Cooling of electronic devices requires the use of heat spreaders whose function is to allow the spreading of the heat flux lines in the 3-D space and to increase the exchange area with the coolant. The objective of this analysis is to estimate the convective heat transfer coefficient of a microchannel heat sink that corresponds to a maximum amount of heat removed from heat source placed on the top surface of the sink. This problem is solved using an optimal control technique in which we control the solution of the heat equation with the convective boundary condition, taking the heat transfer coefficient as the control. A conjugate gradient method is used to solve the optimal control problem. The results show that the temperature distributions corresponding to the controlled solution are lower than those corresponding to the uncontrolled solution. This study can provide guidance in designing micro heat pipe sinks, which have emerged as an effective technique for cooling electronic components.

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