Three-dimensional numerical optimization of a manifold microchannel heat sink

A three-dimensional analysis procedure for the thermal performance of a manifold microchannel heat sink has been developed and applied to optimize the heat-sink design. The system of fully elliptic equations, that govern the flow and thermal fields, are solved by a SIMPLE-type finite volume method, while the optimal geometric shape is traced by a steepest descent technique. For a given pumping power, the optimal design variables that minimize the thermal resistance are obtained iteratively. The procedure is robust and the optimal state is reached within six global iterations. Comparing with the comparable traditional microchannel heat sink, the thermal resistance is reduced by more than a half while the temperature uniformity on the heated wall is improved by tenfold. The sensitivity of the thermal performance on each design variable is also examined and presented in the paper. Among various design variables, the channel width and depth are more crucial than others to the heat-sink performance. The optimal dimensions and corresponding thermal resistance have a power-law dependence on the pumping power.     

Optimum thermal performance of microchannel heat sink by adjusting channel width and height

A three-dimensional numerical model of the microchannel heat sink is presented to study the effects of heat transfer characteristics due to various channel heights and widths. Based on the theory of a fully developed flow, the pressure drop in the microchannel is derived under the requirement of the flow power for a single channel. The effects of two design variables representing the channel width and height on the thermal resistance are investigated. In addition, the constraint of the same flow cross section is carried out to find the optimum dimension. Finally, the minimum thermal resistance and optimal channel width with various flow powers and channel heights are obtained by using the simulated annealing method.     

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.     

Analysis and optimization of electrokinetic microchannel heat sink

A mixed (electroosmotic and pressure-driven) flow microchannel heat sink has been studied and optimized with the help of three-dimensional numerical analysis, surrogate methods, and the multi-objective evolutionary algorithm. Two design variables; the ratio of the microchannel width-to-depth and the ratio of fin width-to-depth of the microchannel are selected as the design variables while design points are selected through a four-level full factorial design. The single-objective optimization is performed taking overall thermal resistance as the objective function and Radial Basis Neural Network as the surrogate model while for multi-objective optimization pumping power is considered as the objective function along with the thermal resistance. It is observed that the optimum design shifted towards the lower values of the ratio of the channel width-to-depth and the higher values of the ratio of fin width-to-depth of channel with increase of the driving source. The trade-off between the two conflicting objectives has been found and discussed in detail in light of the distribution of Pareto-optimal solutions in the design space. The ratio of channel width-to-depth is found to be higher Pareto-sensitive (sensitivity along the Pareto-optimal front) than the ratio of fin width-to-depth of the channel.     

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.     

Influence of sloping baffle plates on the mass transport and performance of PEMFC

Sloping baffle plates are installed numerically in the flow channel of proton exchange membrane fuel cell (PEMFC) to promote the mass transport in the porous electrode and the fuel cell performance. The sloping angle of baffle plate on the mass transport and performance of PEMFC are investigated and optimized. The numerical results show that the sloping angle of baffle plate influences the velocity distribution, flow resistance in the flow channel, and the intensity of mass transport between the channel and porous electrode. Larger sloping angle increases the velocity in the vertical direction which brings stronger squeeze effect between the channel and porous electrode, but it also reduces the squeeze area and increases the flow resistance. An optimization for the sloping angle of baffle plate is carried out. The baffle plate with the sloping angle of 45° shows the best performance in PEMFC net power considering the pumping power caused by the pressure loss. The effect of the baffle plate number is also investigated and optimized. The fuel cell current density increases with the baffle plate number, but the increment rate is decreased. The pumping power increases almost linearly with the baffle plate number. The PEMFC with six sloping baffle plates installed in the channel is found to be optimal in terms of the net power.     

Combined local microchannel-scale CFD modeling and global chip scale network modeling for electronics cooling design

Microchannel cold plates enjoy increasing interest in liquid cooling of high-performance computing systems. Fast and reliable design tools are required to comply with the fluid mechanics and thermal specifications of such complex devices. In this paper, a methodology accounting for the local as well as the device length scales of the involved physics is introduced and applied to determine the performance of a microchannel cooler. A unit cell of the heat transfer microchannel system is modeled and implemented in conjugate CFD simulations. The fluidic and thermal characteristics of three different cold plate mesh designs are evaluated. Periodic boundary conditions and an iteration procedure are used to reach developed flow and thermal conditions. Subsequently, two network-like models are introduced to predict the overall pressure drop and thermal resistance of the device based on the results of the unit cell evaluations. Finally, the performance figures from the model predictions are compared to experimental data. We illustrate the cooling potential for different channel mesh porosities and compare it to the required pumping power. The agreement between simulations and experiments is within 2%. It was found that for a typical flow rate of 250 ml/min, the thermal resistance of the finest microchannel network examined is reduced by 7% and the heat transfer coefficient is increased by 25% compared to the coarsest channel network. On the other hand, an increase in pressure drop by 100% in the case of densest channel network was found.     

Optimization of microchannel-based cooling systems

Abstract

In this article, microchannel systems for cooling applications such as in the thermal management of electronic equipment are investigated and optimized. Numerical simulations are carried out to study the conjugate heat transfer and flow behavior. The numerical model has been validated by comparing with analytical results. Two sets of design variables are evaluated: (Set I) Incoming flow rate and the number of channels and (Set II) Incoming flow rate and heat flux input. Response surfaces are used to represent the thermal and fluid behavior in the microchannel systems. Based on the polynomial response surface (PRS) modeling results, a multi-objective optimization problem is formulated to reduce both pumping power and thermal resistance. Two major practical concerns, hot-spot temperature and pressure difference, serve as optimization constraints. With varying weights on the two conflicting objectives, Pareto frontiers are obtained. It is also shown that an optimal configuration exists under pressure and temperature constraints. This study provides a feasible design domain and optimal solutions for microchannel-based cooling systems. The optimization process can also be applied to different applications of similar thermal systems.     

Constructal optimisation of conjugate triangular cooling channels with internal heat generation

This paper presents the development of the three-dimensional flow architecture of conjugate cooling channels in forced convection with internal heat generation within a solid. Two types of cross-section channel geometries were used. The first involved equilateral triangles with three equal legs in length and all three internal angles of 60°. The second was isosceles right triangles with two legs of equal length and internal angles of 90°, 45° and 45°. Both the equilateral triangle and isosceles right triangle are special case of triangle that can easily and uniformly be packed and arranged to form a larger constructs. The configurations were optimised in such a way that the peak temperature of the heat generating solid was minimised subject to the constraint of a fixed global volume of the solid material. The cooling fluid was driven through the channels by the pressure difference across the channel. The degrees of freedom of the channels were aspect ratio, hydraulic diameter and channel to channel spacing ratio. The shape of the channel was allowed to morph to determine the best configuration that gives the lowest thermal resistance. A gradient-based optimisation algorithm was applied in order to search for the best optimal geometric configurations that improve thermal performance by minimising thermal resistance for a wide range of dimensionless pressure difference. The effects of porosities, applied pressure and heat generation rate on the optimal aspect ratio and channel to channel spacing are reported. It was found that there are unique optimal design variables for a given pressure difference. The numerical results that were obtained were in agreement with the theoretical formulation using scale analysis and method of intersection of asymptotes. Results obtained show that the effects of applied dimensionless pressure drop on minimum thermal resistance were consistent with those obtained in the open literature.     

Designing environmentally sustainable electronic cooling systems using exergo‐thermo‐volumes

Thermo‐volumes allow the design engineer to expediently understand the thermal resistance of a given cooling solution (an indicator of performance) along with its flow resistance (an indicator of the pumping power, or energy consumption, which will be required by the fluid handler). In the present work, we expand upon thermo‐volumes by including the lifetime exergy cost (in units of Joules of availability destroyed) as a means to enable the consideration of resource consumption (and thus the environmental sustainability) of the cooling solution. To achieve these exergo‐thermo‐volumes, we reinterpret previous definitions of thermo‐volumes in terms of the entropy generated during heat transfer and fluid flow. The Guoy–Stodola theorem is used to convert this entropy generation into an ‘operational’ exergy loss. Next, based on the material choice and assembly processes used in creating the product, an embedded exergy consumption that accounts for the amount of exergy destroyed during extraction, transportation and disposal of the material is attached to the operational exergy loss. Thus, the total ‘cradle‐to‐cradle’ exergy loss of the solution is devised. In this framework, the optimal solution will be that which destroys the minimal amount of exergy. Correspondingly, instead of relying upon the coefficient of performance (which is focused on operational consumption), we propose evaluation of cooling solutions in terms of the heat removal capacity per unit lifetime exergy consumption. The paper concludes by illustrating applicability of the method to the design of an enterprise server. It should be noted that although the paper is focused on electronics cooling solutions, the methodology is designed to be sufficiently general for use in any thermal management application. Copyright © 2009 John Wiley & Sons, Ltd.     

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.     

Off-highway heavy-duty truck under-hood thermal analysis

A full-size of machine-level, under-hood thermal analysis has been conducted using CFD. In particular, an iterative approach has been developed and was used to speed up the convergence of the numerical solution of the energy equation, where the large heat source term poses a computational challenge. The Reynolds Averaged Navier–Stokes (RANS) method was applied to simulate under-hood turbulent flow, while a net-radiation enclosure model was included in the energy equation. The numerical results are used to verify and validate the concept design and prototyping of off-highway heavy-duty trucks, including parameters and components such as: the speed of cooling fans; core size of the heat exchangers; temperature; pressure drop; thickness of insulation and design options of the heat shield. Another objective is to benchmark a one-dimensional lumped in-house tool for industrial cooling system concept design and analysis. The CFD method is a powerful tool that can identify possible design drawbacks, evaluate design options, improve the heat transfer efficiency and provide optimal engineering solutions and strategies for complicated heavy-duty thermal management.     

流动风阻网格模型与热仿真设计方法优化动力电池模组结构的研究

风冷系统因结构简单、成本低等特点,在热管理系统中占据重要地位。目前常规的风冷热管理设计方法存在重复性工作多、设计时间长的缺点。本文提出空气流动风阻网格模型结合热力学模型仿真的设计方法,先采用空气流动风阻网格模型获得优化的电池结构,再采用热力学模型进行仿真求解,获得优化的电池模组的流场和温度场分布特性。仿真结果验证了优化结构的准确性。优化结果表明,“C”字形结构更有利于提升模组内单体电池冷却效果的一致性,并且优化后的“C”字形结构进一步提升了电池模组内单体电池温度场的一致性。此外,计算结果发现模组内空气流动方向为上进下出时可进一步降低模组内单体电池的最高温度,提升单体电池温度场的一致性。     

Optimum design of a channel roughened by dimples to improve cooling performance

Staggered arrays of dimples imprinted on opposite surfaces of an internal flow channel have been formulated numerically to enhance turbulent heat transfer compromising with pressure drop. The channel is simulated with the help of three-dimensional Reynoldsaveraged Navier-Stokes (RANS) analysis. Three nondimensional design variables based on dimple size and channel dimensions and two objectives related to heat transfer and pressure drag have been considered for shape optimization. A weighted-sum method for multi-objective optimization is applied to integrate multiple objectives into a single objective and polynomial response surface approximation (RSA) coupling with a gradient based search algorithm has been implemented as optimization technique. By the present effort, heat transfer rate is increased much higher than pressure drop and the thermal performance also has shown improvement for the optimum design as compared to the reference one. The optimum design produces lower channel height, wider dimple spacing, and deeper dimple as compared to the reference one.     

Optimum design of a channel roughened by dimples to improve cooling performance

Staggered arrays of dimples imprinted on opposite surfaces of an internal flow channel have been formulated numerically to enhance turbulent heat transfer compromising with pressure drop. The channel is simulated with the help of three-dimensional Reynolds-averaged Navier-Stokes (RANS) analysis. Three non-dimensional design variables based on dimple size and channel dimensions and two objectives related to heat transfer and pressure drag have been considered for shape optimization. A weighted-sum method for multi-objective optimization is applied to integrate multiple objectives into a single objective and polynomial response surface approximation (RSA) coupling with a gradient based search algorithm has been implemented as optimization technique. By the present effort, heat transfer rate is increased much higher than pressure drop and the thermal performance also has shown improvement for the optimum design as compared to the reference one. The optimum design produces lower channel height, wider dimple spacing, and deeper dimple as compared to the reference one.     

A Correction Factor-Based General Thermal Resistance Formula for Heat Exchanger Design and Performance Analysis

Methods for the analysis of heat exchangers with various flow arrangements modeling, design, and performance are essential for heat transfer system modeling and its integration with other energy system models. This paper proposes the use of the linear-transfer law for the heat exchanger design and performance analysis as a function of the thermal resistance related to the ratio of a linear temperature difference to the total heat transfer rate. Additionally, we derived a correction factor that represents the influence of the flow arrangement on the heat transfer performance by the effective thermal conductance, as a function of correction factor, heat transfer coefficient, and surface area. Based on the effective thermal conductance, we propose the hot-end NTU and cold-end NTU for deriving a standardized and general thermal resistance formula for different types of heat exchangers by the combination of the correction factor with linear-transfer law. Moreover, for parallel-flow, cross-flow, and 1-2 Tubular Exchanger Manufacturers Association(TEMA) E shell-and-tube heat exchangers, we derived and obtained alternative correction factor expressions without introducing any temperatures. Two cases about heat exchanger design and performance analysis show that the calculation processes using the correction factor-based general thermal resistance are straightforward without any iteration and the calculation results are accurate. Finally, the experimental validation shows that the general thermal resistance formula is appropriate for analyzing the heat transfer performance. That is, the correction factor-based general thermal resistance formula provides a standardized model for heat exchanger analysis and heat transfer/integrated energy system modeling using the heat current method.     

Heat-conduction optimization based on constructal theory

An analysis of the “tree-like network” construct method is presented. The high effective-conduction channel distribution has been optimized, without the premise that the new-order assembly construct must be assembled by the optimized last-order construct. The “tree-like network” construct method is faultiness. A more optimal construct is obtained, and when the thermal conductivities and the proportion of the two heat-conduction materials are constants, the limit of the minimum-heat resistance is derived. These conclusions can be used as a guide for engineering applications.     

Thermal investigation of the conjugate heat transfer problem in multi-row circular minichannels

A numerical three-dimensional flow and conjugate heat transfer in circular minichannel-based multi-row heat sink is presented in this article. Effects of geometrical parameters including channel dimensions, channel arrangements (inline or staggered), and the number of channel rows with a single-pass flow on the thermal performance of the heat sink are presented. The determination of the bottom surface temperature, average heat transfer coefficient, thermal resistance as well as the pressure drop was reported. The number of rows and the diameter of the circular channel for a constant Reynolds number were found to have a remarkable cooling effect on the heat sink. It was found out that in the case of using four channel rows with the channel diameter of 1?mm, the cooling capacity is 88.5?W/cm² compared to 28?W/cm² for a single row 1?mm diameter.     

Benchmark Solution for a Three-Dimensional Mixed-Convection Flow,Part 1: Reference Solutions

A solution to a benchmark problem for a three-dimensional mixed-convection flow in a horizontal rectangular channel heated from below and cooled from above (Poiseuille-Rayleigh-Bénard flow) is proposed. This flow is a steady thermoconvective longitudinal roll flow in a large-aspect-ratio channel at moderate Reynolds and Rayleigh numbers (Re = 50, Ra = 5,000) and Prandtl number Pr = 0.7. The model is based on the Navier-Stokes equations with Boussinesq approximation. We propose reference solutions resulting from computations on large grids, Richardson extrapolation (RE), and cubic spline interpolations. The solutions obtained with one finite-difference, one finite-volume, and two finite-element codes are in good agreement, and reference values for the flow and thermal fields and for the heat and momentum fluxes are given with four to five significant digits.     

Three-dimensional multi-scale fluid distributor assembly minimizing total viscous dissipation

In this paper, a novel multi-scale transport network geometry has been addressed by means of constructal theory. The channel dimensions are given and justified with an engineering criterion into the design itself. The first stage of this work consists of assembly optimization, which is formulated as follows: find the distribution of channel radii and angle that minimizes total viscous dissipation (or pumping power, pressure drop) under the constraints of fixed total volume of channels and tube material consumed. Analytical resolutions of the problem of optimal channel size distribution for tree-like networks used as flow distributors are obtained. In the subsequent stages, a large number of flow configurations are constructed based on the optimal channel size. The resulting structure is an optimized multi-scale flow distributor. Furthermore, for such configuration, the equality of pressure drops ensuring flow rate uniformity at the outlet ports of the distributor is demonstrated theoretically. Finally, CFD simulations are employed to investigate fully developed smooth turbulent flow on different branch junctions. Numerical results are found to be in good agreement with predicted analytical results and support the relationship between the pressure drop and the liquid flow rate at the inlet port of the constructal liquid distributor.