Natural Convective Heat Transfer From a Vertical Cylinder With an Exposed Upper Surface

Natural convective heat transfer from a vertical cylinder which has a uniform heat flux at its surface and which has an exposed horizontal top surface has been numerically studied. The cylinder is mounted on an adiabatic cylindrical base which has the same diameter as the heated cylinder. In some circumstances the mean Nusselt number for the curved surface of the cylinder can be adequately predicted using vertical flat plate equations, i.e., by ignoring curvature effects, and in some circumstances the overall mean Nusselt number for the system considered can be adequately predicted by ignoring the heat transfer from the exposed upper surface of the cylinder. The flow has been assumed to be axisymetric about the vertical cylinder axis and to be steady and laminar. 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, these equations being written in terms of dimensionless variables and the solution being obtained using a commercial finite element method based code, FIDAP. 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 have been considered. The conditions under which the heat transfer from the exposed upper surface can be neglected compared to that from the cylindrical wall in the evaluation of the mean Nusselt number has been deduced and the conditions under which curvature effects can be ignored in evaluating the mean Nusselt number for the curved surface of the cylinder have been investigated.