Numerical Investigation of Buoyancy Effect Associated with a Continuously Moving Horizontal plate

Abstract

This work presents numerical studies of the effects of buoyancy force parameter, B_f, coupled with viscous dissipation on the convective heat transfer in a fluid-filled rectangular cavity. The cavity is bounded by a hot horizontal plate maintained at temperature T_w and moving continuously at velocity U_w. It is also bounded on the left vertical and lower horizontal sides by cold isothermal walls and an adiabatic vertical wall on the right. The cavity was filled with quenching medium. The study was carried out for different quenching media such as oil with Prandtl number, Pr = 10, air with Prandtl number, Pr = 0.7 and liquid metal with Prandtl number, Pr = 0.01, for various bouyancy parameters in the range 5 x 10^-3 ≤ B_f ≤ 10^-2, fixed Eckert numbers, Ec = 1.0 and mixed convection parameter, Gr/Re² = 1.0, in order to characterize the nature of the flow patterns and energy distribution. The flow governing equations including the momentum and energy equations were thereby solved using the finite difference method. The results are presented in the form of profiles for temperature, velocity and local Nusselt numbers. The results show that the buoyancy force parameter has significant influence on the velocity and temperature profile for a Prandtl number higher than unity at fixed viscous dissipation. Further results show that an increase in the buoyancy force parameter for a Prandtl number greater than unity leads to a significant increase in the maximum velocity attainable in the cavity. The results would be useful as baseline data for manufacturing and material processing industries involved with wire drawing, continuous rolling and glass fiber productions.

Keywords: Buoyancy effect, Finite difference scheme, Heat transfer, Isotherms, Mixed Convection