Least-squares natural element method for radiative heat transfer in graded index medium with semitransparent surfaces

The least-squares natural element method (LSNEM) is employed for solving radiative heat transfer problem in two-dimensional semitransparent graded index medium with semitransparent and diffusely reflecting surfaces. LSNEM is an extension of natural element method (NEM). Unlike the NEM based on Galerkin discretization, the least-squares weighted residuals approach is employed to spatially discretize the radiative heat transfer equations in LSNEM. Radiative heat transfer problem in rectangular enclosure filled with graded index medium having opaque surfaces is examined to verify the LSNEM. Afterwards, radiative heat transfer in the semicircular enclosure with an inner circle filled with graded index medium is studied. Two kinds of refractive index distributions are considered. The studies show that the refractive index distributions and optical boundary conditions of the surfaces greatly influence the radiative transfer. Effects of the extinction coefficient are investigated on the temperature distributions and radiative heat fluxes.