Constructal design and thermal analysis of microchannel heat sinks with multistage bifurcations in single-phase liquid flow

Based on constructal theory, five different cases with multistage bifurcations are designed as well as one case without bifurcations, and the corresponding laminar fluid flow and thermal performance have been investigated numerically. All laminar fluid flow and heat transfer results are obtained using computation fluid dynamics, and a uniform wall heat flux thermal boundary condition is applied all heated surfaces. The inlet velocity ranges from 0.66 m/s to 1.6 m/s with the corresponding Reynolds number ranging from 230 to 560. The pressure, velocity, temperature distributions and averaged Nusselt number are presented. The overall thermal resistances versus inlet Reynolds number or pumping power are evaluated and compared for the six microchannel heat sinks. Numerical results show that the thermal performance of the microchannel heat sink with multistage bifurcation flow is better than that of the corresponding straight microchannel heat sink. The heat sink with a long bifurcation length in the first stage (Case 1A) is superior. The usage of multistage bifurcated plates in microchannel heat sink can reduce the overall thermal resistance and make the temperature of the heated surface more uniform (Case 3). It is suggested that proper design of the multistage bifurcations could be employed to improve the overall thermal performance of microchannel heat sinks and the maximum number of stages of bifurcations is recommended to be two. The study complements and extends previous works.     

Constructal Parallel-Flow and Counterflow Microchannel Heat Sinks with Bifurcations

Based on the Constructal Theory, parallel-flow and counterflow microchannels heat sinks with bifurcations are put forward to manage the temperature nonuniformity and further reduce the temperature of microchannel heat sinks bottom plates. Several models with different lengths of bifurcations are designed, and the corresponding laminar fluid flow and heat transfer of all models have been investigated through numerical simulations. The pressure, velocity, temperature distributions, and averaged Nusselt numbers are analyzed in details, and then the overall thermal resistances and overall thermal performance are compared. The results show that the thermal performance of counterflow microchannel heat sinks is better than that of parallel-flow heat sinks for the same geometry, and bifurcation can improve the thermal performance for all cases. It is suggested that a proper design of the length of bifurcation counterflow microchannel can be employed to improve the overall thermal performance of microchannel heat sinks. The study complements and extends previous works.     

Numerical Analysis of Flow and Thermal Performance of Liquid-Cooling Microchannel Heat Sinks with Bifurcation

Single-phase liquid-cooling microchannels have received great attention to remove the gradually increased heat loads of heat sinks. Proper changes of the flow path and/or heat transfer surface can result in much better thermal performance of microchannel heat sinks. In this study, a kind of rectangular straight microchannel heat sink with bifurcation flow arrangement has been designed, and the corresponding laminar flow and heat transfer have been investigated numerically. Four different configurations are considered. The effects of the bifurcation ratio (the initial channel number over the bifurcating channel number) and length ratio (the channel length before bifurcation over the bifurcation channel length) on laminar heat transfer, pressure drop, and thermal resistance are considered and compared with those of the traditional straight microchannel heat sink without bifurcation flow. The overall thermal resistances subjected to inlet Reynolds number and pumping power are compared for the five microchannel heat sinks. Results show that the thermal performance of the microchannel heat sink with bifurcation flow is better than that of the corresponding straight microchannel heat sink. The heat sinks with larger bifurcation ratio and length ratio provide much better thermal performance. It is suggested to employ bifurcation flow path in the liquid-cooling microchannel heat sinks to improve the overall thermal performance by proper design of the bifurcation position and number of channels.     

Comparative Study of the Flow and Thermal Performance of Liquid-Cooling Parallel-Flow and Counter-Flow Double-Layer Wavy Microchannel Heat Sinks

Applications of microchannel heat sinks for dissipating heat loads have received great attention. Wavy channels are recognized to be an alternative cooling technology to enhance the heat transfer, and are successfully applied in heat exchangers. In this article, three kinds of liquid-cooling double-layer microchannel heat sinks, such as a rectangular straight microchannel heat sink, a parallel-flow wavy microchannel heat sink, and a counter-flow double-layer wavy microchannel heat sink, have been designed and the corresponding laminar flow and heat transfer have been investigated numerically. The effects of the wave amplitude and volumetric flow ratio on heat transfer, pressure drop, and thermal resistance are also observed. Results show that the counter-flow double-layer wavy microchannel heat sink is superior at a larger flow rate, and a more uniform temperature rise is achieved. For a slightly larger flow rate, the parallel flow layout shows better performance. In addition to the overall thermal resistance, other criteria for evaluation of the overall thermal performance, e.g., (Nu/Nu₀)/(f/f₀) and (Nu/Nu₀)/(f/f₀)^1/3, are applied and similar results are obtained.     

Parametric study on the combined thermal and hydraulic performance of single phase micro pin-fin heat sinks part I: Square and circle geometries

This paper is the first part of a three paper series studying the overall performance of a micro pin-fin heat sink with single phase liquid flow and different pin-fin geometries operating under and similar conditions. Two different heat sinks, one with square shaped pin-fins and the other with circular pin-fins are selected for study in this paper. The paper focuses on studying the effect of thermal resistance and pressure drop of micro heat sinks when subjected to various factors such as pitch distance in axial and transverse directions, aspect ratio of the pin-fin, hydraulic diameters of the pin-fin, and the liquid flow rate through the device. A figure of merit (FOM) involving both the thermal resistance and pressure drop across the heat sink is introduced in the paper and the performance is evaluated on the basis of this FOM. The heat sinks are subjected to uniform heat flux at the bottom of the heat sink and the characteristic study is based on constant Reynolds number of liquid flow at the entrance of the channel. Water is used as the fluid in this study. The study is conducted over the Reynolds number range of 50–500. The characteristic study is carried out with the help of simulations developed using commercially available computational fluid dynamics software CoventorWare?. The characteristic study carried out in this paper is divided into four cases. In the first case the axial pitch distance is varied between 350 μm and 650 μm by keeping the aspect ratio of the pin-fin structure constant at 0.5. For the second case the transverse pitch distance is varied between 150 μm and 300 μm and the aspect ratio is kept the same as in the first case. Third case studies the effect of varying the aspect ratio (between 0.33 and 1) of the pin-fin structures by keeping both pitches constant. Case four studies the variation in the performance of the heat sink with the change in the hydraulic diameter of the pin-fins. The study conducted in this paper reveals the importance of considering the pressure drop along with the thermal resistance in evaluating the overall performance of the micro pin-fin heat sink. At low Reynolds number (below 300) the heat sinks with circular pin-fins shows better performance compared with heat sinks with square pin-fins and vice versa at high Reynolds number (above 300). FOM varies considerably with the change in the parameters like axial pitch distance, transverse pitch distance, aspect ratio and hydraulic diameter of the pin-fins.     

Numerical study of the inlet/outlet arrangement effect on microchannel heat sink performance

In this study, fluid flow and heat transfer in microchannel heat sinks are numerically investigated. The three-dimensional governing equations for both fluid flow and heat transfer are solved using the finite-volume scheme. The computational domain is taken as the entire heat sink including the inlet/outlet ports, inlet/outlet plenums, and microchannels. The particular focus of this study is the inlet/outlet arrangement effects on the fluid flow and heat transfer inside the heat sinks.The microchannel heat sinks with various inlet/outlet arrangements are investigated in this study. All of the geometric dimensions of these heat sinks are the same except the inlet/outlet locations. Because of the difference in inlet/outlet arrangements, the resultant flow fields and temperature distributions inside these heat sinks are also different under a given pressure drop across the heat sink. Using the averaged velocities and fluid temperatures in each channel to quantify the fluid flow and temperature maldistributions, it is found that better uniformities in velocity and temperature can be found in the heat sinks having coolant supply and collection vertically via inlet/outlet ports opened on the heat sink cover plate. Using the thermal resistance, overall heat transfer coefficient and pressure drop coefficient to quantify the heat sink performance, it is also found these heat sinks have better performance among the heat sinks studied. Based on the results from this study, it is suggested that better heat sink performance can be achieved when the coolant is supplied and collected vertically.     

Conjugate heat transfer in fractal-shaped microchannel network heat sink for integrated microelectronic cooling application

The hydrodynamic and thermal characteristics of fractal-shaped microchannel network heat sinks are investigated numerically by solving three-dimensional N–S equations and energy equation, taking into consideration the conjugate heat transfer in microchannel walls. It is found that due to the structural limitation of right-angled fractal-shaped microchannel network, hotspots may appear on the bottom wall of the heat sink where the microchannels are sparsely distributed. With slight modifications in the fractal-shaped structure of microchannels network, great improvements on hydrodynamic and thermal performance of heat sink can be achieved. A comparison of the performance of modified fractal-shaped microchannel network heat sink with parallel microchannels heat sink is also conducted numerically based on the same heat sink dimensions. It is found that the modified fractal-shaped microchannel network is much better in terms of thermal resistance and temperature uniformity under the conditions of the same pressure drop or pumping power. Therefore, the modified fractal-shaped microchannel network heat sink appears promising to be used for microelectronic cooling in the future.     

Modeling of double-layer triangular microchannel heat sink based on thermal resistance network and multivariate structural optimization using firefly algorithm

Abstract

The micro-channel heat dissipation system has minor specifications and good thermal conductivity per unit, which is the best choice for heat dissipation of micro-chips. By optimizing the cross section of microchannel, the heat exchange efficiency and temperature uniformity can be effectively improved. In this article, a double-layer triangular microchannel heat sink is proposed, which uniquely combines triangular cross section and double-layer structure to obtain a better heat dissipation performance. A new thermal resistance network model is established. At the same time, the model of pressure drop in microchannel heat sink is obtained by use of fluid theory. Taking thermal resistance and pressure drop as optimization objectives, the thermal resistance of double-layer triangular microchannel heat sink is 0.284?K/W and the pressure drop is 1386.89?Pa by using the firefly algorithm based on the Pareto optimal solution set, obtaining the optimal structural parameters. The thermal-flow-solid coupling simulation analysis shows that the thermal resistance and theoretical analysis error is 5.19%, and the pressure drop and theoretical analysis error is 9.49%, which can verify the accuracy of the thermal resistance network model. This article has a guiding significance for the thermal resistance analysis and heat dissipation improvement of non-rectangular cross section microchannel heat sinks.     

Optimization of Microchannel Heat Sinks Using Genetic Algorithm

In this study, a genetic algorithm is employed to minimize the entropy generation rate in microchannel heat sinks. The entropy generation rate allows the combined effects of thermal performance and pressure drop to be assessed simultaneously as the heat sink interacts with the surrounding flow field. Previously developed models for the heat transfer, pressure drop and entropy generation rate are used in the optimization procedure. The results of optimization are compared with existing results obtained by the Newton–Raphson method. It is observed that the GA gives better overall performance of the microchannel heat sinks.     

Thermal performance of plate-fin vapor chamber heat sinks

Since vapor chambers exhibit excellent thermal performance, they are suited to use as bases of heat sinks. This work experimentally studies the thermal performance of plate-fin vapor chamber heat sinks using infrared thermography. The effects of the width, height and number of fins and of the Reynolds number on the thermal performance are considered. Experimental data are compared with corresponding data for conventional aluminum heat sinks. The results show that generated heat is transferred more uniformly to the base plate by a vapor chamber heat sink than by a similar aluminum heat sink. Therefore, the maximum temperature is effectively reduced. The overall thermal resistance of the vapor chamber heat sink declines as the Reynolds number increases, but the strength of the effect falls. The effect of the fin dimensions on the thermal performance is stronger at a lower Reynolds number. At a low Reynolds number, a suitable number of fins must be chosen to ensure favorable thermal performance of the vapor chamber heat sink. However, at a high Reynolds number, the thermal performance improves as the fin number increases.     

Averaging approach for microchannel heat sinks subject to the uniform wall temperature condition

The present paper is devoted to modeling methods for thermal analysis of microchannel heat sinks. The averaging approach presented in earlier works for the case of constant surface heat flux is extended to the problems subject to the uniform wall temperature condition. The solutions for velocity and temperature distributions are obtained by solving one-dimensional averaged governing equations without resorting to a two-dimensional direct numerical simulation. General solutions for both high-aspect-ratio and low-aspect-ratio microchannel heat sinks are presented. Asymptotic solutions in high-aspect-ratio and low-aspect-ratio limits are also given in explicit form. The solutions presented in the paper are validated by comparing them with the results of direct numerical simulation. The friction factors, Nusselt numbers and thermal resistances for microchannel heat sinks with a uniform base temperature are obtained from the presented solutions. The effects of the aspect ratio and the porosity on the friction factor and the Nusselt number are presented. Finally, characteristics of the thermal resistance of the microchannel heat sink are discussed.     

Hotspot Analysis of Double-Layer Microchannel Heat Sinks

ABSTRACT

The performance of double-layer microchannel heat sinks are evaluated comparatively for the parallel flow, counter flow, and transverse flow configurations with and without hotspots as heating condition. Conjugate heat transfer analysis is performed by solving three-dimensional Navier–Stokes and energy equations using a finite volume solver. The flow is considered to be steady, incompressible, and laminar. Functional relations between the thermophysical properties of water and temperature are developed and used for numerical calculations with variable fluid properties. The thermal resistances, maximum temperature increase at the hotspots, temperature variation among the hotspots, and pressure drops are evaluated for the three heat-sink designs with two hotspot schemes (single hotspot at the center of the heat sink and multiple hotspots distributed uniformly at six peripheral locations). For the single-hotspot case, the parallel flow heat sink exhibited the lowest thermal resistance and temperature rise at the hotspot. For all the six multiple hotspot cases, the transverse flow heat sink exhibited the lowest thermal resistance and temperature variation among the hotspots.     

The characteristics of convective heat transfer in microchannel heat sinks using Al2O3 and TiO2 nanofluids

The present study aims to provide an overall analysis about nanofluids flowing through microchannel heat sinks. Al₂O₃ and TiO₂ nanofluids based on deionized water with particle volume fractions of 0%, 0.1%, 0.5%, 1.0% were prepared by the two-step dispersion method. Nonionic surfactant polyvinylpyrrolidone (PVP) was added into the nanofluids to avoid particle aggregation and enhance stability. An ImageIR 3350 was used to get the temperature distribution on the substrate of microchannel heat sinks. The results reveal that the thermal conductivity and dynamic viscosity of Al₂O₃ and TiO₂ nanofluids are both improved with the increase of particle volume fraction. Compared with a rectangular microchannel heat sink, the performance of heat transfer in fan-shaped microchannel heat sink is more strengthened using Al₂O₃ nanofluids. The thermal motion of nanoparticles could promote the interruption of laminar flow and intensify the heat transfer between fluids and channel walls. The cyclical change with a fixed period on equivalent diameter could also help destroy the boundary layers.     

Modulating fluid rheology and confinement toward augmenting the performance of a double layered microchannel heat sink

The improvement of the cooling performance of liquid-cooled microchannel heat sinks used for densely packed electronic circuits is sorted via passive techniques like tuning substrate or coolant properties. We propose a design for enhancing heat sink performance by simulataneously modifying the channel geometry and tuning the fluid rheology. By modeling the coolant as a power law fluid, its rheological behavior is varied ranging from shear-thinning to shear-thickening, alongside Newtonian fluid. We introduced tapering to the middle wall that separates the bottom and top channels of a double layered microchannel heat sink (DL-MCHS), causing both channels to converge. This convergence not only increases the flow velocity within the downstream microchannel but also reduces the apparent viscosity of the shear-thinning fluid being subjected to shear, resulting in enhanced thermal and hydraulic performance. We analyze the results from both the first and the second law of thermodynamics context, demonstrating that a tapered DL-MCHS with shear-thinning fluid outperforms a straight partition wall DL-MCHS with Newtonian coolant. However, we also discovered that extreme tapering compromises thermodynamic viability, but by fine-tuning the extent of tapering, we inferred that a DL-MCHS with shear-thinning fluid can become viable with little compromise in the thermal performance.     

Effects of fin shapes on heat transfer in microchannel heat sinks

In the present study, compact water cooling of high‐density, high‐speed, very‐large‐scale integrated (VLSI) circuits with the help of microchannel heat exchangers were investigated analytically. This study also presents the result of mathematical analysis based on the modified Bessel function of laminar fluid flow and heat transfer through combined conduction and convection in a microchannel heat sink with triangular extensions. The main purpose of this paper is to find the dimensions of a heat sink that give the least thermal resistance between the fluid and the heat sink, and the results are compared with that of rectangular fins. It is seen that the triangular heat sink requires less substrate material as compared to rectangular fins, and the heat transfer rate per unit volume has been almost doubled by using triangular heat sinks. It is also found that the effectiveness of the triangular fin is higher than that of the rectangular fin. Therefore, the triangular heat sink has the ability to dissipate large amounts of heat with relatively less temperature rise for the same fin volume. Alternatively, triangular heat sinks may thus be more cost effective to use for cooling ultra‐high speed VLSI circuits than rectangular heat sinks.     

A numerical model for heat sinks with phase change materials and thermal conductivity enhancers

The effectiveness of thermal conductivity enhancers (TCEs) in improving the overall thermal conductance of phase change materials (PCMs) used in cooling of electronics is investigated numerically. With respect to the distribution of TCE and PCM materials, the heat sink designs are classified into two types. The first type of heat sink has the PCM distributed uniformly in a porous TCE matrix, and the second kind has PCM with fins made of TCE material. A transient finite volume method is used to model the heat transfer; phase change and fluid flow in both cases. A generalized enthalpy based formulation and numerical model are used for simulating phase change processes in the two cases. The performance of heat sinks with various volume fractions of TCE for different configurations is studied with respect to the variation of heat source (or chip) temperature with time; melt fraction and dimensionless temperature difference within the PCM. Results illustrate significant effect of the thermal conductivity enhancer on the performance of heat sinks.     

Cooling performance of a microchannel heat sink with nanofluids

In this paper, the cooling performance of a microchannel heat sink with nanoparticle–fluid suspensions (“nanofluids”) is numerically investigated. By using a theoretical model of thermal conductivity of nanofluids that accounts for the fundamental role of Brownian motion, we investigate the temperature contours and thermal resistance of a microchannel heat sink with nanofluids such as 6 nm copper-in-water and 2 nm diamond-in-water. The results show that the cooling performance of a microchannel heat sink with water-based nanofluids containing diamond (1 vol.%, 2 nm) at the fixed pumping power of 2.25 W is enhanced by about 10% compared with that of a microchannel heat sink with water. Nanofluids reduce both the thermal resistance and the temperature difference between the heated microchannel wall and the coolant. Finally, the potential of deploying a combined microchannel heat sink with nanofluids as the next generation cooling devices for removing ultra-high heat flux is shown.     

Numerical simulation of fluid flow and heat transfer in a microchannel heat sink with offset fan-shaped reentrant cavities in sidewall

The paper is focused on the investigation of fluid flow and heat transfer characteristics in a microchannel heat sink with offset fan-shaped reentrant cavities in sidewall. In contrast to the new microchannel heat sink, the corresponding conventional rectangular microchannel heat sink is chosen. The computational fluid dynamics is used to simulate the flow and heat transfer in the heat sinks. The steady, laminar flow and heat transfer equations are solved in a finite-volume method. The SIMPLEX method is used for the computations. The effects of flow rate and heat flux on pressure drop and heat transfer are presented. The results indicate that the microchannel heat sink with offset fan-shaped reentrant cavities in sidewall improved heat transfer performance with an acceptable pressure drop. The fluid flow and heat transfer mechanism of the new microchannel heat sink can attribute to the interaction of the increased heat transfer surface area, the redeveloping of the hydraulic and thermal boundary layers, the jet and throttling effects and the slipping over the reentrant cavities. The increased heat transfer surface area and the periodic thermal developing flow are responsible for the significant heat transfer enhancement. The jet and throttling effects enhance heat transfer, simultaneously increasing pressure drop. The slipping over the reentrant cavities reduces pressure drop, but drastically decreases heat transfer.     

Minimizing the entropy generation rate of the plate-finned heat sinks using computational fluid dynamics and combined optimization

The multi-parameter constrained optimization procedure integrating the design of experiments (DOE), response surface models (RSM), genetic algorithm (GA), mixed integer optimization (MOST), and computational fluid dynamics (CFD) is proposed to design the plate finned heat sinks by minimizing their rates of entropy generation. The results of three cases demonstrate that the combination optimization algorithm is feasible. In these cases, the overall rate of entropy generation decreases as the result of introducing the additional constrained variables into the optimization procedure. Consequently, the general thermal and fluid performance of the heat sink is dramatically improved.Based on the results derived by the optimization, the overall thermal and fluid performance of the plate finned heat sinks with both side and top bypass flow is investigated. In addition, two correlations describing Nusselt number and friction factor, as the functions of geometrical and operational parameters, are established by means of the multivariate non-linear regression analysis. The specific expressions to compute the thermal resistance and the rate of entropy generation are deduced.     

Optimum thermal design of microchannel heat sinks by the simulated annealing method

By adopting the simulated annealing method, a three-dimensional numerical simulation is executed to minimize the thermal resistance of the microchannel heat sink corresponding to the optimum specification under the fixed flow power. The depths of the microchannel heat sink in this study are fixed at either 1 cm or 2 cm. Based on the theory of the fully developed flow, the pressure drop between the inlet and exit in each single channel can be analytically derived if the flow power and the associated specification of the microchannel heat sink are fixed in advance. Then, this pressure drop will be used as the input condition to calculate the temperature distribution of the microchannel heat sink. For the first part of the optimum analysis, the fin width, and channel width are chosen as the design variables to find their optimum sizes. As to the second part of the present analysis, three design variables including channel height, fin width and channel width are individually prescribed as a suitable range to search for their optimum geometric configuration when the other specifications of the microchannel heat sink are fixed as 24 different cases.