A numerical study of laminar and turbulent opposing mixed convective flow over a vertical plate with a uniform surface heat flux

Abstract

Paper presented to the 10th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics, Florida, 14-16 July 2014.

When there is a forced flow over a body that has a surface temperature that is different from the temperature of the undisturbed forced flow the buoyancy forces that arise due to the density differences associated with the temperature differences in the flow can have a significant effect on the flow and consequently on the heat transfer rate from the body. Flows such as these are termed mixed- or combined natural and forced convective flows. The present paper reports on the study of mixed convective flow over a thin vertical flat plate which has a uniform surface heat flux for conditions under which transition from laminar to turbulent flow occurs. Attention has been restricted to the case where the buoyancy forces act in the opposite direction to the forced flow, i.e., to the case of opposing mixed convective flow. Most existing studies of this type of situation have assumed that steady laminar flow exists. Laminar, transitional, and turbulent flow situations have been considered in the present study and the development of unsteady flow has been allowed for. The forced flow has been assumed to be steady and the Boussinesq approach has been used. The solution has been obtained by numerically solving the governing equations subject to the boundary conditions using the commercial CFD solver, ANSYS FLUENT©. The kepsilon turbulence model with the full effect of buoyancy forces accounted for and with standard wall functions has been used in obtaining the solutions. The heat transfer rate from the surface of the plate has been expressed in terms of the mean Nusselt number based on the overall plate length and the difference between the overall mean plate temperature and the undisturbed fluid temperature. This Nusselt number depends on the values of the heat flux Rayleigh number based on the plate length, the Reynolds number based on the value of the forced velocity ahead of the plate and on the plate length, and the Prandtl number. Results have been obtained for a Prandtl number of 0.74, i.e., essentially for the value for air. The conditions under which the flow can be assumed to be purely forced convective and under which the flow can be assumed to be purely natural convective have been investigated.