Natural convection from a discrete heat source on the bottom of a horizontal enclosure

Steady, natural convection from a discrete flush-mounted rectangular heat source on the bottom of a horizontal enclosure is studied numerically. Three-dimensional form of Navier–Stokes equations are solved by using multigrid technique. Rayleigh number based on the enclosure height is varied from 103 until unstable flow is predicted for a fixed Prandtl number of 0.71. Aspect ratio of the source is varied until it fully covered the entire width of the bottom plate. The enclosure is cooled from above and insulated from the bottom. Effect of vertical boundary conditions on the rate of heat transfer from the heat source is studied. It is found that the rate of heat transfer is not so sensitive to the vertical wall boundary conditions. The limit of the maximum Rayleigh number to obtain a convergent solution decreases as the aspect ratio of the source is increased. The variation of Nusselt number as a function of Rayleigh number and aspect ratio of the source is reported.