Optimal thermal design of microchannel heat sinks with different geometric configurations

In this study, three-dimensional models of microchannel heat sinks (MCHSs) with different geometric configurations (such as single-layered- (SL), double-layered- (DL) or tapered-(T)-channels) are constructed by an optimization procedure. This procedure integrates a direct problem solver with a simplified conjugate-gradient method as the optimizer. The overall thermal resistance of an MCHS is the objective function to be minimized with respect to geometric parameters, such as the number of channels, channel width ratio, channel aspect ratio and tapered ratios, as the search variables. The optimal thermal resistance is found to decrease in the following order: the initial guess parallel channel (IGP channel), SL-, DL- and T-channel designs. In addition, the T-channel design has the minimum temperature difference and the most uniform temperature distribution, followed by the DL-, SL- and IGP-channel designs. Moreover, the optimal thermal resistance reduces with the pumping power for the various channel configuration designs, and the lowest thermal resistance corresponds to the T-channel design. The larger the pumping power, the larger the decrement in thermal resistance. Therefore, the optimal T-channel is the best MCHS design when considering thermal resistance and temperature distribution uniformity.     

Constructal design of forced convection cooled microchannel heat sinks and heat exchangers

Heat transfer from arrays of circular and non-circular ducts subject to finite volume and constant pressure drop constraints is examined. It is shown that the optimal duct dimension is independent of the array structure and hence represents an optimal construction element. Solutions are presented for the optimal duct dimensions and maximum heat transfer per unit volume for the parallel plate channel, rectangular channel, elliptic duct, circular duct, polygonal ducts, and triangular ducts. Approximate analytical results show that the optimal shape is the isosceles right triangle and square duct due to their ability to provide the most efficient packing in a fixed volume. Whereas a more exact analysis reveals that the parallel plate channel array is in fact the superior system. An approximate relationship is developed which is very nearly a universal solution for any duct shape in terms of the Bejan number and duct aspect ratio. Finally, validation of the relationships is provided using exact results from the open literature.     

Forced convection heat transfer in microchannel heat sinks

This paper presents an analysis of forced convection heat transfer in microchannel heat sinks for electronic system cooling. In view of the small dimensions of the microstructures, the microchannel is modeled as a fluid-saturated porous medium. Numerical solutions are obtained based on the Forchheimer–Brinkman-extended Darcy equation for the fluid flow and the two-equation model for heat transfer between the solid and fluid phases. The velocity field in the microchannel is first solved by a finite-difference scheme, and then the energy equations governing the solid and fluid phases are solved simultaneously for the temperature distributions. Also, analytical expressions for the velocity and temperature profiles are presented for a simpler flow model, i.e., the Brinkman-extended Darcy model. This work attempts to perform a systematic study on the effects of major parameters on the flow and heat transfer characteristics of forced convection in the microchannel heat sink. The governing parameters of engineering importance include the channel aspect ratio (α_s), inertial force parameter (Γ), porosity (ε), and the effective thermal conductivity ratio (k_r). The velocity profiles of the fluid in the microchannel, the temperature distributions of the solid and fluid phases, and the overall Nusselt number are illustrated for various values of the problem parameters. It is found that the fluid inertia force alters noticeably the dimensionless velocity distribution and the fluid temperature distribution, while the solid temperature distribution is almost insensitive to the fluid inertia. Moreover, the overall Nusselt number increases with increasing the values of α_s and ε, while it decreases with increasing k_r.     

Analysis of heat transfer characteristics of double-layered microchannel heat sink

Numerical analysis is performed to examine the heat transfer characteristics of a double-layered microchannel heat sink. The three-dimensional governing equations are solved by the finite volume method. The effects of substrate materials, coolants, and geometric parameters such as channel number, channel width ratio, channel aspect ratio, substrate thickness, and pumping power on the temperature distribution, pressure drop, and thermal resistance are discussed. Predictions show that the heat transfer performance of the heat sink is improved for a system with substrate materials having a higher thermal conductivity ratio. A coolant with high thermal conductivity and low dynamic viscosity also enhances the heat transfer performance. The pressure drop decreases with the channel aspect ratio and channel width ratio. Further, the thermal resistance of the microchannel heat sink can be minimized by optimizing the geometric parameters. Finally, the results show that for the same geometric dimensions, the thermal performance of the double-layered microchannel heat sink is better than that of the single-layered one, by an average of 6.3%.     

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.     

Optimum thermal design of triangular,trapezoidal and rectangular grooved microchannel heat sinks

A three-dimensional numerical simulation is conducted to investigate the effect of geometrical parameters on laminar water flow and forced convection heat transfer characteristics in grooved microchannel heat sink (GMCHS). Four geometry variables which are; the depth, tip length, pitch and orientation of the cavities are taken into account in order to optimize the aluminum heat sink design. These geometric parameters could change the cavity shape from triangular to trapezoidal and then to rectangular shape. The governing and energy equations are solved using the finite volume method (FVM). The performance of GMCHS is evaluated in terms of Nusselt number ratio, thermal/hydraulic performance (JF) and isotherm and streamlines contours. The results showed that the trapezoidal groove with groove tip length ratio of δ = 0.5, groove depth ratio β = 0.4, groove pitch ratio of ψ = 3.334, grooves orientation ratio of ζ = 0.00 and Re = 100 is the optimum thermal design for GMCHS with Nusselt number enhancement of 51.59% and friction factor improvement of 2.35%.     

Analysis of microchannel heat sinks for electronics cooling

This paper presents an analytical and numerical study on the heat transfer characteristics of forced convection across a microchannel heat sink. Two analytical approaches are used: the porous medium model and the fin approach. In the porous medium approach, the modified Darcy equation for the fluid and the two-equation model for heat transfer between the solid and fluid phases are employed. Firstly, the effects of channel aspect ratio (α_s) and effective thermal conductivity ratio (k?) on the overall Nusselt number of the heat sink are studied in detail. The predictions from the two approaches both show that the overall Nusselt number (Nu) increases as α_s is increased and decreases with increasing k?. However, the results also reveal that there exists significant difference between the two approaches for both the temperature distributions and overall Nusselt numbers, and the discrepancy becomes larger as either α_s or k? is increased. It is suggested that this discrepancy can be attributed to the indispensable assumption of uniform fluid temperature in the direction normal to the coolant flow invoked in the fin approach. The effect of porosity (ε) on the thermal performance of the microchannel is subsequently examined. It is found that whereas the porous medium model predicts the existence of an optimal porosity for the microchannel heat sink, the fin approach predicts that the heat transfer capability of the heat sink increases monotonically with the porosity. The effect of turbulent heat transfer within the microchannel is next studied, and it is found that turbulent heat transfer results in a decreased optimal porosity in comparison with that for the laminar flow. A new concept of microchannel cooling in combination with microheat pipes is proposed, and the enhancement in heat transfer due to the heat pipes is estimated. Finally, two-dimensional numerical calculations are conducted for both constant heat flux and constant wall temperature conditions to check the accuracy of analytical solutions and to examine the effect of different boundary conditions on the overall heat transfer.     

Effect of geometric configuration on the laminar flow and heat transfer in microchannel heat sinks with cavities and fins

A numerical simulation is performed to investigate the characteristics of flow and heat transfer in microchannels with cavities and fins. Nine microchannels with various shaped cavities and fins are presented and compared to the smooth microchannel. The effect of cavity and fin shapes on the flow field and temperature field is analyzed. Results show that the presence of cavity and fin can increase the heat transfer area, intensify mainstream disturbance, and induce chaotic advection, which result in obvious heat transfer enhancement. The shape of cavity or fin has a great influence on the hydrodynamic and thermal performance for such micro heat sinks. Based on the performance evaluation criterion (PEC), the overall performance of the microchannel is evaluated. The combination of cavities and fins leads to lower bottom temperature, lower net temperature gradient of fluid, and better heat transfer performance, which has the potential to meet the increased heat removal requirement.     

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.     

Heat transfer enhancement in microchannel heat sinks using nanofluids

Heat transfer enhancement in a 3-D microchannel heat sink (MCHS) using nanofluids is investigated by a numerical study. The addition of nanoparticles to the coolant fluid changes its thermophysical properties in ways that are closely related to the type of nanoparticle, base fluid, particle volume fraction, particle size, and pumping power. The calculations in this work suggest that the best heat transfer enhancement can be obtained by using a system with an Al₂O₃–water nanofluid-cooled MCHS. Moreover, using base fluids with lower dynamic viscosity (such as water) and substrate materials with high thermal conductivity enhance the thermal performance of the MCHS. The results also show that as the particle volume fraction of the nanofluid increases, the thermal resistance first decreases and then increases. The lowest thermal resistance can be obtained by properly adjusting the volume fraction and pumping power under given geometric conditions. For a moderate range of particle sizes, the MCHS yields better performance when nanofluids with smaller nanoparticles are used. Furthermore, the overall thermal resistance of the MCHS is reduced significantly by increasing the pumping power. The heat transfer performance of Al₂O₃–water and diamond–water nanofluids was 21.6% better than that of pure water. The results reported here may facilitate improvements in the thermal performance of MCHSs.     

An improved porous medium model for microchannel heat sinks

In this paper, a new porous medium model for microchannel heat sinks is presented. The substrate is taken into account in the temperature equation. Thus, an approximate boundary condition at the position of the bottom of microchannel is avoided. For hydrodynamically and thermal fully developed flow in the microchannel, an analytical solution is derived. The normalized temperatures from the present analytical solution are compared with those from three-dimensional numerical simulation and the previous porous medium model. The present model and the numerical simulation correctly reproduce the temperature distribution while the previous porous medium model cannot describe the temperature distribution in the substrate and in the region near the channel bottom. The convective thermal resistance calculated from the present model shows good agreement with that from numerical simulation without any additional modification since the substrate has been taken into account. With the increase of the channel height, the discrepancy between the numerical simulation and the porous medium model increases. Much attention should be given to the cases with high aspect ratio.     

A review of heat and fluid flow characteristics in microchannel heat sinks

Heat transfer and flow characteristic in microchannel heat sinks (MCHS) are extensively studied in the literature due to high heat transfer rate capability by increased heat transfer surface area relative to the macroscale heat sinks. However, heat transfer and fluid flow characteristics in MCHS differ from conventional ones because of the scaling effects. This review summarizes the studies that are mainly based on heat transfer and fluid flow characteristic in MCHS. There is no consistency among the published results; however, everyone agrees on that there is no new physical phenomenon in microscale that does not exist at macroscale. Only difference between them is that the effect of some physical phenomena such as viscous dissipation, axial heat conduction, entrance effect, rarefaction, and so forth, is negligibly small at macroscale, whereas it is not at microscale. The effect of these physical phenomena on the heat transfer and flow characteristics becomes significant with respect to specified conditions such as Reynolds number, Peclet number, hydraulic diameter, and heat transfer boundary conditions. Here, the literature was reviewed to document when these physical phenomena become significant and insignificant.     

Enhancement of thermal performance in double-layered microchannel heat sink with nanofluids

A three-dimensional analysis aimed at enhancing the thermal performance of a double-layered microchannel heat sink by using a nanofluid and varying the geometric parameters has been conducted. A system of fully elliptic equations that govern the flow and thermal fields are solved using the finite volume method. The analysis indicates that the dominant factors determining the thermal resistance of the channel include the type of nanofluid; particle volume fraction; geometric parameters of the channel, such as the channel number, channel width ratio, channel aspect ratio; and pumping power. The results indicate that the greatest enhancement in channel cooling can be expected when an Al₂O₃–water nanofluid is used. The thermal resistance of the channel can be minimized by properly adjusting the particle volume fraction under various pumping powers; the minimum thermal resistance depends on the geometric parameters. The study also reveals that the relationship between the thermal resistance and channel number, channel width ratio, or channel aspect ratio exhibits a decrease followed by an increase. The thermal performance of the channel can usually be improved by decreasing the channel number or channel aspect ratio, or increasing the channel width ratio. Finally, increasing the pumping power reduces the overall thermal resistance. An Al₂O₃ (1%)–water nanofluid shows an average improvement in thermal performance of 26% over that of pure water for a given pumping power. However, the design’s effectiveness declines significantly under high pumping power. In particular, the thermal resistance obtained by employing nanofluids was not necessarily lower than that of water under all pumping powers, but it can be reduced by properly adjusting the geometric parameters under optimal conditions.     

Optimization of fractal-like branching microchannel heat sinks for single-phase flows

Fractal-like branching flow networks in disk-shaped heat sinks are numerically optimized to minimize pressure drop and flow power. Optimization was performed using a direct numerical search, gradient-based optimization, and genetic algorithm. A previously validated one-dimensional pressure drop and heat transfer model, with water as the working fluid, is employed as the objective function. Geometric constraints based on fabrication limitations are considered, and the optimization methodology is compared with results from a direct numerical search and a genetic algorithm.The geometric parameters that define an optimal flow network include the length scale ratio, width scale ratio, and terminal channel width. Along with disk radius, these parameters influence the number of branch levels and number of channels attached to the inlet plenum. The geometric characteristics of the optimized flow networks are studied as a function of disk radius, applied heat flux, and maximum allowable wall temperature. A maximum inlet plenum radius, minimum interior channel spacing, and ranges of terminal channel widths and periphery channel spacing are specified geometric constraints. In general, all geometric constraints and the heat flux have a significant influence on the design of an optimal flow network. Results from a purely geometrically derived network design are shown to perform within 15% of the direct search and gradient-based optimized configurations.     

Experimental investigation for sequential triangular double-layered microchannel heat sink with nanofluids

This study examined new innovative design of aluminum rectangular and triangular double-layered microchannel heat sink (RDLMCHS) and (TDLMCHS), respectively, using Al₂O₃–H₂O and SiO₂–H₂O nanofluids. A series of experimental runs for different channel dimensions, different nanoparticles concentrations and types and several pumping powers showed excellent hydrothermal performance for DLMCHS over traditional single-layer (SLMCHS). The results showed that the sequential TDLMCHS provided a 27.4% reduction in the wall temperature comparing with RDLMCHS and has better temperature uniformity across the channel length with less than 2 °C. Sequential TDLMCHS provided 16.6% total thermal resistance lesser than the RDLMCHS at low pumping power and the given geometry parameters. Pressure drop observation showed no significant differences between the two designs. In addition, larger number of channels and smaller fin thickness referred less thermal resistance rather than only increasing the pumping power. Higher nanoparticle concentration showed better thermal stability for both nanofluids than pure water. The Al₂O₃–H₂O nanofluid (0.9 vol.%) showed best performance with the temperature difference of 1.6 °C and lowest thermal resistance of 0.13 °C/W·m².     

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.     

Three-dimensional numerical simulation of heat and fluid flow in noncircular microchannel heat sinks

A three-dimensional model of heat transfer and fluid flow in noncircular microchannel heat sinks is developed and analyzed numerically. It is found that Nusselt number has a much higher value at the inlet region, but quickly approaches the constant fully developed value. The temperature in both solid and fluid increases along the flow direction. In addition, the comparison of thermal efficiencies is conducted among triangular, rectangular and trapezoidal microchannels. The result indicates that the triangular microchannel has the highest thermal efficiency.     

Effect of substrate thickness and material on heat transfer in microchannel heat sinks

Heat and fluid flow in microchannels of size (200μm × 200 μm, 5 cm long) of different substrate thicknesses (t = 100 μm–1000 μm) and different MEMS (Microelectromechanical Systems) materials (Polyimide, Silica Glass, Quartz, Steel, Silicon, Copper) was studied to observe the effects of thermal conductivity and substrate thickness on convective heat transfer in laminar internal flows.The results of the model were first validated by the theoretical results recommended by standard forced convection problem with H1 (Constant heat flux boundary condition) condition before the results from the actual microchannel configurations were obtained. Thereafter, general Nusselt number results were obtained from the models of many microchannel configurations based on the commercial package COMSOL MULTIPHYSICS^® 3.4 and were discussed on both local and average basis.A general Nusselt number correlation for fully developed laminar flow was developed as a function of two dimensionless parameters, namely Bi, Biot number and relative conductivity k¹, to take the conduction effects of the solid substrate on heat transfer into account. It was also demonstrated when the commonly used assumption of constant heat flux boundary (H1) condition is applicable in heat and fluid flow analysis in microfluidic systems. For this, a new dimensionless parameter was employed. A value of 1.651 for this suggested dimensionless parameter (Bi^0.04k^1?0.24) corresponds to 95% of the Nusselt number associated with the constant heat flux boundary condition so that it could be set as a boundary for the applicability of constant heat flux boundary (H1) condition in microfluidic systems involving heat transfer.     

A comparative analysis of innovative microchannel heat sinks for electronic cooling

In this work, a comparative analysis of innovative microchannel heat sinks such as two-layered and multi-layered microchannel heat sinks (MCHS), or thin films within flexible complex seals and cooling augmentation using microchannels with rotatable separating plates, is presented. A compilation of the numbers of layers, main characteristics, setups, advantages and disadvantages, thermal resistance, pumping power in double-layer (DL-MCHS) and multi-layer MCHS (ML-MCHS) is presented. In addition, the thermal resistance is analyzed in order to present a comparison between the single-layer MCHS (SL-MCHS) and multi-layer microchannels. The results of comparison indicates that double-layer and multi-layer MCHS have lower thermal resistance and require smaller pumping power and they resolve the high streamwise temperature rise problem of SL-MCHS.