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This article presents fully three-dimensional conjugate heat transfer analysis and a multi-objective, constrained optimization to find sizes of pin-fins, inlet water pressure, and average speed for arrays of micro pin-fins used in the forced convection cooling of an integrated circuit with a uniformly heated 4 × 3 mm footprint and a centrally located 0.5 × 0.5 mm hot spot. Sizes of micro pin-fins having cross sections shaped as circles, symmetric airfoils, and symmetric convex lenses are optimized to completely remove heat due to a steady, uniform heat flux of 500 W cm−2imposed over the entire footprint (background heat flux) and a steady, uniform heat flux of 2000 W cm−2imposed on the hot spot area only (hot spot heat flux). The two simultaneous objectives are to minimize maximum substrate temperature and minimize pumping power, while keeping the maximum temperature constrained below 85°C and removing all of input thermal energy by convection. The design variables are the inlet average velocity and size of the pin-fins. A response surface is generated for each of the objectives and coupled with a genetic algorithm to arrive at a Pareto frontier of the best trade-off solutions. Numerical results show that, for a specified maximum temperature, optimized arrays with pin-fins having symmetric convex lens shapes create the lowest pressure drop, followed by the symmetric airfoil and circular cross-section pin-fins. An a posteriori three-dimensional stress–deformation analysis incorporating hydrodynamic and thermal loads shows that Von-Mises stress for each pin-fin array is significantly below the yield strength of silicon, thus, confirming structural integrity of such arrays of micro pin-fins. [ABSTRACT FROM PUBLISHER]

Given a micro pin-fin array cooling scheme with these constraints: (a) given maximum allowable temperature of the material (the hot spot temperature), (b) given inlet cooling fluid temperature, (c) given total pressure loss (pumping power affordable), and (d) given overall thickness of the entire micro pin-fin cooling array, find the maximum possible average heat flux on the hot surface and find the maximum possible heat flux at the hot spot under the condition that the entire amount of the inputted heat is removed by the cooling fluid. The goal was to create an optimum performance map for a cooling micro array having specified inlet coolant temperature and maximum temperature. Fully 3D conjugate heat transfer analysis was performed on each of the randomly created candidate configurations. Response surfaces based on Radial Basis Functions were coupled with a genetic algorithm to arrive at a Pareto set of best trade-off solutions. These Pareto optimized configurations indicate the maximum physically possible heat fluxes for specified material and constraints. Detailed off-design performance maps of such Pareto-optimized cooling arrays of micro pin-fins were calculated that demonstrate superior on-design and off-design performance of pin-fins having symmetric convex cross sections as opposed to the commonly used circular cross sections. [ABSTRACT FROM AUTHOR]