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.     

Combined Numerical Optimization and Constructal Theory for the Design of Microchannel Heat Sinks

This study deals with the geometric optimization of a silicon based microchannel heat sink using a combined numerical optimization and constructal theory. The objective is to minimize the wall peak temperature subject to various constraints. The numerical simulations are carried out with fixed volumes ranging from 0.7 mm³ to 0.9 mm³ and pressure drop between 10 kPa to 60 kPa. The effect of pressure drop on the optimized aspect ratio, solid volume fraction, hydraulic diameter, and the minimized peak temperature are reported. Results also show that as the dimensionless pressure drop increases the maximized global thermal conductance also increases.     

Constructal Optimization of Microchannel Heat Sinks With Noncircular Cross Sections

This article reports the numerical geometric optimization of three-dimensional microchannel heat sinks with rectangular, elliptic, and isosceles triangular cross sections. The cross-sectional areas of the mentioned microchannels can change according to the degrees of freedom, that is, the aspect ratio and the solid volume fraction. Actually, the purpose of geometric optimization is to determine the optimal values of these parameters in such a way that the peak temperature of the wall is minimized. The effects of solid volume fraction and pressure drop upon the aspect ratio, hydraulic diameter, and peak temperature of the microchannels are investigated. Moreover, these microchannel heat sinks are compared with each other at their optimal conditions. Considering the constraints and geometric parameters for the optimization of the present study, it is revealed that microchannel heat sinks with rectangular and elliptic cross sections have similar performances, while microchannels with isosceles triangular cross sections show weaker performances. The optimal shapes of all three kinds of channels are achieved numerically and compared with the approximate results obtained from scale analysis, for which good agreements are observed.     

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.     

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.     

Performance of Microchannel Heat Sinks with Newtonian and Non-Newtonian Fluids

In this paper, the flow behavior and heat transfer performance of a microchannel heat sink is examined. Microchannel heat sink is a heat exchanger that is used to control the temperature of electronic devices with high heat flux capacity. A comprehensive thermal model for a microchannel should include a three-dimensional conduction analysis in the solid parts, followed by an extensive three-dimensional developing flow in the fluid region. The heat transfer analysis in the transition region of the fluid section is a crucial matter. Hydrodynamic and thermal entrance lengths are two important parameters, among others, which are studied in the solution. To examine the potential of using a non-Newtonian fluid, the power law model was used for both Newtonian and non-Newtonian fluids. The numerical solution of the problem was based on a finite difference approach using a control volume with staggered grid system. The SIMPLE algorithm was applied to the problem, and convection terms were estimated using QUICK method. A comparison of the Newtonian and non-Newtonian results showed that for shear thinning fluids, the pressure drop could reduce up to 45%, while for shear thickening fluids, it can increase up to 48%. The same comparison for the Nusselt number showed about a 160% increase with shear thinning fluids and a 43% decrease with shear thickening fluids. The thermal resistance at a Reynolds number of 50 will reduce approximately 25% with shear thinning fluids and will increase approximately 5% with shear thickening fluids. At higher values of the Reynolds number, the changes in the value of the thermal resistance are more pronounced.     

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.     

Methods for Thermal Optimization of Microchannel Heat Sinks

This article presents a quantitative analysis of the effects of sand–bentonite backfill materials on the thermal performance of borehole heat exchangers (BHEs). Laboratory thermal probe tests were conducted to measure the thermal conductivity of sand–bentonite mixtures under different mixed ratios. Based on microscopic observations, the mechanism of bentonite affecting heat conduction between the sand grains was analyzed. Then field tests were carried out to compare the thermal performance of two double U-shaped BHEs with different backfill materials. Test results showed that the thermal conductivity of sand–bentonite mixtures first increased with increasing percentage of bentonite by dry mass, then reached a peak at the range from 10% to 12%, beyond which the thermal conductivity decreased quickly. For the BHE with an optimal sand–bentonite backfill material, the heat injection and heat extraction rate were enhanced on average by 31.1% and 22.2%, respectively, compared with the case with a common sand–clay material. These results can provide helpful guide for the design of ground source heat pump systems.     

Analysis of Multilayer Mini- and Microchannel Heat Sinks in Single-Phase Flow Using One- and Two-Equation Porous Media Models

This article is devoted to an examination of the application of one- and two-equation porous media theory for modeling the thermal-fluid behavior of stacked multilayer micro- or minichannel heat sinks. The objectives of the article are to examine generalizations of the geometric scaling that is elucidated by adopting a porous media approach. This article examines the relative accuracy and computational efficiency of one- and two-equation approaches. The error between the two models and the experimental data is examined by an error map given as a function of conductivity ratios, Darcy number, and Reynolds number.     

Prediction of Heat Transfer Coefficient in Saturated Flow Boiling Heat Transfer in Parallel Rectangular Microchannel Heat Sinks: An Experimental Study

This study focuses mainly on the prediction of saturated flow boiling heat transfer in microchannels. A wide range of experiments has been carried out with de-ionized water to obtain a comprehensive data set. Experiments of mass fluxes of 51–728.7 kg/m²s, wall heat fluxes of 36–221.7 kW/m², vapor qualities of 0.01–0.69, liquid Reynolds number of 7.72–190, aspect ratios of 0.37–5.00 (with a constant hydraulic diameter of 100 µm) and hydraulic diameters of 100–250 µm (for constant aspect ratio = 1). A new correlation including the aspect ratio effect is proposed to predict the heat transfer coefficient for saturated flow boiling in microchannels. The proposed correlation shows very good predictions with an overall mean absolute error of 16.9% and 86.4%, 96.2% and 99.5% of the predicted data falling within ±30, ±40 and ±50% error bands, respectively.     

Numerical Evaluation of Flow and Heat Transfer in Plate-Pin Fin Heat Sinks with Various Pin Cross-Sections

A numerical investigation of the thermal and hydraulic performance of 20 different plate-pin fin heat sinks with various shapes of pin cross-sections (square, circular, elliptic, NACA profile, and dropform) and different ratios of pin widths to plate fin spacing (0.3, 0.4, 0.5, and 0.6) was performed. Finite volume method-based CFD software, Ansys CFX, was used as the 3-D Reynolds-averaged Navier-Stokes Solver. A k-ω based shear-stress-transport model was used to predict the turbulent flow and heat transfer through the heat sink channels. The present study provides original information about the performance of this new type of compound heat sink.     

A One-Dimensional Heat Transfer Model Analysis of Heat Sinks

A one-dimensional steady-state heat transfer model of heat sinks is proposed to determine the heat sink size needed for a given heat source. Both the temperature distribution and the maximum heat source temperature solution are presented analytically. The results are in closed form and can be conveniently used for determining the heat sink size. The two most important dimensionless parameters that describe the geometry and heat transfer characteristics of the heat sinks are defined and their influences on the maximum temperature of heat sinks are analyzed. The results show that the maximum heat source temperature decreases with the heat sink size. It is also shown that if the heat sink size is large enough then the effectiveness in reducing the maximum heat source temperature by increasing the heat sink size is significantly decreased.     

Turbulent Heat Transfer in the Entrance Region of a Tube

Correlation of the data for heat transfer between a fluid in turbulent flow and the entrance region of a tube is made for the entrance shapes normally used in heat exchangers. Equations representing the variation of the “average heat transfer” with tube length, Reynolds number, and Prandtl number are suggested.     

非圆形微通道热沉的流动换热特性数值模拟

建立了非圆形硅微通道内单相流动和换热过程的三维模型,并分别对三角形、矩形和梯形微通道中流动换热进行了数值模拟.研究发现,截面平均努塞尔数在通道入口处数值最大,然后沿流体流动方向急剧减小,直至流动充分发展时趋于恒定.固体和流体温度沿流动方向近似线性升高.换热面壁温仅沿流动方向升高,在垂直于流动方向,温度则基本保持均衡;雷诺数对微通道的流动与换热特性存在着较大的影响,雷诺数越大,其对应的努塞尔数也越大.对3种微通道的热经济性分析比较发现,三角形通道的热有效性最高.     

Numerical Study of Nanofluid Condensation Heat Transfer in a Square Microchannel

This study presents a numerical study of nanofluid condensation heat transfer inside a single horizontal smooth square tube. The numerical results are compared to previous experimental predictions, and show that the heat transfer coefficient can be improved 20% by increasing the volume fraction of Cu nanoparticles by 5% or increasing the mass flux from 80 to 110 kg/m² s. Reducing the hydraulic diameter of the microchannel from 200 to 160 µm led to an increase in average condensation heat transfer coefficient of 10%. A new correlation estimating Nusselt number for condensation of nanofluids or pure vapor is proposed. It predicts average condensation heat transfer, with good agreement with the computed values.     

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.     

Laminar Forced-Convective Heat Transfer with Varying Properties in the Entrance Region of Flat Rectangular Ducts

Numerical results for air undergoing laminar forced-convective heat transfer in the entrance region of a flat rectangular duct with uniform wall temperature are obtained for Uniform inlet velocity and temperature profiles. The coupled governing partial differential equal ions are solved in discretized form with property variations being updated through physical property relations. This enables the physical property and thermofluid solutions to converge simultaneously, resulting in a realistic solution to the governing equations. Constant-property results are also obtained, and Nusselt numbers of both the constant-and variable-property models are compared with those of other numerical computations. The results of the variable-property model are also compared with available experimental data. The variable-property results exhibit excellent correlation with the available experimental data. A sensitivity analysis is performed to determine the effects of individual property variations on local Nusselt numbers.     

Numerical Analysis of EDL Effect on Heat Transfer Characteristic of 3-D Developing Flow in a Microchannel

It has been suggested that microchannels are very effective heat transfer devices. However, the electrical double layer (EDL) effect in microchannels is suspected to be significant. In this article, two EDL models together with Navier-Stokes equations are used to compute 3-D developing microchannel flow. The Poisson-Boltzmann model (PBM) has been shown to be a promising tool in studying the EDL effect for developed microchannel flow, with acceptable accuracy and efficiency. However, it has been reported that the assumption of Boltzmann distribution in the PBM for electric ion concentration distribution is questionable in the developing flow. The Nernst-Planck model (NPM), with its two extra partial differential equations (PDEs), to predict the ion concentration distribution has been suggested to be a more appropriate model for developing microchannel flow, but more RAM and CPU are needed as compared to the PBM. The governing equations for both models are discretized for developing rectangular microchannel flows in Cartesian coordinates. An additional source term, which is related to the electric potential resulting from the EDL effect is introduced in the conventional z-axis momentum equation as a body force, thereby modifying the flow characteristics. A finite-volume scheme is used to solve the PDEs. The results predicted by both EDL models with and without EDL effects are shown. It is concluded that the differences in heat transfer performance of a microchannel predicted using the two models are insignificant. However, the performance of the microchannel is significantly affected by the EDL effect.     

Numerical Investigation of PCM Based Heat Sinks with Embedded Metal Foam/Crossed Plate Fins

Three-dimensional numerical models for phase change material based heat sinks equipped with thermal conductivity enhancers like aluminum metal foam and crossed plate fins are validated with the experimental data found in literature. For the aluminum metal foam embedded in the heat sink filled with phase change material, the porosity and the pores per inch of the metal foam were varied and natural convection currents were studied. Maintaining the volume fraction of the phase change material as a constant, the thermal performance enhancement as a result of the introduction of thermal conductivity enhancer into the heat sinks is determined.     

Analysis of the Transient Single-Phase Thermal Performance of Micro-Channel Heat Sinks

The objective of this study is to examine the transient single-phase thermal behavior of micro-channel heat sinks during startup and over a short-duration power surge, and to investigate the effects of property and geometry parameters on this behavior. The transient analysis required the solution of three-dimensional conjugate heat transfer in the heat sink. These solutions were obtained numerically using the finite control-volume method and the numerical accuracy of the results was carefully assessed. Accuracy of the numerical model was validated by comparisons with available experimental data. The behavior of heat sinks with different values for the fin width, channel width, material thickness between the top of the channels and top of the heat sink, and different sink materials was examined during startup from a uniform initial temperature with a uniform input heat flux, followed by a short-duration power surge from the steady-state condition. It is concluded that increasing the fin width or channel width increases the steady-state and maximum transient temperatures in the solid, and that increasing the material thickness between the heat-sink channels and the chip or using a material with larger density and specific heat increases the transient period and lowers the maximum transient temperature in the solid during the power surge.