Random variable transformation for generalized stochastic radiative transfer in finite participating slab media

S.A. El-Wakil, M. Sallah and A.M. El-Hanbaly

Physica A: Statistical Mechanics and its Applications, 2015, vol. 435, issue C, 66-79

Abstract: The stochastic radiative transfer problem is studied in a participating planar finite continuously fluctuating medium. The problem is considered for specular- and diffusly-reflecting boundaries with linear anisotropic scattering. Random variable transformation (RVT) technique is used to get the complete average for the solution functions, that are represented by the probability-density function (PDF) of the solution process. In the RVT algorithm, a simple integral transformation to the input stochastic process (the extinction function of the medium) is applied. This linear transformation enables us to rewrite the stochastic transport equations in terms of the optical random variable (x) and the optical random thickness (L). Then the transport equation is solved deterministically to get a closed form for the solution as a function of x and L. So, the solution is used to obtain the PDF of the solution functions applying the RVT technique among the input random variable (L) and the output process (the solution functions). The obtained averages of the solution functions are used to get the complete analytical averages for some interesting physical quantities, namely, reflectivity and transmissivity at the medium boundaries. In terms of the average reflectivity and transmissivity, the average of the partial heat fluxes for the generalized problem with internal source of radiation are obtained and represented graphically.

Keywords: Continuously stochastic radiative transfer; Finite participating planar medium; Random variable transformation (RVT) technique; Integral transformation; SPECULAR- AND diffusly-reflecting boundaries; Average partial heat fluxes (search for similar items in EconPapers)
Date: 2015
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:435:y:2015:i:c:p:66-79

DOI: 10.1016/j.physa.2015.04.033

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