Enhanced multi-objective optimization of a microchannel heat sink through evolutionary algorithm coupled with multiple surrogate models

A liquid flow microchannel heat sink has been optimized with the help of three-dimensional numerical analysis and multiple surrogate methods. Two objective functions, thermal resistance and pumping power have been selected to assess the performance of the microchannel heat sink. The design variables related to the width of the microchannel at the top and bottom, depth of the microchannel, and width of fin, which contribute to objective functions, have been identified and a three-level full factorial design was selected to exploit the design space. The numerical solutions obtained at these design points were utilized to construct surrogate models, namely Response Surface Approximations, Kriging and Radial Basis Neural Network. A hybrid multi-objective evolutionary algorithm coupled with surrogate models is applied to find out global Pareto-optimal solutions. The accuracy of the surrogate models has been discussed in view of their predictions and trade-off analysis was performed in view of conflicting nature of the two objectives. The Pareto-optimal sensitivity of the design variables has been found out to economically compromise with the design variables. The application of the multiple surrogate methods not only improves quality of multi-objective optimization but also gives the feedback of the fidelity of the optimization model.     

Numerical simulation and multiobjective optimization of a microchannel heat sink with arc-shaped grooves and ribs

ABSTRACT

In order to obtain the optimal structure size of a microchannel heat sink (MCHS) with arc-shaped grooves and ribs according to the actual demand, multiple parameters that influence the performance of the microchannel are analyzed by combining the multi-objective evolutionary algorithm (MOEA) with computational fluid dynamics (CFD). The design variables include the relative groove height, relative rib height and relative rib width, and the two objective functions are to minimize the total thermal resistance and pumping power in constant volume flow rate. The influences of the design variables on the two objective functions are analyzed by CFD firstly. The results show that each design variable has a different impact on the two functions. The competitive relationship between the two objective functions is depicted in plots of the Pareto front obtained by MOEA. Pareto sensitivity analysis is carried out to find that the relative rib height has the most significant impact on the two objective functions.     

Performance Analysis and Design Optimization of Gapped Pin-Fin in a Cooling Channel

Performance analysis and optimization of a circular pin-fin with inside gaps in a rectangular cooling channel were performed at Reynolds number, 10,000, using three-dimensional Reynolds-averaged Navier–Stokes equations and a multi-objective genetic algorithm. The low-Reynolds-number version of the shear stress transport model was used as turbulence closure. A parametric study was also performed to identify the geometrical effects of the pin-fin on heat transfer and pressure drop. The straight and reference gapped pin-fins yielded better performances than those of the circular pin-fin without the gap in terms of both heat transfer and pressure drop. The objective of the optimization was to maximize the heat transfer and minimize the pressure loss, simultaneously. The area-averaged Nusselt number and pressure loss coefficient were considered as objective functions, and three design variables related to the geometry of the gapped pin-fin were chosen for the optimization. Twenty-seven design points were generated using Latin hypercube sampling in the design space, and response surface approximation models were constructed for the objective functions. The optimization results were analyzed using five representative solutions on the Pareto-optimal front. The objective functions were found to be significantly affected by variation in the design variables, especially, the width of front gap and the rear gap angle.     

Numerical Optimization for Nanofluid Flow in Microchannels Using Entropy Generation Minimization

This study presents the numerical simulation of the three-dimensional incompressible steady and laminar fluid flow of a trapezoidal microchannel heat sink using nanofluids as a cooling fluid. Navier–Stokes equations with a conjugate energy equation are discretized by the finite-volume method. Numerical computations are performed for inlet velocity (W _in = 4 m/s, 6 m/s, and 10 m/s), hydraulic diameter D _h  = 106.66 μm, and heat flux (q″ = 200 kW/m². Numerical optimization is demonstrated as a trapezoidal microchannel heat sink design which uses the combination of a full factorial design and the genetic algorithm method. Three optimal design variables represent the ratio of upper width and lower width of the microchannel (1.2 ≤ α ≤ 3.6), the ratio of the height of the microchannel to the difference between the upper and lower width of the microchannel (0.5 ≤ β ≤ 1.866), and the volume fraction (0 ≤ φ ≤ 4%). The dimensionless entropy generation rate of a trapezoidal microchannel is minimized for fixed heat flux and inlet velocity. Numerical results for the system dimensionless entropy generation rate show that the system dimensionless friction entropy generation rate increases with Reynolds number; on the contrary, the higher the Reynolds number, the lower the system dimensionless thermal entropy generation rate. The results below show that the two-phase model gives higher enhancement than the single-phase model assuming a steadily developing laminar flow.     

Shape optimization of three-dimensional channel roughened by angled ribs with RANS analysis of turbulent heat transfer

A numerical procedure for optimizing the shape of three-dimensional channel with angled ribs extruded on both walls is presented to enhance turbulent heat transfer. The response surface based optimization is used as an optimization technique with Reynolds-averaged Navier–Stokes analysis of fluid flow and heat transfer. Shear stress transport (SST) turbulence model is used as a turbulence closure. Computational results for heat transfer rate show good agreements with experimental data. Four dimensionless variables such as, rib pitch-to-rib height ratio, rib height-to-channel height ratio, streamwise rib distance on opposite wall to rib height ratio, and the attack angle of the rib are chosen as design variables. The objective function is defined as a linear combination of heat transfer and friction loss related terms with a weighting factor. D-optimal method is used to determine the training points as a mean of design of experiment. Sensitivity of the objective function to each design variable has been evaluated. And, optimal values of the design variables have been obtained in a range of the weighting factor.     

NUMERICAL SHAPE OPTIMIZATION FOR HIGH PERFORMANCE OF A HEAT SINK WITH PIN-FINS

The design optimization of a 7 × 7 pin-fin heat sink is performed numerically. To achieve higher thermal performance of the heat sink, the thermal resistance at the junction of the chip and the heat sink and the overall pressure drop in the heat sink have to be minimized simultaneously. The fin height (h), fin width (w), and fan-to-heat sink distance (c) are chosen as the design variables, and the pressure drop (ΔP) and thermal resistance (θ _ja ) are adopted as the objective functions. To obtain the optimum design values, we used the finite-volume method for calculating the objective functions, the Broydon-Fletcher-Goldfarb-Shanno method for solving the unconstrained nonlinear optimization problem, and the weighting method for predicting the multiobjective problem. The results show that the optimum design variables for the weighting coefficient of 0.5 are as follows: w = 4.653 mm, h = 59.215 mm, and c = 2.669 mm. The objective functions corresponding to the optimal design are calculated as ΔP = 6.82 Pa and θ _ja  = 0.56 K/W. The Pareto solutions are also presented for various weighting coefficients, and they offer very useful data for designing a pin-fin heat sink.     

Torque and efficiency maximization for a wave energy harvesting turbine: an approach to modify multiple design variables

Multiple design variables modifications are carried out for a bidirectional flow turbine used in an oscillating water column wave energy converter to enhance its performance by maximizing the peak torque‐coefficient (TC) and the corresponding efficiency (EFF), which are the objective functions of this problem. The Latin hypercube sampling technique selects samples from a designed space created by the design parameters defined for the blade sweep and aerofoil profile thickness modifications. The objective function values are obtained by solving Reynolds‐averaged Navier–Stokes equations and are approximated by surrogate models. The models help in generating populations of the genetic algorithm, which finally produces a set of optimal designs in a Pareto optimal front. Only two extreme designs among the five clustered points are further evaluated by solving Reynolds‐averaged Navier–Stokes equations to cross‐check the validity of the optimization steps. It is found that the TC is increased by 33% and the EFF is decreased by 5% at one extreme cluster point, while the other extreme point gives that both the TC and the EFF are higher by 1.8% and 2.9%, respectively, as compared with the reference geometry. The optimal geometry has a wider operating range, which is an important parameter to get continuous power from a wave energy converter. Copyright © 2016 John Wiley & Sons, Ltd.     

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.     

Shape Optimization of a Dimpled Channel to Enhance Heat Transfer Using a Weighted-Average Surrogate Model

Shape optimization of a rectangular channel with the opposite walls roughened by staggered arrays of dimples has been performed not only to enhance turbulent heat transfer but also to reduce friction loss. The dimpled channel shape is defined by three geometric design variables, and the design points within design space are selected using Latin hypercube sampling. The shape of the channel is optimized with three-dimensional (3-D) Reynolds-averaged Navier–Stokes analysis and surrogate approximation methods. A weighted-sum method for multi-objective optimization is applied to integrate multiple objectives related to heat transfer and friction loss into a single objective. A weighted-average surrogate model is employed for this optimization. By the optimization, the objective function value is improved largely and heat transfer rate is increased much higher than pressure loss increase due to shape deformation. The optimum design results in lower channel height, wider dimple spacing, and deeper dimple. The flow mechanism shows the heat transfer rate is increased mainly in the rear portion of the dimple.     

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.     

Multi-objective optimization design of condenser in an organic Rankine cycle for low grade waste heat recovery using evolutionary algorithm

The optimum design of a condenser is significant in an organic Rankine cycle to achieve higher waste heat utilization efficiency. Based on the mathematical model of a condenser using plate heat exchanger (PHE), some key geometric parameters on the total heat transfer surface area and pressure drop of the condenser are examined. In order to obtain geometric parameters of a plate heat exchanger, a multi-objective optimization of the condenser in organic Rankine cycle is conducted to achieve the optimal geometry design. The total heat transfer surface area and pressure drop are selected as two objective functions to minimize both total heat transfer surface area and pressure drop under the constant heat transfer rate and LMTD conditions. The plate width, plate length and plant distance are selected as the decision variables. Non-dominated sorting generic algorithm-II (NSGA-II) which is an effective multi-objective optimization method is employed to solve this multi-objective optimization design of PHE. The results show that an increase in channel distance or plate width increases the total heat transfer surface area and decreases pressure drop in the condenser. It is noted that the plate length of PHE has a positive effect on the optimization design of PHE. By multi-objective optimization design of the PHE, a Pareto optimal point curve is obtained, which shows that a decrease in total heat transfer surface area of a condenser can increase the pressure drop through the condenser.     

Shape Optimization of a Dimpled Channel to Enhance Turbulent Heat Transfer

ABSTRACT

Numerical optimization of a dimpled channel has been carried out to enhance the turbulent heat transfer. The response surface-based optimization is used as an optimization technique with three-dimensional Reynolds-averaged Navier–Stokes analysis. Computational results for heat transfer rate show good agreement with the experimental data. The objective function is defined as a linear combination of heat transfer- and friction loss-related terms with a weighting factor. Twenty-seven training points obtained by full factorial designs for three design variables construct a reliable response surface. In the sensitivity analysis, it is found that the objective function is most sensitive to the ratio of dimple depth to dimple print diameter. Optimal values of the design variables have been obtained in a range of the weighting factor.     

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.     

Objective function proposed for optimization of convective heat transfer devices

In this work, a general method using exergy analysis has been proposed to achieve a compromise between heat transfer effectiveness and pressure loss in heat transfer optimization problems involving internal channels. The proposed method is applied to the design optimization of a channel roughened by staggered arrays of dimples for heat transfer augmentation. Optimization is performed using surrogate-based optimization techniques and three-dimensional Reynolds-averaged Navier–Stokes analysis. Three nondimensional design variables are defined using the dimpled channel height, dimple print diameter, dimple spacing, and dimple depth. The objective function is defined as the net exergy gain considering the exergy gain by heat transfer, and exergy losses generated by friction and heat transfer. Twenty design points are generated using Latin hypercube sampling, and the Kriging model is used as a surrogate model to approximate the objective function values in the design space. Through optimization, the objective function is successfully improved with respect to the reference geometry.     

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.     

Optimal thermal operation of liquid-cooled electronic chips

A novel framework is developed to determine the optimal operating conditions of water cooled microprocessor chips through a tradeoff between heat recovery from the coolant and the chip thermal reliability. For illustration, a manifold microchannel heat sink is evaluated experimentally and computationally. First, a single objective optimization is demonstrated by combining the heat recovery and chip reliability into a single parameter. Then, multi-objective optimizations are performed by using Pareto optimality and Multi-Criteria Design Analysis. Using conservative guidelines, these approaches suggest that for an optimal coolant flow rate of 1 l/m, optimal coolant inlet temperature lies between 40 and 50 °C.     

Optimization of heat pipe with axial “Ω”-shaped micro grooves based on a niched Pareto genetic algorithm (NPGA)

A niched Pareto genetic algorithm based approach is utilized to optimize a heat pipe with axial “Ω”-shaped micro grooves. The effects of the structural parameters are evaluated and optimized with respect to the heat transfer performance in order to model the heat transfer capability and total thermal resistance of this novel heat pipe. Using the heat transfer capability and total thermal resistance as the objective function and the structure parameters as the decision variable, the optimization design for the heat pipe is performed using the niche genetic algorithm. The results indicate that the heat transfer capability and the total heat resistance are inversely coupled and as a result, the optimization must be constructed on the application objective. Using the niched Pareto genetic algorithm and the pre-specified application constraints, a Pareto-optimal solution set can be determined and the optimal design for a given application is selected.     

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.     

基于复合进化算法和Navier-Stokes方程求解技术的透平叶栅气动优化设计

提出了基于复合进化算法和Navier-Stokes方程求解技术的透平叶栅气动设计方法。复合遗传算法是结合进化算法与单纯形法,通过对群体中的最差个体采用单纯形法进行改造,提高进化遗传算法的搜索效率。透平叶栅的气动优化设计目标是总压损失最小。总压损失的计算采用Reynolds平均Nayier-Stokes方程求解技术,紊流模型采用Baldwin-Lomax代数紊流模型。优化设计变量是叶栅型线参数化Bezier曲线控制点坐标,优化设计得到叶栅的总压损失减小了20％。设计结果证明了本文所提出的优化技术对透平叶栅气动设计是一种有效的方法。     

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.