The spectral collocation method for transient combined radiation and conduction heat transfer in a planar participating medium with spatially variable refractive index is introduced and formulated. The angular dependence of the problem is discretized by discrete ordinates method and the space dependence is expressed by Chebyshev polynomial and discretized by spectral collocation method. Due to the exponential convergence of spectral methods, very high accuracy can be obtained even using a small resolution for present problem. Numerical results in one-dimensional planar slab by Chebyshev collocation spectral-discrete ordinates method (SP-DOM) are compared with those available data in references. Effects of various parameters such as the variable thermal conductivity, the scattering albedo, the emissivity of boundary, the conduction-radiation parameter, the optical thickness, and the graded index are studied for absorbing, emitting, and anisotropic scattering medium. The SP-DOM has been found to successfully and efficiently deal with transient combined radiation and conduction heat transfer problem in graded index medium.
A linearized spectral collocation method for Riesz space fractional nonlinear reaction‐diffusion equations
