For heat transfer through building insulations such as fiberglass, radiation and conduction are important modes of heat transfer. Moreover, materials like fiberglass scatter radiation in a highly anisotropic manner. The equations for heat transfer by simultaneous conduction and radiation are a coupled pair, one of which is of the nonlinear integrodifferential type. Exact solution for transient heat transfer in this case is not available, and the approximate solution available is the two-flux model. The two-flux model does not give good results for transient, combined mode heat transfer, through an absorbing, emitting, and anisotropically scattering medium. In this thesis a higher order approximate solution has been developed. It is found that this model gives appreciably better results than the two-flux model. / Master of Science