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Existence theory for a one-dimensional problem arising from the boundary layer analysis of radiative flows

2011; Elsevier BV; Volume: 53; Issue: 8 Linguagem: Inglês

10.1016/j.pnucene.2011.06.005

1878-4224

F.S. de Azevedo, M. J. Thompson, Esequia Sauter, Marco T. Vilhena,

Gas Dynamics and Kinetic Theory

We consider a simplified system of equations which models the transfer of energy with conductive, convective and radiative effects inside a convex region filled with a compressible fluid whose velocity field is known. The asymptotic analysis for positive but small distance from an optically thick medium leads to a one-dimensional system of differential equation which couples the temperature and the radiative intensity. We show that this system obeys a conservation law and this feature is explored in order to reduce the problem to a single one-dimension transport equation with anisotropic scattering. This equation admits a formulation in terms of integral operators in a suitable function space which allows us to establish the existence of a solution and infer its behavior far from the boundary. We also provide numerical simulations and comparison with the theoretical results which we have shown in order to validate our methodology.