Develop a Galerkin finite element formulation for the two-dimensional analysis of radiative heat transfer with an emitting, absorbing, and conducting gray medium in a two-dimensional rectangular...

Develop a Galerkin finite element formulation for the two-dimensional analysis of radiative heat transfer with an emitting, absorbing, and conducting gray medium in a two-dimensional rectangular enclosure that is infinitely long in directions normal to the cross section shown. There is no scattering in the medium. The rectangular region has a uniform heating q'" W/m3 throughout its volume. The steady two-dimensional temperature distribution is to be determined. For simplicity, use a grid having the same increment size in both the x and y directions. All of the boundary walls are black and are at the same temperature T_w.