Formulation of space-angular fractional radiative transfer equation in participating finite slab clumpy media

Abstract

Space-angular fractional radiative transfer equation has been derived depending on the invariance of the functional potential and the Euler–Lagrange functional of the radiative-transfer intensity. Pomraning–Eddington technique is employed to unzip the space-fractional radiative transfer through a clumpy medium. The medium is considered as an anisotropic scattering participating finite slab with specular reflecting boundaries. The fractional differential operator is taken in terms of the Jumarie Riemann–Liouville representation. The resultant space-fractional equation has diffusion parameter depends on both the single scattering albedo and the anisotropic parameter of the medium. Laplace transformation method is used to solve the obtained space-fractional differential equation, whose solution is obtained in terms of the Mittag–Leffler function. Numerical calculations are carried out to investigate the effects of the fractional exponent and the other radiative-transfer parameters on the radiation density and net flux through the medium. In addition, the reflectivity and transmissivity from the medium boundaries are calculated and represented graphically.

KEYWORDS:

• Fractional radiative transfer equation
• anisotropic radiative scattering
• Jumarie Riemann–Liouville fractional differential operator
• Pomraning–Eddington technique
• Mittag–Leffler function
• participating clumpy media

Disclosure statement

No potential conflict of interest was reported by the author(s).