Abstract
A parabolic flow between two horizontal parallel plates is considered, when the lower plate is heated and the upper plate is cooled uniformly. When the temperature difference between the top and bottom of the fluid layer exceeds a critical value, roll-type convection occurs with the axes parallel to the mean flow. The governing equations are solved numerically using the Boussinesq approximation for the range of Rayleigh number, 3 Rac_??_Ra_??_7 Rac, where Rac is the value of the Rayleigh number at which infinitesimal perturbations can be just maintained. The Prandtl number is taken as 0.713. In all cases investigated, the system achieves a steady state. The thus calculated distribution of the velocity component in the direction of the mean flow agrees well with Mori and Uchida's experiment (1966) for Ra=4.69 Rac and the Reynolds number=513. The agreement between the calculated and experimental temperature fields is rather poor however.
For the range of Rayleigh numbers considered, the non-dimensional Nusselt number is found to vary in proportion to the 0.328 power of the Rayleigh number, very close to the 1/3 power variation predicted on dimensional reasoning for the Benard-Rayleigh convection problem.
