A Numerical Study of Laminar and Turbulent Mixed Convective Flow Over a Vertical Isothermal Plate

Mixed (or combined) convective flow is flow with heat transfer in which there is a forced flow but in which the buoyancy forces that arise due to temperature variations in the flow have a significant effect on the flow and therefore on the heat transfer rate. In such flows the buoyancy forces can also have a very significant influence on the conditions under which transition from laminar to turbulent flow occurs. In the present study this effect of the buoyancy forces on the conditions under which transition occurs have been studied for the particular case of flow in the vertically upward direction over a heated vertical flat plane surface that is maintained at a uniform temperature that is higher than the temperature of the undisturbed fluid flow, i.e., attention has been restricted to assisting (or aiding) mixed convective flow. The flow has been assumed to be steady and it has also been assumed that the fluid properties are constant except for the density change with temperature which gives rise to the buoyancy forces, this having been treated by using the Boussinesq approach. The solution has been obtained by numerically solving the governing equations subject to the boundary conditions using the commercial cfd solver, FLUENT. The k-epsilon turbulence model with full account being taken of the buoyancy forces has been used in obtaining the solutions. The mean heat transfer rate from the surface expressed in terms of the mean Nusselt number depends on the Reynolds number based on the free-stream forced velocity and the length of the heated surface, on the Rayleigh number based on the length of the heated surface and the overall surface to free-stream temperature difference, and on the Prandtl number. Results have only been obtained for a Prandtl number of 0.74. Solutions have been obtained for a series of increasing Rayleigh numbers between 10⁵ and 10¹² for a series of Reynolds numbers between approximately 1 and 10⁷.