Unsteady free convective flow in an enclosure with a stepwise periodically varying side-wall heat flux

Free convective flow in a square enclosure with one of the vertical walls heated and with the opposite vertical wall cooled to a uniform temperature, the remaining walls being adiabatic, has been numerically studied The heat flux at the heated wall is spatially uniform but is, in general, varying in a stepwise manner with time. The flow has been assumed to be laminar and two-dimensional. Fluid properties have been assumed constant except for the density change with temperature that gives rise to the buoyancy forces. The governing equations, expressed in terms of stream function and vorticity, have been written in dimensionless form. The resultant equations have been solved using the finite-element method Because of the possible applications that motivated the study, results have only been obtained for a Prandtl number of 0.7. Results have then been obtained for modified Rayleigh numbers between 1,000 and 1,000,000 for a wide range of dimensionless amplitudes and periods of the heaf flux variation.