Role of Prandtl number in the interaction phenomenon of surface radiation with an opposing mixed convection within a differential heated cavity

Abstract

A numerical analysis has been done for opposing mixed convection resulting due to wall movement and buoyancy induced by a clockwise fluid motion in a differentially heated cavity. The effect of Prandtl number (Pr) and wall surface emissivity (?{lunate}) has been investigated for different values of Richardson number. The net radiation method has been employed to simulate the effect of surface radiation. The energy equation along with its nonlinear boundary condition is treated with the Newton-Raphson scheme. As momentum and energy equations are coupled with each other through their source terms, an iterative solution procedure is employed. A vorticity-stream function formulation of the momentum equation has been adopted and solved by using an underrelaxation parameter of 0.45. The effect of Prandtl number with respect to the transformation of a multi-cellular structure of streamline into a unicellular structure has been analyzed. For the same Richardson number (Ri) with an increase in Prandtl number, the flow and heat transfer phenomena changes from a buoyancy-induced dominated flow to a shear-induced dominated flow, which leads to some exciting results with respect to wall movement as well. Furthermore, the role of surface radiation in this respect has been emphasized. Nusselt number variation with the Prandtl number and surface emissivity has also been presented. � 2012 Wiley Periodicals, Inc.