Transient conduction-radiation heat transfer in participating media using the lattice Boltzmann method and the discrete transfer method

The lattice Boltzmann method (LBM) is used to solve the energy equation of a problem involving conduction and radiation heat transfer with and without heat generation. Both steady and transient situations are considered. To demonstrate that the two different kinds of methods can be coupled, the radiative information for the governing energy equation is computed using the discrete transfer method and the LBM is used to solve the energy equation. For validation purposes, a I-D planar conducting and radiating medium is considered. Radiatively, the medium is absorbing, emitting, and scattering. Boundaries of the medium are assumed at the specified temperatures. The heat-generation rate is considered uniform and constant throughout the medium. Transient and steady-state medium temperature and heat flux distributions are found for various values of the scattering albedo, emissivity, and conduction-radiation parameter. Results obtained by solving the energy equation using the LBM are compared against those solving the same using the finite-difference method and with those reported in the literature. Very good agreement is obtained.