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Second Thermal and Fluids Engineering  Conference

ISSN: 2379-1748
ISBN: 978-1-56700-430-4

OPTIMAL DESIGN OF LONGITUDINAL-FIN HEAT SINKS ACCOUNTING FOR SIMULTANEOUSLY DEVELOPING FLOWAND CONJUGATE EFFECTS

Georgios Karamanis
Department of Mechanical Engineering, Tufts University, Medford, MA, 02155

Marc Hodes
Department of Mechanical Engineering, Tufts University, Medford, MA, 02155; Bell Laboratories, Murray Hill, USA

Abstract

Longitudinal-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, e.g., electronics cooling applications where heat spreaders or vapors chambers are utilized to make the base of heat sinks essentially isothermal.

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