Thermal optimization of a microchannel heat sink with trapezoidal cross section

A microchannel heat sink shape optimization has been performed using response surface approximation. Three design variables related to microchannel width, depth, and fin width are selected for optimization, and thermal resistance has been taken as objective function. Design points are chosen through a three-level fractional factorial design of sampling methods. Navier-Stokes and energy equations for steady, incompressible, and laminar flow and conjugate heat transfer are solved at these design points using a finite volume solver. Solutions are carefully validated with the analytical and experimental results and the values of objective function are calculated at the specified design points. Using the numerically evaluated objective-function values, a polynomial response surface model is constructed and the optimum point is searched by sequential quadratic programming. The process of shape optimization greatly improves the thermal performance of the microchannel heat sink by decreasing thermal resistance of about 12% of the reference shape. Sensitivity of objective function to design variables has been studied to utilize the substrate material efficiently.