Solution of the Krook kinetic equation model and non-equilibrium thermodynamics of a rarefied gas affected by a non-linear thermal radiation field

Thermodynamic Study of the Unsteady BGK Model for a Binary Gas Mixture Affected by a Nonlinear Thermal Radiation Field

“…The gas mixture fills the upper half of the space ( 0 y  ), which is bounded by an infinite immobile flat plate (y=0), in a uniform pressure S P [2,13]. The plate is heated suddenly.…”

“…The fresh portions of gas are brought into the neighborhood of the source of heat, carrying their heat with them into other regions [25]. We assume that the temperature of the upward going gas particles is 1 T  , while the temperature of the downward going gas particles is 2 T  [13,26]. The corresponding concentrations are 1 n  and 2 n  .We use the Liu-Lees model of the two-stream Maxwell distribution function near the plate [17,27] for particles of the  type, which can be represented as:…”

“…There are very few articles in the literature concerning this topic [3][4][5][6][7][8][9], compared to the huge amount of papers in the case of a single gas; see e.g. [10][11][12][13][14][15][16].…”

“…The magnitude of radiative heat fluxes can have profound effects on combustion performance and environmental impact. For this purpose, Abourabia and Abdel Wahid [13], have introduced a new approach for studying the influence of a thermal radiation field upon a rarefied neutral gas. This idea was applied to a steady problem of the half space filled by a neutral gas specified by a flat rested heated plate.…”

“…Now, we have to solve two systems of partial differential equations (one for each component of the gas mixture) instead of one system of ordinary differential equations as we done before in [13].…”