Abstract: Simultaneous transient conduction and radiation heat
transfer with heat generation is investigated. Analysis is carried out
for both steady and unsteady situations. two-dimensional gray
cylindrical enclosure with an absorbing, emitting, and isotropically
scattering medium is considered. Enclosure boundaries are assumed
at specified temperatures. The heat generation rate is considered
uniform and constant throughout the medium. The lattice Boltzmann
method (LBM) was used to solve the energy equation of a transient
conduction-radiation heat transfer problem. The control volume finite
element method (CVFEM) was used to compute the radiative
information. To study the compatibility of the LBM for the energy
equation and the CVFEM for the radiative transfer equation, transient
conduction and radiation heat transfer problems in 2-D cylindrical
geometries were considered. In order to establish the suitability of the
LBM, the energy equation of the present problem was also solved
using the the finite difference method (FDM) of the computational
fluid dynamics. The CVFEM used in the radiative heat transfer was
employed to compute the radiative information required for the
solution of the energy equation using the LBM or the FDM (of the
CFD). To study the compatibility and suitability of the LBM for the
solution of energy equation and the CVFEM for the radiative
information, results were analyzed for the effects of various
parameters such as the boundary emissivity. The results of the LBMCVFEM
combination were found to be in excellent agreement with
the FDM-CVFEM combination. The number of iterations and the
steady state temperature in both of the combinations were found
comparable. Results are found for situations with and without heat
generation. Heat generation is found to have significant bearing on
temperature distribution.