Numerical model of mixed convection heat transfer between a series of vertical parallel plates with planar heat sources

Abstract

Heat transfer between a series of vertical parallel plates with planar heat sources has been studied numerically. The series of plates formed a series of channels, or cooling passages, in which fluid could flow. Heat dissipation from the heat generating surfaces was accomplished by laminar mixed convection, in which forced and free convection effects were considered, and conjugate conduction through the plate. The forced flow at the channel inlet was assumed to be that of an upward flowing uniform velocity profile. The bottom surface of the plate was set to the inlet flow temperature. The Boussinesq approximation was invoked to account for the variations in fluid density. The computational domain was extended beyond the channel exit, which allowed for the calculation of the heat transfer from the ends of the plates as well as the capture of the flow structure at the exit and beyond. A finite volume based method employing the SIMPLER algorithm was used for the numerical calculations. Independent parameters that were varied in this study included the buoyancy parameter (Gr/Re), the ratio of the plate conductivity to the fluid conductivity (K), and the ratio of the plate thickness to the channel width (W/B). The velocity profiles within the channel were observed to skew substantially to the hot wall as Gr/Re increased and K decreased. There was also a significant difference between the hot and cold surface heat fluxes at low values of K, while the heat flux distribution on both surfaces was essentially identical for K=100. The constant temperature boundary condition at the bottom of the plate acted as a sink at high values of K. At the top of the plate, the effect of the exposed surface was also to reduce the wall temperatures near the vicinity of the plate tip, although heat was not removed out the plate top nearly as effectively as at the plate bottom. Also, an extended wake developed beyond the plate top for asymmetric heating cases, which included recirculation zones as far as 10 channel widths from the exit.