HIGHER ORDER DIFFERENTIAL APPROXIMATION OF RADIATIVE ENERGY TRANSFER IN A CYLINDRICAL GRAY MEDIUM
HIGENYI, JAMES K. D.
Doctor of Philosophy
The spherical harmonics method is applied to develop and solve approximate differential equations of radiative transfer in an emitting, absorbing, isotropically scattering and gray medium. Boundary conditions of Marshak type consistent with a particular approximation are derived and used in the solutions. Three types of thermal conditions for the medium are considered: radiative equilibrium, uniform heat generation and a parabolic internal heat generation. Two higher order approximations, P(,3) and P(,5) approximations, are formulated and solved for one-dimensional problems; the medium is bounded by concentric or hollow cylindrical surfaces. Numerical results exhibit great improvement for the P(,3) approximation over the P(,1) approximation and a less rapid improvement for the P(,5) approximation. An axially symmetric problem is also analysed. In this case, only the P(,1) approximation is considered for a gray medium within a finite hollow or finite concentric cylindrical enclosure. The numerical results show that the accuracy of the differential approximation is of the same order for both the axially symmetric and one-dimensional problems under the same geometric and thermal conditions.