Most methods for designing electronics cooling schemes do not offer the information on what levels of heat fluxes are maximally possible to achieve with the given material, boundary and operating conditions. Here, we offer an answer to this inverse problem posed by the question below. Given a micro pin-fin array cooling with these constraints:

- given maximum allowable temperature of the material,

- given inlet cooling fluid temperature,

- given total pressure loss (pumping power affordable), and

- given overall thickness of the entire electronic component,

find out 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 completely removed by the cooling fluid. This problem was solved using multi-objective constrained optimization and metamodeling for an array of micro pin-fins with circular, airfoil and symmetric convex cross sections that is removing all the heat inputted via uniform background heat flux and by a hot spot. The goal of this effort was to identify a cooling pin-fin shape and scheme that is able to push the maximum allowable heat flux as high as possible without the maximum temperature exceeding the specified limit for the given material. 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 frontier of best trade-off solutions. The Pareto optimized configuration indicates the maximum physically possible heat fluxes for specified material and constraints.

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