Natural convective heat transfer from an isothermal vertical cylinder with a square cross-section which has an exposed horizontal top surface has been numerically studied. The exposed upper surface is maintained at the same temperature as the vertical walls of the cylinder. The cylinder is mounted on a flat horizontal adiabatic base plate. The interest in this situation stems from the fact that it is an approximate model of some electrical component cooling situations. The flow has been assumed to be steady and laminar and it has 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 three-dimensional governing equations, these equations being written in terms of dimensionless variables. The numerical solution has been obtained using a commercial finite element method based code, FIDAP. The solution has the following parameters: the Rayleigh number, Ra, based on the height of the heated cylinder, h, and the overall temperature difference Tw − Tf, the dimensionless size of the square cross-section of the cylinder surface, W = w/h, w being the size of the cross-section, and the Prandtl number, Pr. Because of the applications that motivated this study, results have only been obtained for Pr = 0.7. A wide range of the other governing parameters has been considered. The conditions under which the heat transfer from the exposed upper surface can be neglected compared to that from the vertical side walls in the evaluation of the mean Nusselt number for the entire cylinder have been explored.
Modeling of convective heat transfer in prismatic channels of different cross section geometry