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.     

Multi-Objective Optimization of an Inverse Trapezoidal-Shaped Microchannel

The microchannel with inverse trapezoidal cross section in a micro heat sink has been optimized using three-dimensional Navier–Stokes analysis and a multi-objective evolutionary algorithm. Thermal resistance and pressure drop were selected as objective functions to evaluate the performance of the microchannel heat sink. Three design variables related to the width, depth, and angle of the channel, respectively, were selected for optimization. Parametric study has been performed with the three design variables prior to the optimization to analyze the variation of objective functions with the design variables, and thus to determine the design space for the optimization. Using a finite-volume solver, Navier–Stokes and energy equations for laminar flow and conjugate heat transfer were solved for the constant mass flow rate of 0.000598 kg/s. Latin hypercube sampling was utilized to select the design points. A surrogate model for each objective function was constructed using the values of the objective function calculated at the design points. Pareto-optimal solutions were obtained to find the optimal designs of the microchannel. Pareto sensitivity analysis was performed for the design variables along the Pareto optimal front, and it was found that both the objective functions were most sensitive to the design variable that is related to the width of the microchannel.     

Multi-Objective Optimization of a Row of Film Cooling Holes Using an Evolutionary Algorithm and Surrogate Modeling

Multi-objective shape optimization of a row of laidback fan-shaped film cooling holes has been performed using a hybrid multi-objective evolutionary approach in order to achieve an acceptable compromise between two competing objectives: the enhancement of film cooling effectiveness and the reduction of aerodynamic loss. In order to perform comprehensive optimization of a film cooling hole shape, the injection angle of the hole, lateral expansion angle of the diffuser, forward expansion angle of the hole, and pitch-to-hole diameter ratio are chosen as design variables. Forty experimental designs within the design spaces are selected using the Latin hypercube sampling method. The response surface approximation method is used to construct the surrogate using objective function values calculated at the experimental points using Reynolds-averaged Navier-Stokes analysis. The shear stress transport turbulence model is used as a turbulence closure. The optimization results are processed using the Pareto-optimal method. The Pareto-optimal solutions are obtained using a combination of a evolutionary algorithm and a local search method. The optimum designs are grouped using the k-means clustering technique, and the three optimal points selected in the Pareto-optimal solutions are evaluated by numerical analysis. The optimum designs give enhanced objective function values compared to the experimental designs.     

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.     

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.     

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.     

Multi-objective optimization of annular fin array with B-spline curve based fin profiles

The design of annular fin array with variable thickness fin profiles defined by B-spline curves is studied as a multi-objective optimization problem for simultaneously maximizing heat transfer rate and minimizing thermal stress. Maximization of surface e?ciency and augmentation factor as well as minimization of fin volume are considered as additional objective functions for further assessment of fin array performance. Evaluating the objective values through hybrid spline difference method, different cases are investigated by solving the optimization model by non-dominated sorting genetic algorithm II. The proposed scheme should aid designers in selecting compromise optimal solutions for practical problems.     

Optimization of a Microchannel Heat Sink with Varying Channel Heights and Widths

The optimal tapered channel design of a microchannel heat sink is obtained by a combined optimization procedure that includes a model of a three-dimensional microchannel heat sink and a simplified conjugate-gradient method. The objective function to be minimized is the overall thermal resistance with the number of channels N, channel-width ratio β, height-tapered ratio Λ _y , and width-tapered ratio Λ _z as the design parameters. It is shown that the thermal resistance in all its relationships with the individual parameters exhibits a decrease followed by an increase. The thermal resistance is sensitive to the variations in the channel number, channel-width ratio, or width-tapered ratio while less sensitive to the height-tapered ratio. Optimization results show that for a given pumping power (0.5 W), the optimal design variables are N = 78, β = 0.78, Λ _z  = 0.59, and Λ _y  = 0.81 with a corresponding minimum overall thermal resistance of 0.087 K W^?1. These optimal design variables produce a 37.6% decrement in thermal resistance compared to the initial parallel-channel design estimate (N = 71, β = 0.85, Λ _z  = 0.99, and Λ _y  = 0.99). Additionally, as the pumping power increases, the optimal thermal resistance decreases and the corresponding optimal values of N increase; whereas, β, Λ _z , and Λ _y decrease.     

Shape optimization of rib-roughened surface to enhance turbulent heat transfer

This work presents an investigation on numerical optimization technique coupled with Reynolds-averaged Navier-Stokes analysis of flow and heat transfer for design of rib-roughened surface in case of single surface roughened in two-dimensional channel. Standard k-ε model is used as a turbulence closure. The objective function is defined as a function of heat transfer coefficient and friction drag coefficient with weighting factor. And, the ratio of width-to-height of the rib and the ratio of pitch-to-height are selected as design variables. Three different weighting factors and two sets of initial values of the design variables in each case are tested. In case of double design variable, the histories of design variables and objective function are complicated, and the number of iterations is very sensitive to the initial values of design variables. However, overall performance of the optimization process is proved quite reliable.     

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.