A numerical method for predicting natural convection in horizontal cylinders with asymmetric boundary conditions

A numerical technique is developed to predict the two-dimensional transient natural convection heat transfer within a horizontal cylinder. Finite difference analogs of the Navier-Stokes and thermal energy equations are solved in the stream function-vorticity framework. The solution method, which is a modification of an alternating-direction implicit (ADI) scheme wherein the convective terms are evaluated explicitly, is found to be computationally more efficient than either an ADI or an explicit method. Unlike previous work, the present technique will accommodate completely arbitrary temperature boundary conditions. Thus, rather than considering an annular space or half of a symmetric cylinder, the solutions are determined for a full cylinder. A Cartesian form of the governing equations is employed at the point $\text{r= 0}$ where the polar coordinate equations become singular. The computed results are found to be in good agreement with previously published experimental data.