Combined conduction and radiation in an absorbing, emitting and scattering cylindrical medium using the finite element method.

Abstract

The purpose of this study was to formulate and solve the problem of transient combined conduction and radiation in a grey absorbing, emitting and scattering medium of cylindrical geometry. The medium is bounded by grey diffuse surfaces at known temperatures. The problem was solved by the Galerkin finite element method using linear interpolating functions. The transient terms were handled using the Crank-Nicolson scheme with the time steps chosen to avoid temperature fluctuations at early times. The results were compared with exact solutions for the extreme cases, i.e., pure conduction and radiative equilibrium. Results are also compared with an approximate solution for the case of combined conduction and radiation. The effects of various parameters on the solutions are presented in tabular as well as graphical forms. The results obtained compare well with the exact solutions. The Galerkin finite element technique is well suited to this problem because of the ease with which integrals with variable limits can be handled.