## OPTIMIZED LONGITUDINAL-FIN HEAT SINKS ACCOUNTING FOR 2 NON-UNIFORM HEAT TRANSFER COEFFICIENT
## AbstractLongitudinal-fin heat sinks (LFHS) are ubiquitous. However, their optimization is based upon the often invalid assumption of uniform heat transfer coefficient along the fin and prime surfaces, resource-consuming brute-force numerical optimization and/or laborious experiments. We develop an algorithm requiring minimal computations to compute the optimal fin thickness and spacing of a fully-shrouded LFHS that minimizes its thermal resistance under conditions of hydrodynamically and thermally fully developed laminar flow. The base of the heat sink (HS) is assumed to be isothermal. Our results are relevant to, e.g., microchannel cooling applications where base isothermality can be achieved by using a heat spreader or vapor chamber. Prescribed quantities are the density, viscosity, thermal conductivity and specific heat capacity of the fluid, the thermal conductivity and height of the fins, the width and length of the HS and the pressure gradient, or, if the optimal length of the HS is also of interest, the pressure drop across the HS. The present study is distinct from previous work because we do not assume a uniform heat transfer coefficient, but fully capture the velocity and temperature fields by numerically solving the conjugate heat transfer problem in dimensionless form as per an existing approach. The thermal resistance is expressed as a function of dimensionless parameters to maintain generality. Once the optimal dimensionless fin thickness and spacing are obtained, their dimensional counterparts are computed algebraically. The optimization method is illustrated by optimizing an LFHS in the context of direct liquid cooling. |

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