Effect of aspect ratio on laminar heat transfer behavior of a non-Newtonian fluid in an electronics coldplate

Abstract The present note delineates the effect of duct aspect ratio on the heat transfer characteristics for laminar forced convection of inelastic non-Newtonian fluids in a nonuniformly heated rectangular duct, which is an integral part of an electronics coldplate, where the flow is hydrodynamically developed but thermally developing as often encountered in coldplates used in the cooling of phased array radar. The governing equations are solved by a finite volume method. The effects of shear thinning, given by the Carreau equation, and the viscous dissipation, characterized by the Brinkman number, are examined via the the friction factor, the Nusselt number, and the bulk fluid temperature for duct aspect ratios ranging from 1. to 0.2. The results indicate that when viscous dissipation is present, the heat transfer from the heated surface of the duct is not significantly increased as the aspect ratio decrease (i.e., the area of heat transfer increases); however, with a decreasing duct aspect ratio the rate of increase of the bulk fluid temperature with axial distance is significant. Also, the product of the Fanning friction factor and the Reynolds number will not be significantly increased with decreasing aspect ratio for a shear thinning fluid. Consequently, the use of a duct aspect ratio near 1 will provide the best overall design for cooling ducts used in electronics coldplate heat removal systems when the flow is hydrodynamically developed and thermally developing.