2007/02/22 by Rabindra Nath Das, Das, Rabindra Nath
Engineering · Environmental Science · Physics and Astronomy · #Astrophysics (astro-ph) #Atmospheric aerosols and clouds #Calibration and Measurement Techniques #FOS: Physical sciences #Radiative Heat Transfer Studies #astro-ph
paper · pdf · doi:10.48550/arxiv.astro-ph/0702602
42 pages submitted to JMAA Feb 20 2007 ref no JMAA-07-556
arxiv created 2007/02/22 · openalex publication_date 2007/02/22 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In Radiative transfer, the intensities of radiation from the bounding faces of finite slab are obtained in terms of X- and Y- functions of Chandrasekhar . Those are non linear non homogeneous coupled integral equations . Those non linear integral equations are meromorphically extended to the complex plane to get linear non homogeneous coupled integral equations. Those linear integral equations are converted to linear singular integral equations with. linear constraints . Those singular integral equations are then transformed to non homogeneous Riemann Hilbert Problems. Solutions of those Riemann Hilbert Problems are obtained using the theory of linear singular integral equations to decouple those X- and Y- functions. New forms of linear non homogeneous decoupled integral equations are derived for X- and Y- function separately with new linear constraints. Those new decoupled integral equations are transformed into linear singular integral equations to get two new separate non homogeneous Riemann Hilbert problems and to find solutions in terms of one known N- function and five new unknown functions in complex plane . All five functions are represented in terms of N-functions using the theory of contour integration >. Those X- and Y- functions are finally expressed in terms of that N - function and also in terms of H- functions of Chandrasekhar and of integrals in Cauchy principal value sense in the complex plane and real plane. both for conservative and non conservative cases . The H - functions for semi infinite atmosphere are derived as a limiting case from the expression of X- function of finite atmosphere.