Transient, combined conduction and radiation in an absorbing, emitting, and isotropically scattering solid sphere

Transient, combined conduction and radiation is solved in an absorbing, emitting, and isotropically scattering solid sphere with a black boundary initially at a uniform temperature and for times t greater than 0 subjected to a constant temperature at the spherical surface. The collocation method is used to solve the radiation part of this problem and the implicit finite difference scheme is used to solve the conduction part. The effects of the conduction-to-radiation parameter, the single scattering albedo, the optical thickness of the medium on the temperature distribution and the heat flux in the medium are examined.