Numerical investigation on hydrothermal characteristics of microchannel heat sinks with PCM inserts for effective thermal management applications

Abstract

Purpose

The purpose of the paper is to develop an efficient thermal management system, which effectively dissipate the heat generated from the electronic devices. The present paper focuses at the modeling of microchannel heat sinks (MCHSs) with phase change materials (PCMs) insets to deal with the fluctuating heat generated from the electronic components.

Design/methodology/approach

In this paper, a novel approach is introduced to enhance the thermal performance of MCHSs through the integration of conjugate heat transfer and energy storage. Numerical investigations were conducted on six novel models of PCM-based hybrid MCHSs using ANSYS-FLUENT. The hydrothermal characteristics of six PCM-based hybrid MCHS models were analyzed and compared with an MCHS model without PCM.

Findings

The numerical model used for this study exhibited a good agreement with existing experimental and simulation results documented in the literature. The hybrid MCHS models developed in the present analysis showed superior thermal characteristics compared to MCHS without PCM. About 12% improvement in the thermal performance factor and a 7.3% reduction in thermal resistance were observed in the proposed MCHS models. A negligible influence of the PCM channel shape and aspect ratio (AR) was observed on the MCHS performance.

Research limitations/implications

As the present work is a numerical investigation, the computational time and computational cost requirements are the main implication for the research.

Practical implications

High pumping power requirement and expensive manufacturing methods of the microfluidic devices are the main practical implications. Leakage problem is also a challenge for development of these heat sinks.

Originality/value

The surge in the heat generated by electronic components is a limiting factor for the conventional MCHSs. To accommodate the surge, researchers have explored energy storage methods using PCM-based passive MCHS but these are effective only during the phase change process. To address this limitation, novel PCM-based hybrid MCHSs, which combine convective heat transfer with energy storage capabilities, have been modeled in the present work. There is an ample opportunity for further exploration of hybrid MCHSs with PCM.

Nomenclature

A_b

= Area of base of the MCHS (m²);

H

= Height of the heat sink (m);

H_C

= Height of the channel (m);

H_P

= Height of the PCM layer (m);

L

= Length of heat sink (m);

p

= Pressure (pa);

q

= Heat flux applied at bottom surface (W/m²);

R_T

= Total thermal resistance (K W⁻¹);

t₁

= Heat sink top rib thickness (m);

t₂

= Heat sink bottom rib thickness (m);

${\overline{T}}_b$

= Average temperature of bottom surface of the MCHS (K);

T_f

= Temperature of the fluid (K);

T_in

= Inlet temperature of the fluid (K);

v_in

= Inlet velocity (m/s²);

W

= Width of the heat sink (m);

W_c

= Width of the channel (m);

W_p

= Width of the PCM layer (m);

W_t

= Gap between the microchannels (m); and

x, y, z

= Cartesian coordinates (m).

Abbreviations

MC

= Microchannel;

MCHS

= Microchannel heat sink;

MEPCM

= Microencapsulated phase change material;

Nu

= Nusselt number;

PCM

= Phase change material; and

Re

= Reynolds number.

Greek symbols

α

= Thermal diffusivity (m²/s);

μ

= Dynamic viscosity (pas); and

ρ

= Density (Kg/m³).

Subscripts

b

= Base of the channel;

C

= Channel;

f

= Fluid;

in

= Inlet; and

T

= Total.

1. Introduction

The escalating demand for enhanced functionality and high performance in electronic devices and computer processors has resulted in significant heat generation, necessitating the implementation of efficient cooling systems to ensure optimal operation and reliability. However, the ongoing trend toward miniaturization has introduced additional complexities in heat removal due to limited space availability (Manova et al., 2022; Zhang et al., 2022). To address these challenges, a multitude of innovative thermal management systems, such as microchannel heat sinks (MCHSs), have been developed, offering remarkable compactness to effectively manage heat dissipation. MCHSs have emerged as a promising solution for thermal management in electronic applications, effectively addressing the associated challenges (Khan et al., 2022). The initial work on MCHSs in 1981 demonstrated their ability to dissipate a heat flux of 790 W/cm², triggering further research and development of miniature heat-dissipating devices (Tuckerman and Pease, 1981). Researchers have used innovative techniques to enhance the hydrothermal performance of MCHSs.

Considerable improvements in the hydrothermal performance of heat sinks can be achieved through various modifications in geometry (Alihosseini et al., 2020). Existing literature contains numerous studies focusing on geometric modifications and optimization techniques. For instance, Zhang et al. conducted an experimental investigation on rectangular-shaped multiport microchannels with different geometric parameters, revealing a significant increase in heat transfer with the introduction of roughness at high Reynolds numbers (Re) (Zhang et al., 2014). They also highlighted the noticeable influence of entrance effects on heat transfer, particularly in laminar flow regions. Another numerical study examined the performance of MCHS with rectangular ribs and sinusoidal cavities, revealing a substantial reduction in pressure loss through the combination of ribs and cavities (Ghani et al., 2017). Moreover, it was observed that the Nusselt number (Nu) and friction factor increased as the relative width and length of the ribs increased. Salah et al. reported through their numerical study that reducing the channel spacing from 50 μm to 0.5 μm had a negligible effect on the hydrodynamic characteristics of microchannel flow (Salah et al., 2017). They also noted that increasing Re led to an increase in entrance length, pressure loss and maximum local entrance shear stress, while the local apparent friction number decreased due to the increased kinetic energy.

Shi et al. conducted an optimization study on MCHS with secondary flow to minimize thermal resistance and pumping power (Shi et al., 2019). Their findings showed that increasing the width ratio of the secondary channel to the microchannel resulted in a decrease in pumping power due to reduced fluid velocity. The pitch ratio of the secondary channel to the microchannel significantly influenced heat transfer, with an increase in heat transfer attributed to an increase in fluid velocity with higher pitch ratios. In another study, Kose et al. performed a parametric study on MCHSs with three different configurations, optimizing them using the non-dominated sorting genetic algorithm-II (Kose et al., 2022). They observed that rectangular MCHSs exhibited high heat transfer at low aspect ratios (ARs), albeit with an increase in pumping power. The optimum geometric parameters identified were an apex angle of 500 for triangle-shaped channels and a junction angle of 600 for trapezoid-shaped channels, resulting in improved thermal performance. Furthermore, rectangular microchannels required 40% and 17% less pumping power compared to triangular and trapezoidal microchannels, respectively. In addition to geometric optimization, significant research has been conducted on the working fluid of microchannels, exploring the use of various nanofluids and PCM slurries. A study by Shahsavar et al. investigated the first and second law performance of an MCHS using a water-based hybrid nanofluid containing carbon nanotube (CNT) and Fe₃O₄ nanoparticles (Shahsavar et al., 2021). The results demonstrated that the heat transfer coefficient, frictional entropy generation and pumping power increased with rising Reynolds number (Re) and the concentration of Fe₃O₄ and CNT nanoparticles. Moreover, the MCHS exhibited maximum performance and minimum entropy generation at low and high concentrations of Fe₃O₄ and CNT nanoparticles, respectively.

Yang et al. conducted a numerical investigation on MCHS using water-based CuO nanofluids, observing an increase in pressure drop within the MCHS (Yang et al., 2014). They also reported that the thermal resistance obtained from the two-phase model was more accurate than the one-phase model. In a study by Shi et al., a heat transfer analysis was performed on MCHSs using Al₂O₃-water nanofluids, revealing improved thermal characteristics with increasing nanoparticle concentration (Shi et al., 2018). Specifically, heat transfer coefficient increased by 5.86% and 8.49% with nanofluid concentrations of 1% and 2%, respectively. Sarafraz et al. conducted an experimental investigation on the hydrothermal performance of rectangular microchannels using water-based graphene nano-platelet (GNP) nanofluid flow. The results showed an 80% improvement in the Nusselt number and heat transfer coefficient (h) with a slight increase in friction factor and pressure loss (Sarafraz et al., 2019). It was also noted that the combined effect of Brownian motion and thermophoresis enhanced heat transfer at the cost of increased pressure loss.

Dai et al. examined the hydrothermal behavior of porous MCHSs with microencapsulated PCM (MEPCM) suspension, using the volume-averaging method based on the Forchheimer–Brinkman–Darcy equation (Dai et al., 2021b). Four different porosity configurations of heat sinks were studied: linearly increasing porosity (LIP), linearly decreasing porosity (LDP), stepwise increasing porosity (SIP) and stepwise decreasing porosity (SDP). It was observed that higher porosity and pore size reduced thermal resistance and improved heat sink performance. Notably, a significant reduction in thermal resistance was achieved with a higher amplitude variation of porosity in the stepwise increasing case, while the stepwise decreasing case increased thermal resistance. Ho et al. conducted an experimental examination of water-based nano-encapsulated PCM (NEPCM) suspension in parallel MCHS (Ho et al., 2020b). They used NEPCM particles with a size range of 250–350 nm, consisting of Eicosane as the core encapsulated with a formaldehyde shell. The study demonstrated a 70% increase in heat transfer and a 45% improvement in the performance index when NEPCM was used in the MCHS. However, the heat transfer improvement decreased at high Reynolds numbers due to a reduction in sensible heat and an increase in the working fluid’s viscosity with the addition of NEPCM particles.

Flow boiling has also been used in MCHSs for applications requiring high heat dissipation. Alugoju et al. conducted a 3D conjugate numerical study on diverging MCHSs using the volume of fluid (VoF) model in combination with the phase change model (Alugoju et al., 2020). The study aimed to examine the flow boiling and unsteady heat transfer behavior of diverging MCHSs. It was found that decreasing the hydraulic diameter reduced bubble nucleation time. Furthermore, at low wall contact angles, the separation rate of bubbles from the wall decreased, leading to localized hotspots. Another numerical investigation by Luo et al. focused on sub-cooled flow boiling in a manifold MCHS with different inlet and outlet width ratios (Luo et al., 2019). The study revealed the significant influence of the manifold ratio and heat flux on the thermal resistance and pressure loss of the heat sink. By varying the manifold ratio of the heat sink, a 43.3% reduction in pressure drop was achieved. The study also recommended an optimum manifold ratio of 1 to 2 for improved thermal performance.

The utilization of phase change materials (PCMs) is a popular trend in thermal management due to their ability to absorb large amounts of heat during phase change while maintaining nearly isothermal conditions. Debich et al. conducted a parametric study on PCM-based heat sinks with fins for thermal management of mechatronic components (Debich et al., 2020). The study analyzed the heat sink’s performance at various input power levels, PCM materials, heat sink geometries, and PCM volume fractions. Among the studied PCMs (salt hydrate and paraffin), n-Eicosane exhibited the highest thermal energy storage capacity. Baby and Balaji performed an experimental study on a plate fin heat sink matrix with PCM exposed to various heat loads (Baby and Balaji, 2014). They found that PCM-based heat sinks effectively functioned even under intermittent and transient heat load. Rehman et al. implemented an experimental analysis on Copper foam composite PCM-based heat sinks for electronic cooling (Rehman et al., 2018). The study investigated the charging and discharging temperature and time of the heat sink using various PCMs. It was observed that PCMs with low melting temperatures showed better performance at lower heat loads.

The literature reviewed so far emphasizes the focus of researchers on enhancing the hydrothermal performance of MCHS. These efforts involve refining the geometry and internal structure, incorporating extended surfaces, and using working fluids with superior thermos-physical properties. While conventional MCHS can dissipate a constant heat load, the heat generated by electronic components fluctuates based on operational conditions. To accommodate these fluctuations, researchers have explored energy storage methods using PCM-based passive MCHS. However, PCM-based heat sinks are effective only during the phase change process. To address this limitation, a novel of PCM-based hybrid MCHS, which combine convective heat transfer with energy storage capabilities, has been proposed in the present work. The literature suggests that there is ample opportunity for further exploration of hybrid MCHSs with PCM in the field of thermal management of electronics.

In the present simulation analysis, six novel models of hybrid MCHSs with PCM were numerically investigated using ANSYS-FLUENT. The performance of these MCHS models was compared to that of an MCHS without PCM, to identify the model which exhibiting superior thermal characteristics. The combined effect of heat flux and Reynolds number on the liquid fraction was also investigated. In addition, the impact of PCM channel shape and AR was also examined.

2. Physical model

The computational domain is depicted in Figure 1, providing a schematic diagram. In addition, Figure 2 presents a front view of the hybrid MCHS. In this configuration, water, serving as the working fluid, is circulated within the rectangular microchannels to dissipate heat from the MCHS. The area beneath the microchannels is filled with PCM. This particular heat sink is primarily designed for thermal management applications in electronics. As electronic components generate nonuniform and transient heat during operation, the inclusion of PCM in the MCHS aims to accommodate these variations. PCM has the ability to absorb a significant amount of heat during the melting phase without a substantial increase in temperature. Consequently, this feature mitigates temperature fluctuations in both the MCHS and the electronic parts attached to it.

In the current configuration, the width of the microchannel, PCM layer and MCHS is denoted by W_C, W_P and W, respectively. The height of the microchannel, PCM layer and MCHS is represented by H_C, H_P and H, respectively. The gap between adjacent microchannels is indicated as t_w, while L corresponds to the length of the MCHS. H_t denotes the gap between the PCM layer and microchannels. The web thickness at the top and bottom of the MCHS is defined as t₁ and t₂, respectively. The dimensions of the heat sink used in this study can be found in Table 1.

For the current numerical investigation, Copper is chosen as the material for the MCHS, while water is selected as the working fluid. Paraffin is used as the PCM inserted into the MCHS. The thermo-physical properties of paraffin can be found in Table 1. The heat source, representing the electronic component, is assumed to be attached to the bottom wall of the MCHS, resulting in a heat flux imposed on the base. The remaining walls of the MCHS are considered adiabatic. In this study, we examined an MCHS model without PCM and six hybrid MCHS models with PCM. These models are as follows:

• Model 1 (M1): MCHS without PCM

• Model 2 (M2): MCHS with PCM below the microchannels

• Model 3 (M3): MCHS with PCM above the microchannels

• Model 4 (M4): MCHS with internal fins integrated in PCM

• Model 5 (M5): MCHS with divided PCM below the microchannels

• Model 6 (M6): MCHS with divided PCM above the microchannels

• Model 7 (M7): MCHS with alternative PCM and microchannels

Figure 3 illustrates the six PCM-based microchannel heat sink (MCHS) models examined in the present study. The PCM in Figure 3 is indicated with green color.

3. Mathematical model

Assumptions

The following assumptions were made in the present numerical study:

• The thermo-physical properties of PCM, working fluid and substrate material were constant and independent of temperature.

• The flow of working fluid in the microchannels was assumed to be steady, incompressible and laminar.

• The effects of gravity and other forces were neglected.

• The microchannel walls were assumed to be straight and smooth.

Governing equations

The fundamental equations that govern the flow in a microchannel are continuity, momentum equations and energy equations. These are

Continuity equations: (1) $$\frac{\partial u}{\partial x}+\frac{\partial v}{\partial y}+\frac{\partial w}{\partial z}=0$$

Momentum equations: (2) $$\rho \left(u\frac{\partial u}{\partial x}+v\frac{\partial u}{\partial y}+w\frac{\partial u}{\partial z}\right)=-\frac{\partial p}{\partial x}+\mu (\frac{{\partial }^{2}u}{\partial x^2}+\frac{{\partial }^{2}u}{\partial y^2}+\frac{{\partial }^{2}u}{\partial z^2})$$ (3) $$\rho \left(u \frac{\partial v}{\partial x}+v\frac{\partial v}{\partial y}+w\frac{\partial v}{\partial z} \right)=-\frac{\partial p}{\partial y}+\mu \left( \frac{{\partial }^{2}v}{\partial x^2}+\frac{{\partial }^{2}v}{\partial y^2}+\frac{{\partial }^{2}v}{\partial z^2} \right)$$ (4) $$\rho \left(u\frac{\partial w}{\partial x}+v\frac{\partial w}{\partial y}+w\frac{\partial w}{\partial z}\right)=-\frac{\partial p}{\partial z}+\mu (\frac{{\partial }^{2}w}{\partial x^2}+\frac{{\partial }^{2}w}{\partial y^2}+\frac{{\partial }^{2}w}{\partial z^2})$$

Energy equations: (5) $$u\frac{\partial T}{\partial x}+v\frac{\partial T}{\partial y}+w\frac{\partial T}{\partial z}=\frac{1}{\alpha }(\frac{{\partial }^{2}T}{\partial x^2}+\frac{{\partial }^{2}T}{\partial y^2}+\frac{{\partial }^{2}T}{\partial z^2})$$

Heat conduction equations for solid part: (6) $$\frac{\partial }{\partial x}\left(k\frac{\partial T}{\partial x}\right)+\frac{\partial }{\partial y}\left(k\frac{\partial T}{\partial y}\right)+\frac{\partial }{\partial z}\left(k\frac{\partial T}{\partial z}\right)=0$$

Boundary conditions

For this analysis, it was considered that the heat source (components of electronics) is fastened to the MCHS base and all the other walls of the MCHS are insulated. The boundary conditions implemented for this analysis are as below:

• No slip condition at the walls of the microchannel: (7) $$\text{u\hspace{0.17em}= 0,\hspace{0.17em}v\hspace{0.17em}= 0}$$

• A uniform and constant heat flux is imposed at MCHS base: (8) $$\frac{\partial T}{\partial y}{|}_{\text{y}=0,\text{\hspace{0.17em}x}=0-\text{W}}=\frac{q}{k}$$

• All the faces of the MCHS except MCHS base are considered as insulated, so adiabatic condition applied to these walls: (9) $$\frac{\partial T}{\partial y}{|}_{\text{y}=\text{H},\text{\hspace{0.17em}x}=0-\text{W}}=0\text{at\hspace{0.17em}top\hspace{0.17em}wall}$$ (10) $$\frac{\partial T}{\partial x} {|}_{\text{y}=0-\text{H},\text{\hspace{0.17em}x}=0,\text{\hspace{0.17em}W}}=0\text{at\hspace{0.17em}side\hspace{0.17em}walls}$$

• The coupled wall boundary condition is considered at the liquid-solid interfaces.

For the working fluid, the inlet conditions are applied as follows: (11) $${\text{u\hspace{0.17em}=\hspace{0.17em}v\hspace{0.17em}=\hspace{0.17em}0\hspace{0.17em}and\hspace{0.17em}w\hspace{0.17em}=\hspace{0.17em}v}}_{\text{in}}{\text{\hspace{0.17em}T}}_{\text{f}}{\text{\hspace{0.17em}=\hspace{0.17em}T}}_{\text{in}}$$

The present numerical study considered Copper and Water as the substrate material and working fluid, respectively. The inlet temperature (Tin) for the working fluid was set at 300 K, and the inlet velocity was determined based on the Reynolds number (Re). The outlet boundary condition for the working fluid was set as pressure outlet.

Thermo-physical properties

Thermo-physical properties considered in the present analysis for the substrate (copper), working fluid (water) and the PCM (paraffin) are listed in Table 2 (Su et al., 2015; Yadav and Soni, 2017).

Definition of parameters

In this section, the parameters used to evaluate and compare the behavior of the MCHS are specified. The prime parameter for assessing the heat transfer characteristics of the MCHS is the thermal resistance. The average thermal resistance of the MCHS (R_T) is defined as follows: (12) $${\text{R}}_{\text{T}}=\frac{{\overline{T}}_b-T_{in}}{q A_b}\text{K}/\text{W}$$where,

T¯_b = average MCHS base temperature;

q = heat flux imposed at the MCHS base; and

A_b = base area of the MCHS.

For fluid flow, the inlet Reynolds number (Re) is expressed as: (13) $$Re=\frac{{\rho }_f{\text{u}}_{\text{in}}{\text{D}}_{\text{h}}}{{\mu }_f}$$where,

D_h = hydraulic diameter of the microchannel; and

u_in = inlet velocity of the working fluid.

The hydraulic diameter can be defined as: (14) $${\text{D}}_{\text{h}}=\frac{4{\text{A}}_{\text{c}}}{{\text{P}}_{\text{c}}}=\frac{2{\text{H}}_{\text{c}}{\text{W}}_{\text{c}}}{{\text{H}}_{\text{c}}+{\text{W}}_{\text{c}}}$$

The pressure loss of the microchannel flow can be calculated as: (15) $$\Delta \text{P}={\text{P}}_{\text{in}}-{\text{P}}_{\text{out}}$$where,

P_in = inlet pressure; and

P_out = outlet pressure.

The friction factor (f_z) is expressed as: (16) $$f_z=\frac{2\Delta P{D}_h}{L_z{\rho }_f{u}_{in}{}^2}$$where,

L_z = MCHS length; and

ρ_f = density of the working fluid.

The local heat transfer coefficient (h) based on the inlet working fluid temperature and the Nusselt number (Nu) are defined as: (17) $$h_z=\frac{ q_w}{T_{wz}-T_{f,in}}$$ (18) $$N{u}_z=\frac{ h_z{D}_h}{K_f}$$where,

q_w = imposed heat flux;

T_wz = local MCHS base temperature; and

k_f = thermal conductivity of the working fluid.

The average heat transfer coefficient (h_z¯) and total Nusselt number (Nu¯_z) are given by: (20) $${\overline{ h}}_z=\frac{ q_w}{{\overline{T}}_{wz}-T_{f,in}}$$ (19) $${\overline{Nu}}_z=\frac{ {\overline{h}}_z{D}_h}{K_f}$$where,

T¯_wz = average MCHS base temperature.

The thermal performance factor (TPF) is used to investigate the improvement in thermal performance of the PCM-based heat sink models compared to Model 1 (MCHS without PCM). TPF is expressed as: (21) $$\text{Thermal performance factor }\left(\text{TPF}\right)=\frac{\left(N{u}_i/N{u}_1\right)}{{\left(f_i/f_1\right)}^{1/3}}$$where,

Nu_i and f_i are the Nu and friction factor of the test model;

Nu₁ and f₁ are the Nu and friction factor of the Model 1 (base model).

The Poiseuille number (Po) is expressed as: (22) $$\text{Po}=f \text{Re}$$

For laminar fluid flows, the Poiseuille number is more significant than the friction factor because it is a pure constant and independent of the thermo-physical properties of the fluid (Damean and Regtien, 2001).

Phase change material

In the present work, porosity-enthalpy method was implemented to model the simulation in PCM-based MCHS. The heat transfer inside the PCM channel was occurred by Natural convection, which can be a suitable approach during phase change. In the PCM section, for this numerical simulation it was assumed that the change in viscosity and the volume of PCM during the process of phase change are neglected. The Boussinesq approximation is used in this work to demonstrate the influence of natural convection over the solidification process. With all these assumptions, momentum equation are written as (Farahani et al., 2021): (23) $$u\frac{\partial \left({\rho }_{eff}v\right)}{\partial x}+v\frac{\partial \left({\rho }_{eff}v\right)}{\partial y}=-\frac{\partial P}{\partial y}+\frac{\partial }{\partial x}\left[{\mu }_{eff}\left(\frac{\partial v}{\partial x}\right)\right]+\frac{\partial }{\partial y}\left[{\mu }_{eff}\left(\frac{\partial v}{\partial y}\right)\right]+{\left(\rho \beta \right)}_{eff}\left(T-T_c\right)g$$where,

T, ⍴_eff and µ_eff are the temperature, effective density and effective viscosity of the PCM respectively.

g and β are the gravitational acceleration and liquid fraction respectively.

The liquid fraction value of the PCM in the MCHS is defined as (Milyani et al., 2022; Taghilou and Khavasi, 2020): (24) $$\text{B}=\{\begin{array}{ll}0\hfill & \text{T}<{\text{T}}_{\text{s}}\hfill \\ \frac{\text{T}-{\text{T}}_{\text{S}}}{{\text{T}}_{\text{L}}-{\text{T}}_{\text{S}}}\hfill & {\text{T}}_{\text{s}}\le \text{T}\le {\text{T}}_{\text{L}}\hfill \\ 1\hfill & {\text{T}}_{\text{s}}<\text{T}\hfill \end{array}$$where, T_L and T_S are the liquidus and solidus temperatures of the PCM.

4. Numerical analysis

Numerical method

The simulation of the current problem was conducted using ANSYS-FLUENT. The velocity-pressure coupling was implemented using the SIMPLE algorithm. For the energy and momentum equations, a second-order upwind scheme was used for spatial discretization. The convergence criteria was set at 1 × 10⁻⁵ for continuity and momentum equations, and 1 × 10⁻⁶ for the energy equation. The numerical procedure is illustrated as a flow chart in Figure 4.

Grid independence study

An adaptive type of mesh with advanced global and local settings are used to discretize the problem setup. An unstructured tetrahedral mesh was used in the present work. The near-wall boundary is discretized with very fine mesh using the inflation layers by creating fine prisms adjacent to the boundary walls.

In numerical simulations, it is crucial to ensure that the solution remains independent of the grid size. The accuracy and computational efficiency of the solution are significantly affected by the grid size. To verify grid independence, a study was performed by analyzing the mean temperature of the MCHS base (heat flux wall) with increasing the number of elements. The number of elements was increase by increasing the number of divisions on each edge and increasing the number of inflation layers near the wall. The mesh structure of the MCHS is illustrated in the Figure 5(a) and (b) Figure 5(c) depicts the mesh structure at a section plane. The variation of the mean temperature of the MCHS base with the number of elements is illustrated in Figure 5(d). The solution at point 7 in Figure 5(d) (corresponding to 51,33,838 elements) was considered as the grid-independent solution. Because, at this mesh size (Point 7) the variation in the mean temperature of the MCHS base was negligible and the computational time required was relatively lower compared to points 8 and 9.

Validation of the model

The current simulation model was validated by comparing the results with literature, specifically, experimental findings from Tuckerman and Pease (Tuckerman and Pease, 1981) and simulation findings from Wong and Muezzin (2013). Table 3 lists the results obtained from the present simulation model and those available in the literature. The validation was carried out for three different sized rectangular MCHSs, which were simulated by applying various heat fluxes at different flow rates. The comparison showed good agreement between the present simulation model and existing literature, with a maximum discrepancy of 3.81% for the experimental findings and 2.35% for the numerical findings.

5. Results and discussion

This section presents and discusses the findings of the current analysis. The analysis was conducted within the Reynolds number range of 100–2,000, considering a heat flux ranging from 10 to 160 W/cm². The working fluid temperature at the inlet was set to 300 K for this analysis.

The variation of thermal resistance (R_T) of MCHS with Reynolds number (Re) and heat flux

The thermal resistance (R_T) is a crucial parameter to evaluate and analyze the performance of MCHS. Figures 6 and 7 depict the total thermal resistance of the MCHS (R_T) variation for the seven MCHS models with Re and heat flux, respectively. It is observed from both figures that MCHS Models 3, 5, 6 and 7 exhibit lower thermal resistance compared with the MCHS without PCM (Model 1), indicating an improvement in MCHS performance with the introduction of PCM. Conversely, MCHS Models 2 and 4 have higher R_T than the MCHS without PCM, indicating poor heat sink performance. These observations demonstrate that the position and shape of the PCM channel have a significant influence on heat sink performance. Introducing the PCM at the bottom position retards the heat flow from the heat source (at the heat sink bottom wall) to the working fluid flowing in the microchannels due to the lower thermal conductivity of the PCM, thus increasing the R_T of the heat sink. Therefore, the introduction of the PCM in the MCHS enhances its performance only when the PCM is positioned at the top of the MCHS.

Notably, although the PCM in MCHS Model 5 is at the bottom position, its thermal resistance is lower than the MCHS without PCM due to the shape of the PCM channel. In Model 5, the PCM channel is divided into 10 equal channels, which increases the effective heat transfer area of the PCM and improves the heat dissipation from the heat source to the working fluid. Among the seven heat sink models, Models 3 and 6 exhibit superior performance with lower thermal conductivity. About 7.3% reduction in thermal resistance of MCHS was achieved when the PCM was inserted above the microchannels.

The variation of liquid fraction with heat flux and Reynolds number (Re)

The liquid fraction signifies the amount of PCM converted from solid phase to liquid phase. Liquid fraction value calculated as per equation (22). The value of liquid fraction lies between 0 and 1, 0 indicates complete solid phase and 1 indicates complete liquid phase. The liquid fraction of the PCM-based MCHS models is a critical parameter that depends on the heat flux and the Re of the working fluid. A rise in Re leads to a reduction in the liquid fraction due to the enhanced heat dissipation by the working fluid. Conversely, the liquid fraction rises with an increase in heat flux. Figure 8 illustrates the variation of the liquid fraction with Re and heat flux for all seven MCHS models. It is observed that MCHS Models 2 and 4 exhibit high liquid fraction values at low heat flux, even at high Re. This is because the PCM (with lower thermal conductivity) in these models is positioned close to the MCHS base, leading to the retardation of the heat flow from the MCHS base to the working fluid. In contrast, the PCM in the remaining four models is positioned at topside and absorbs only the excess heat left by the working fluid, resulting in a lower liquid fraction and mostly solid PCM phase. Among these four models, MCHS Models 3 and 6 were found to have the optimal PCM positions with less thermal resistance. These findings in Figure 8 can be used to determine the optimum Re for a given heat dissipation requirement.

Variation different parameters with Reynolds number (Re)

In the present analysis, the variation of the Nusselt number (Nu), pressure drop, friction factor, Poiseuille number and heat transfer coefficient (h) with Reynolds number (Re) was studied. The analysis included all heat sink models except for Model 4, as it exhibited the lowest performance. Figure 9 depicts the curves of h for the six heat sink models. Among all the heat sink models, the heat sink without PCM (Model 1) demonstrated higher heat transfer coefficients because the heat from the source was solely dissipated by the working fluid. In PCM-based MCHS, a portion of the heat is absorbed and stored in the PCM, resulting in reduced heat dissipation by the working fluid. Consequently, PCM-based heat sinks exhibited lower heat transfer coefficients compared to heat sinks without PCM. Among all PCM-based heat sinks (Models 2–7), Model 6 exhibited the highest h values. At lower Re, the h values were nearly equal for all heat sink models, except for Model 2. As Re increased, the h values increased in all models due to the higher mass flow rate of the fluid flowing in the microchannels.

Figure 10 illustrates the trends of the Nusselt number (Nu) with Reynolds number (Re) for six heat sink models. It was observed that Nu was directly proportional to the heat transfer coefficient due to the uniform cross-section of the microchannel and constant thermal conductivity of the working fluid considered in the present analysis. As a result, the curves of Nu (Figure 10) exhibited a similar trend to the curves of h (Figure 9).

Figures 11 and 12 depict the friction factor and pressure drop variation with respect to Re, respectively. From Figure 11, it can be observed that there was no significant variation in the friction factor across all the models analyzed. This is attributed to the identical shape and surface area of the microchannels in all the MCHS models. Figure 12 demonstrates that the pressure drop variation among the models was negligible at lower Re. However, at higher Re, a noticeable difference in pressure drop was observed among the models due to variations in heat sink temperatures. The variations of temperature of MCHS models are illustrated in temperature contours in Figure 13. Specifically, heat sink Model 3 exhibited a lower pressure drop compared to the other models due to its lower heat sink temperatures.

The variation of the Poiseuille number with respect to Re is shown in Figure 14. Among the studied models, Model 3 exhibited lower Poiseuille number values at higher Re. Although there was no change in the size and shape of the microchannels across all models, the variation in Poiseuille number can be attributed to the variation in pressure drop (Figure 12).

Variation of thermal performance factor

The enhancement in thermal performance of the MCHS models through the incorporation of PCM was investigated and compared using the thermal performance factor (TPF). This improvement in performance was evaluated relative to the MCHS without PCM (Model 1). Figure 15 displays the variation of TPF with Reynolds number (Re) for six PCM-based MCHS models. TPF values greater than 1 were observed for Models 3, 5, 6 and 7, indicating an improvement in thermal performance. Model 6 exhibited the highest increase in TPF, with a maximum enhancement of 12%, attributed to its superior heat transfer characteristics. Conversely, the TPF values of Models 2 and 4 were found to be less than 1, indicating a decrement in their thermal performance.

Effect of shape and aspect ratio of PCM channel

Among the hybrid heat sink models investigated, Model 6, which featured divided PCM at the top side, demonstrated superior performance with lower thermal resistance and higher heat transfer coefficients. Building upon Model 6, an additional study was conducted to assess the influence of the shape and AR of the PCM channel. Various shapes, including Square, Trapezoidal, Triangular and Inverted Triangle, were considered for the PCM channels while maintaining the same channel volume. Figure 16 illustrates the PCM channel shapes analyzed in this study for performance comparison.

Figures 17 and 18 depict the variations of thermal resistance (R_T) and liquid fraction with Re, respectively, for four different PCM channel shapes. Among the examined shapes, the heat sink with a triangular-shaped PCM channel exhibited lower thermal resistance due to a larger effective heat transfer area exposed to the working fluid flow. Conversely, the heat sink with an alternative triangular-shaped PCM channel demonstrated higher thermal resistance as a result of smaller effective heat transfer areas within the PCM channel exposed to the working fluid flow. This observation highlights the significance of a high-volume concentration of PCM and a larger effective heat transfer area near the working fluid flow channel, which enhances the heat transfer rate. The increased heat transfer to the PCM channels correspondingly elevated the liquid fraction. Notably, the heat sink with alternative triangular-shaped PCM channels exhibited a lower liquid fraction due to reduced heat transfer to PCM and more heat dissipated by the working fluid (Figure 18). Lower liquid fraction of the PCM indicates that it can accommodate some more heat when there is a surge in the heat load. This also indicates that MCHS model with alternative triangular-shaped PCM channels has more capacity to sustain large heat loads compared with other shapes.

The performance of the MCHS Model 6 was investigated for seven different ARs of PCM channels while keeping the PCM volume constant. The impact of AR on thermal resistance and liquid fraction is presented in Figures 19 and 20, respectively. The results indicated that the effect of AR on the heat sink resistance and liquid fraction is insignificant due to the small amount of PCM used in the study. However, the impact of AR is expected to become more pronounced with an increase in heat sink size and volume of PCM incorporated.

Social and professional inference

Thermal management poses a significant challenge in the field of electronics due to the increasing heat generation in compact and high performance electronic devices, including high-speed processors. As per Moore’s law, the number of transistors in integrated circuits (ICs) doubles every two years, resulting in greater heat generation within the circuit. To meet the demands of high processing speeds, optimal IC performance, fast internet speeds, rapid data transfer and compactness, efficient and effective thermal management systems are essential. It is well established in literature that the lifespan of electronic components decreases by half for every 10°C increase in temperature. Therefore, implementing proper thermal management systems is crucial for enhancing the lifespan, performance, speed and reliability of electronic devices. The novel heat sink models developed and simulated in this analysis offer compact and highly efficient heat transfer solutions. These heat sink models are expected to address the increasing need for effective heat dissipation and provide optimal thermal management for modern electronic systems.

6. Conclusions

In this study, a numerical analysis was conducted on hybrid MCHS incorporating PCM. The computational model used in this research was validated against existing numerical and experimental models from the literature, demonstrating excellent agreement. The thermal characteristics of six hybrid MCHS models with PCM inserts were thoroughly investigated and compared to an MCHS model without PCM, using various parameters. The key findings of this study are as follows:

• The thermal performance of the MCHS was observed to enhance with insertion of PCM. Among the examined MCHS models, those with PCM positioned above the microchannels exhibited superior thermal performance with lower thermal resistance.

• About 7.3% reduction in thermal resistance was achieved when the PCM inserted above the microchannels.

• Introducing divided PCM at the top of the MCHS (Model 6) resulted in a 12% increase in the thermal performance factor.

• The Nusselt number of the MCHS with divided PCM at the top was higher compared to the other six PCM-based MCHS models.

• Among the various PCM channel shapes studied, the triangular shape demonstrated the lowest thermal resistance, while the alternative triangular shape exhibited higher thermal resistance.

• The impact of AR on thermal resistance, heat sink temperature and liquid fraction was found to be negligible.

These findings contribute to the understanding and optimization of hybrid MCHS with PCM inserts, providing valuable insights for the design and improvement of thermal management systems in electronic devices.

Along with the advantages these hybrid MCHS also have challenges for development. High pumping power requirements and expensive manufacturing methods of microfluidic devices are the main practical implications. Leakage problem is also a challenge for the development of these heat sinks.

Statements and Declarations:

Funding: The authors declare that no funds were received.

Conflict of interest: The authors declare that they have no conflict of interest.

Figure 1.

Computational domain of the analysis

Figure 2.

PCM-based MCHS in front view

Figure 3.

MCHS models with PCM at different location

Figure 4.

The numerical procedure of the present numerical work

Figure 5.

(a) and (b) mesh structure of the MCHS; (c) mesh structure at a section plane; (d) variation of mean temperature of MCHS base with number of elements

Figure 6.

Thermal resistance (R_T) of MCHS variation with Re

Figure 7.

Thermal resistance (R_T) of MCHS variation with heat flux

Figure 8.

Variation of liquid fraction with heat flux and Re

Figure 9.

Heat transfer coefficient (h) variation with Re

Figure 10.

Nusselt number (Nu) variation with Re

Figure 11.

Variation of friction factor with Re

Figure 12.

Pressure drop variation with respect to Re

Figure 14.

Poiseuille number variation with respect to Re

Figure 13.

Temperature contours of MCHS models

Figure 15.

Variation of TPF with Reynolds number (Re)

Figure 16.

Hybrid MCHSs with PCM in different-shaped channels

Figure 17.

Impact of PCM channel shape on thermal resistance

Figure 18.

Impact of PCM channel shape on liquid fraction

Figure 19.

Influence aspect ratio of PCM channel on thermal resistance

Figure 20.

Influence aspect ratio of PCM channel on liquid fraction

Table 1.

MCHS dimensions

Dimensions of the MCHS (mm)
W	5	HP	0.3 (M5 to M7)
WC	0.3		0.2 (M2 to M4)
WP	0.3 (M5 to M7)	L	10
	4.5 (M2 and M3)	b	0.1
	4.8 (M4)	t1	0.1
H	1	t2	0.1 (M3 and M5 to M7)
HC	0.3		0.2 (M2 and M4)

Source: Authors’ own work

Table 2.

Thermo-physical properties

S. No.	Property	Material
		Paraffin	Copper	Water
1	Density(kg/m3)	870 at 300 K780 at 340 K	8,978	998.2
2	Thermal conductivity(W/ m-K)	0.24 at 300 K0.22 at 340 K	387.6	0.6
3	Specific heat (CP)(j/kg-K)	2,900	381	4,182
4	Melting heat(j/Kg)	1,90,000	–	–
5	Viscosity(Kg/m-sec)	0.0057933	–	0.001003
6	Liquidus temperature	331.8 K	–	–
7	Solidus temperature	331 K	–	–

Source: Authors’ own work

Table 3.

Validation of results of present model with experimental and numerical results

Channel width ×height (μm × μm)	Heat flux (W/cm2)	Flow rate (cm3 /s)	Thermal resistance (Rt) (K/W)			Deviation (%)
			Exp. results (Tuckermanand Pease, 1981)	Num. Results (Wong andMuezzin, 2013)	Present work	With exp. results	With num.results
56 × 320	181	4.7	0.110	0.108	0.10	3.81	2.03
55 × 287	277	6.5	0.113	0.113	580.11	2.35	2.35
50 × 302	790	8.6	0.090	0.093	030.0911	1.22	2.04

Source: Authors’ own work