## OPTIMAL DESIGN OF LONGITUDINAL-FIN HEAT SINKS ACCOUNTING FOR SIMULTANEOUSLY DEVELOPING FLOWAND CONJUGATE EFFECTS
## AbstractLongitudinal-fin heat sinks (LFHSs) are ubiquitous. However, their optimization is based upon the often invalid
assumption of a uniform heat transfer coefficient along the fin and prime surfaces, resource-consuming
brute-force numerical optimization, and/or laborious experiments. We express the thermal resistance per unit
width of a fully-shrouded LFHS with an isothermal base in dimensionless form as a function of the conjugate
mean Nusselt number. Then, we develop an algorithm requiring minimal algebraic computations to compute
the optimal fin spacing, thickness and length that minimize its thermal resistance under conditions of simultaneously
developing laminar flow. Prescribed quantities are the density, viscosity, thermal conductivity and
specific heat capacity of the fluid, the thermal conductivity and height of the fins, and the pressure drop across
the LFHS. 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 to compute the conjugate mean Nusselt number for simultaneously
developing flow. The results are relevant to, |

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