solutions of radiative heat transfer in a slab with reflective boundaries

Ultraspherical-polynomials approximation to the radiative heat transfer in a slab with reflective boundaries

“…(20), requires some modification in order to remove singularities encountered at low order terms. The reader can consult Atalay's work [17] for such a modification in the spherical harmonics (P N ) method. Since adaptation of Atalay's idea to the P (λ) N approximation for the conservative case results in tedious algebraic operations, in this study, it has been preferred to use a value of albedo ω very very close to unity.…”

“…For the linearly varying source term S(τ ) = (1/π)(1 − ω)(1 − τ/τ 0 ), a particular solution to the transfer equation is [17] …”

“…The results of Beach et al [16] are to be used as the main basis for comparisons. The spherical-harmonics results of Atalay [17] are expected to be reproduced as a special case of the P (λ) N method for λ = 1/2. For exponentially varying source terms, results from the CFD code FLUENT are also to be obtained and included in comparative assessments.…”

“…The same problem was attacked by Beach et al [16], who used Case's normal-mode expansion technique and produced benchmark-quality results. In a recent study, Atalay obtained numerical solutions to the problem by the spherical-harmonics method [17]. The results of Beach et al [16] are to be used as the main basis for comparisons.…”

Radiative heat transfer in a participating medium with specular–diffuse surfaces

“…For instance, there are zone method [1], Monte Carlo method (MCM) [2], P-N spherical harmonics method [3], discrete ordinates method (DOM) [4], discrete transfer method (DTM) [5], finite-volume method (FVM) [6], finite element method (DOM) [7], meshless method [8], etc.…”