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 0.000598kg/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.