets of algebraic equations are established for pressure, velocity and •
conserved scalars by integrating the governing equations on each control volume. Discretised equations are linearised and solved iteratively.
A pressure-based segregated solution algorithm is used as a solver. The governing equations are solved sequentially and iteratively (i.e. separated from one another), as illustrated in the flowchart in Fig. 3.
Table 1 Shows the mesh size and the skewness mesh quality criteria of each configuration. Configuration A
Configuration B
Configuration C
Configuration D
Mesh parameters
Mesh size
Mesh skewness
Mesh size
Mesh skewness
Mesh size
Mesh skewness
Mesh size
Mesh skewness
Channel domain Sink solid base
994,194 2,114,814
0.24 0.81
3,368,000 6,252,314
0.306 0.87
1,166,778 2,900,824
0.24 0.87
2,481,600 4,042,865
0.28 0.86
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u
∂ 2w ∂ 2w ∂ 2w ⎞ ∂w ∂w ∂w 1 ∂p + ν⎛ 2 + + +v +w =− 2 ∂y ∂z 2 ⎠ ∂x ∂y ∂z ρ ∂z ⎝ ∂x ⎜
⎟
(2c)
where p, ρ and ν are the pressure drop, density and kinematic viscosity of the coolant, respectively. Energy equation for the fluid:
u
kf ∂T ∂T ∂T ∂ 2T ∂ 2T ∂ 2T ⎞ +v +w = +⎛ 2 + + 2 ∂x ∂y ∂z ρCp ∂ x ∂ y ∂z 2 ⎠ ⎝ ⎜
⎟
(3)
where ρ, T, kf and Cp are the density, temperature, thermal conductivity and specific heat at a constant pressure of the coolant, correspondingly. Energy equation for the solid:
∂ 2T ∂ 2T ∂ 2T ⎞ ks ⎛ 2 + + =0 2 ∂ x ∂ y ∂z 2 ⎠ ⎝ ⎜
⎟
(4)
where ks is the thermal conductivity of the solid. 3.3. Boundary conditions The boundary conditions defined in the processor serve as inputs for the model. The fluid and solid domains and boundary conditions are presented in Fig. 2. For the computational zone, boundary conditions are provided as follows: - The inlet water temperature (5)
T = Tin = constant Fig. 3. Flow chart for pressure-based segregated algorithm.
- The bottom wall surface is subjected to a constant heat flux and adiabatic conditions at the others walls
SIMPLE algorithm is used in pressure–velocity coupling for pressure correction. A point implicit (Gauss–Seidel) linear equation solver is used to solve the resultant set of equations for the dependent variable in each cell. The energy and momentum conservation equations are discretised by a second-order upwind interpolation scheme is utilised to calculate cell-face pressure. For the energy equation, the solutions are considered converged when the normalised residual values are less than 10−7 but 10−4 for the other variables. The governing equations for this conjugated heat transfer issue with the above mentioned suppositions can be depicted as follows:
−ks
(7)
- No slip boundary in all channel walls (8)
u = v = w = 0,
- The conjugate boundary condition at the internal surfaces (liquid/ solid interface)
−kf
∂Tf ∂n
= −ks
∂Ts ∂n
(9)
(1) - Zero gauge pressure is assigned at the outlet of the mini-channel heat sink
Momentum equation:
u
(6)
- The uniform inlet is velocity and is assumed
The flow is based on continuity, momentum and energy equations. Continuity equation:
u
∂T ∂T = =0 ∂x ∂z
u = uin = constant
3.2. Governing equations
∂u ∂v ∂w + + =0 ∂x ∂y ∂z
∂T = q, ∂y
∂ 2u ∂ 2u ∂ 2u ∂u ∂u ∂u 1 ∂p + ν⎛ 2 + 2 + 2 ⎞ +v +w =− ∂y ∂z ⎠ ∂x ∂y ∂z ρ ∂x ⎝ ∂x ⎜
p = pout = atmosphere pressure
⎟
∂ 2u
∂ 2u
(2a)
The inlet and outlet of heat sinks are defined as velocity-inlet and pressure-outlet boundaries. The inlet velocity for configuration (A) ranges from 0.0833 m/s to 0.5 m/s, and the corresponding volume flow rate is 0.1–0.6 L/min. The inlet velocity for other configurations is
∂ 2u
∂u ∂u ∂u 1 ∂p + ν⎛ 2 + 2 + 2 ⎞ +v +w =− ∂y ∂z ⎠ ∂x ∂y ∂z ρ ∂x ⎝ ∂x ⎜
(10)
⎟
(2b)
Table 2 Shows the boundary condition type of each configuration. Configurations
Working fluid inlet
Working fluid outlet
Heat sink bottom surface
Heat sink surfaces
A B C D
Velocity-inlet (0.0833–0.5 m/s) Velocity-inlet (0.0416–0.2083 m/s)
Pressure-outlet (P = 0)
Wall with q = 10,000–100,000 W/m2
Insulated wall q = 0 W/m2
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calculated based on that the flow rate is divided equally in the two new channels. The fluid temperature of the inlet is 293 K, and the pressure at the outlet is 0 Pa (gauge pressure). On the bottom wall of the computational domain, a constant heat flux is imposed whilst adiabatic conditions for all other walls are specified. Heat flux density of chip is 10,000–100,000 W/m2. All variables are initiated from the inlet boundary condition. The boundary conditions types for the proposed configurations used in the solver are listed in Table 2.
SMCHS base were drilled, and then thermocouples were installed in the holes to measure the base temperatures. The holes are located at a distance of 4 mm depth from the surfaces of the mini-channel base with equal longitudinal distance. The average bulk wall temperature is measured using K-type thermocouples with 1 mm diameter beads. The temperature measurements of the liquid coolant are made using two additional thermocouples with a space of 1.5 cm near the inlet and outlet of the channel. The pressure drop across the SMCHS is measured using a digital differential manometer. A flow meter is used to measure the water flow rate between 1 and 10 Lpm. A thermal block-based compound is applied to the heater and channel sink to avoid air gaps and ensure an effective heat transfer. The channel with heater assembly is insulated using a glass wool to minimise heat losses. The power provided by a variac was increased by a fixed value, and the flow rate was adjusted using a control valve at a fixed value. The experimental test steady conditions were maintained for 30 min. The volume flow rates in the experiments were observed at 1–6 Lpm with an uncertainty of ± 4%. The heat load is in the range of 40–400 W with an uncertainty of 1%. The inlet temperature of the fluid was kept up at approximately 27 °C, and the maximum temperature of the overall heat sink was maintained at less than 90 °C. The pressure drop accuracy of measurement is within ± 1%.
4. Experimental methodology 4.1. 1Experimental setup and procedure An experimental test rig was manufactured and installed at the Heat Transfer Laboratory of the Mechanical Engineering Department of the University of Technology. The general arrangement of the equipment is indicated schematically in Fig. 4 and photographically in Fig. 5. The test rig was designed for the various operating parameters to be varied and tried. The main components of this apparatus are test modules, cooling fluid, measuring equipment, reservoir, power supply and cooling system. Fig. 6 demonstrates the modules of all SMCHSs. The cooling fluid was distilled water which enters the system from a reservoir through a filter and then passes through the heat sink, where the coolant becomes hot by absorbing heat from the heat source. The coolant must be cooled down before the liquid enters the heat sink again for recirculation. This process was realised using a radiator cooler. Therefore, the hot coolant became cool at the radiator cooler and then went back to the storage tank to continuously recirculate through the system by a pump. The power produced by the pump creates sufficient pressure to push the cooling fluid to pass through the module. The flow rates of coolant are varied during a set of experiments controlled by using a globe valve. A flowmeter is used to measure the volume flow rate inside the loop system. The source of heat is provided at the bottom surface of the SMCHS. The plate-type heater has a maximum heat input of 500 W/230 V and is used as a source of input heat to the SMCHS which can be changed through a variac. The instruments used for measuring the electrical power are voltmeter and ammeter. The AC voltage from the main power supply is reduced using a stepdown transformer; thus, the heat input to the bottom surface of the SMCHS is constant for each test. Five holes through the centreline of the
4.2. Experimental data reduction The heat rejected from the heat sink by the liquid that circulates through the SMCHS was calculated by applying the principle of preservation of energy to control volume, with one input and one output, with no work interactions, and assuming that no changes occurred in the potential kinetic energy and kinetic energy. This is demonstrated by Eq. (11)
̇ p (Tout −Tin ) Q = mC
(11)
The input and output of water temperatures are measured by two Ktype thermocouple probes, placed in the insulated pipes and connected to the heat sink. The thermophysical properties of cooling water at mean fluid temperature, Tmf, Eq. (12) were used in all calculations.
Tmf =
Tout + Tin 2
(12)
The mean -log- temperature-difference (LMTD) through the heat
Fig. 4. Schematic diagram for experimental setup. 133
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Data logger of temperature Ammeter
Digital manometer
Flow meter
Variac Heat sink
Fig. 5. Photographic picture for the experimental test rig.
Configuration A
Configuration B
Configuration C
Configuration D
Fig. 6. The configurations of all SMCHSs.
five reading of thermocouple that measured SMCHS temperatures as
sink was calculated by Eq. (13). Tbase was measured by using five K-type thermocouple wires that were placed at the copper heat sink, in accordance with Saad et al. [30].
LMTD =
(Tbase−Tin )−(Tbase−Tout ) ln
(
(Tbase − Tin) (Tbase − Tout )
)
(17)
Equation (11) disregards the spread of thermal resistance considering the different temperatures among input and output or given the interface thermal resistance between the heat sink and the heater. The conductive thermal resistance was defined by
(13)
For each flow rate, the overall heat transfer coefficient for each heat sink was ascertained by applying Eq. (14) and then reduces to provide Eq. (15).
̇ p (Tout −Tin ) = UAs (LMTD) Q = mC
T1 + T2 + T3 + T4 + T5 5
Tbase =
R cond =
(14)
t ks A
(18)
The total convection thermal resistance is formulated as
U=
̇ p (Tout −Tin ) mC UAs (LMTD)
R conv =
(15)
The SMCHS is different from parallel channel heat sink given several sharp bends. The total thermal resistance of the heat sink by ignoring the effect of heat transfer coefficient at bends is given by
T −T Rt = max min = R cond + R conv + Rfluid Q
1 hav As
(19)
The average heat transfer coefficient is defined by
hav =
(16)
̇ p (Tout −Tin ) mC As (Tbase−Tmf )
(20)
Furthermore, the surface area available for heat transfer (As) for SMCHS configuration A can be written as
The maximum base plate temperature can be calculated from the 134
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the SMCHS (XZ plane) are depicted in Fig. 10. The mass flow rate was set to 0.01 kg/s with the heat flux of 40,000 W/m2 for each case. In all channel configurations, the largest velocity magnitudes are observed after channel meanders because the fluid recirculation results from a flow path from the inlet to the outlet through the channels, hence slightly increasing the velocity and heat transfer coefficient within these channels. For a single-phase flow inside a mini-channel, the heat transfer coefficient is nearly constant when the flow velocity of the coolant is fixed. A flow misdistribution along the flow direction becomes slightly apparent because the conventional serpentine channel is divided into two serpentines with two inlets and two outlets. Configuration (B) offers the optimal uniform distribution of fluid velocity inside the heat sink compared with channel configurations (C) and (D); this phenomenon is the significant effect on heat transfer enhancement. The variation of the Nusselt number with mass flow rate and all SMCHS configurations are illustrated in Fig. 11. The Nusselt number remarkably increases for each configuration whilst the mass flow rate increases. The increases in the Nusselt number is due to the increase in heat transfer caused by an increase in mass flow rate. From these two figures, the largest Nusselt number can be achieved in configuration (B) given a higher heat dissipation than in other types. Fig. 12 exhibits the impact of heat flux on the Nusselt number for all SMCHS configurations. From this figure, The Nusselt number for all configurations slightly increases whilst the heat flux increases. The increase in the Nusselt number is due to the increase in the amount of heat transfer, this behaviour was determined by Ahmed et al. [36].
As = (Hch × Lch × 2) n + (Wch × Lch) n + (πR ch × Hch × 2) nt + (πR ch × Wch) nt
(21)
The capacitive thermal resistance is defined by
Rfluid =
1 1 = ̇ p mC ρWch Hch VCP
(22)
This thermal resistance presents the temperature rise from inlet to outlet in bulk fluid. The Nusselt number, Nu is defined as
Nu =
hav Dh kf
(23)
where Dh represents the hydraulic diameter and is calculated as follows:
Dh =
2Wch Hch Wch + Hch
(24)
5. Results and discussion 5.1. Validation of SMCHS The validation of the numerical results was performed by using the experimental results to verify the capability of the solver to predict accurate and reliable results. The comparison was performed with the base plate temperature and pressure drop, as presented in Figs. 7 and 8, respectively, for SMCHS configuration A. In these figures, the theoretical base plate temperatures and the pressure drop of the fluid agreed well with the experiment results. The deviation between the numerical and the experimental results was observed to be 11% and 8%, correspondingly, with the above parameters. The difference between the valuable of the numerical and the experimental results is because of the assumptions of the numerical simulation and uncertainty of measurements. Moreover, the deviation of the experimental pressure from the theoretical values is high with the increase in mass flow rate. This result may be due to the entrance pressure losses in the channel increase whilst the flow rate increases.
5.3. Experimental results Figs. 13 and 14 demonstrate the effects of mass flow rates and heat loads on the heat transfer coefficient for all SMCHS configurations. The heat transfer coefficient that corresponds to the various mass flow rates for different SMCHS configurations is illustrated in Fig. 13. For each configuration, the heat transfer coefficient increases with the increase in mass flow rate. The most important reason for the increase in the amount of water is the increase in heat transfer coefficient with mass flow rate. The flow potential of the removed heat will increase and cause an increase in the heat transfer coefficient. The largest heat transfer coefficient is achieved in SMCHS configuration (B) given the change in the flow direction and additional recirculation of water that achieved extra heat exchange with the water. Fig. 14 displays the variation of heat transfer coefficient with the heat load with various SMCHS configurations. This figure also demonstrates that the heat transfer coefficient slightly increases when heat load increases for all configurations. Furthermore, the largest heat transfer coefficient can be achieved in SMCHS configuration (B) given a higher heat dissipation than other configurations. Figs. 15 and 16 depict the impacts of mass flow rates and heat loads on the overall thermal resistance for all
5.2. Numerical simulation Fig. 9 displays the contours of temperature in the fluid and solid domains of the SMCHS (XZ plane) at a heat flux of 40,000 W/m2 and water mass flow rate of 0.01 kg/s in a channel for different configurations of serpentine channel. The inlet of the channel is marked in blue. For each case, a low-temperature zone for the plate can be identified near the inlet water because the intensity of heat transfer between copper and water is at its peak at the channel inlet. The temperature difference demonstrates the trend of the heat transfer in the channel to be outward from the inside and upward from the bottom because the heating element is in contact with the copper base plate. The temperature difference between copper plate and water decreases from the inlet to the exit which is affected by flow mixing and acceleration towards the exit. The results show that the bottom surface of the SMCHS with various channel configurations exhibits various temperature distributions. In general, temperature distribution patterns are significantly affected by channel configuration. The temperature of the copper plate is at the maximum in configuration (A) compared with the other three cases as a result of using a single channel, this confirms the numerical results of Ahmed et al. [36]. A suitable channel configuration can achieve a favourable cooling performance; thus, the performance of configuration (B) heat sink model is better than configurations (C) and (D) due to quick heat dissipation to water (the lowest base temperature that corresponds to the lightest shade of green) as an after-effect of the increment in the number of bends for water flow. Velocity contours for various configurations of the serpentine channel in the fluid domain of
Fig. 7. Comparison of numerical and experimental results for base temperature. 135
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configurations, this behaviour is determined by different experiments of authors such as Xiaohong et al. [32] and Ahmed et al. [36]. The effect of heat load on the overall thermal resistance for constant mass flow rate is presented in Fig. 16. The overall thermal resistance diminishes with the expansion of the heat load for all configurations. The maximum overall thermal resistance is achieved for conventional SMCHS (configuration A) compared with all the SMCHS configurations. A comparison of the total pressure drop and the rising mass flow rates for all SMCHS configurations is depicted in Fig. 17. The total pressure drop of water is low over the SMCHS, an increase in the water mass flow rates for all SMCHS configurations increases the pressure drop. Thus, the obtained high volume flow rate requires pumping power with minimal cost considering the low-pressure drop through the SMCHS. The conventional SMCHS (configuration A) achieved a higher pressure drop than the other three configurations. Fig. 8. Comparison of numerical and experimental results for pressure drop.
6. Uncertainty analysis
SMCHS configurations. The relationship between the overall thermal resistance and mass flow rate is illustrated in Fig. 15. The overall thermal resistance is inversely proportional to the mass flow rate for all
The quantities are measured to calculate the heat load is subjected to certain uncertainties due to error in the measurement tools. The
Configuration A
Configuration B
Configuration C
Configuration D
Fig. 9. Temperature contour of the solid and liquid region of the SMCHSs. 136
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Configuration A
Configuration B
Configuration C
Configuration D
Fig. 10. Velocity contour of the solid and liquid region of the SMCHSs.
Fig. 11. Variation of Nusselt number with mass flow rates for all SMCHS configurations.
Fig. 12. Variation of Nusselt number with heat fluxes for all SMCHS configurations.
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Fig. 13. Variation of heat transfer coefficient with mass flow rates for all SMCHS configurations.
Fig. 17. Variation of pressure drop with mass flow rates for all SMCHS configurations.
analysis is suggested by Kline and McClintock [37].
Q = m∘Cp (Tout −Tin )
(25) 2
UQ =
2
2
∘ ⎛ Tout . ∂Q . UT ⎞ + ⎛ Tin . ∂Q . UT ⎞ + ⎛ m . ∂Q . Um∘⎞ out in ∘ ⎝ Q ∂m ⎠ ⎝ Q ∂Tin ⎠ ⎝ Q ∂Tout ⎠ ⎜
⎟
⎜
⎟
⎜
⎟
(26) The uncertainty in the heat load 6%. 7. Conclusions In the present work, numerical and experimental analyses of heat transfer and fluid flow characteristics of a laminar single-phase flow were conducted through the SMCHS. Four configurations of the SMCHS were designed and fabricated. The following conclusions are drawn according to the obtained results:
Fig. 14. Variation of heat transfer coefficient with loads for all SMCHS configurations.
1. The performance comparison of the four configurations of an SMCHS indicated that performance can be significantly improved in serpentines with two inlets and two outlets compared with that in a conventional serpentine with one inlet and one outlet. 2. The conventional serpentine (Configuration A) exhibited the worst uniform temperature distribution with a maximum pressure drop. The percentage enhancements in heat transfer and pressure drop of the new SMCHS to the conventional SMCHS were 136%, 104% and 91% for Configurations B, C and D, respectively. 3. The conventional SMCHS (Configuration A) achieved a higher pressure drop than the other three configurations. The pressure drop enhancements were −28%, −50% and −47% for Configurations B, C and D, correspondingly. 4. Among the three new channel configurations, Configuration B exhibited the maximum enhancement in heat transfer with the minimum thermal resistance. 5. The numerical results agreed well with the experimental results. The deviations between the numerical and experimental results for baseplate temperature and pressure drop of the fluid were 11% and 8%, respectively.
Fig. 15. Variation of thermal resistance with mass flow rates for all SMCHS configurations.
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Fig. 16. Variation of thermal resistance with loads for all SMCHS configurations.
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