Heat sink optimization with application to microchannels

The equations governing the fluid dynamics and combined conduction/convection heat transfer in a heat sink are presented in dimensionless form for both laminar and turbulent flow. A scheme presented for solving these equations permits the determination of heat sink dimensions that display the lowest thermal resistance between the hottest portion of the heat sink and the incoming fluid. Results from the present method are applied to heat sinks reported by previous investigators to study effects of their restrictions regarding the nature of the flow (laminar or turbulent), the ratio of fin thickness to channel width, or the aspect ratio of the fluid channel. Results indicate that when the pressure drop through the channels is small, laminar solutions yield lower thermal resistance than turbulent solutions. Conversely, when the pressure drop is large, the optimal thermal resistance is found in the turbulent region. With the relaxation of these constraints, configurations and dimensions found using the present procedure produce significant improvement in thermal resistance over those presented by all three previous studies