Kinetic Treatment of Exact Solution of Thermal Radiation Field Affected on a Rarefied Gas in Steady    State.

T. Z. Abdel Wahid

Mathematics and statistics Department, El-Madina Higher Institution of Administration and Technology, El-Madina Academy, Egypt.

Accepted 03 December 2013

Abstract

The studying the influence of a thermal radiation field upon a rarefied neutral gas is introduced. We insert the radiation field effect in the force term of the Boltzmann equation. In a frame co-moving with the fluid, analytically the BGK (Bhatnager- Gross- Krook) model kinetic equation is applied. The problem is studied using Liu-Lees model. We apply the moment method using the linearized form of thermal radiation field to follow the behavior of the macroscopic properties of the gas such as the temperature and concentration. They are substituted into the corresponding two stream Maxwellian distribution functions permitting to investigate the non-equilibrium thermodynamic properties of the system (gas + heated plate). The entropy, entropy flux, entropy production, thermodynamic forces, kinetic coefficients are obtained. We verify the celebrated Onsager’s reciprocity relation for the system. The ratios between the different contributions of the internal energy changes based upon the total derivatives of the extensive parameters are estimated via the Gibbs formula. The results are applied to the Argon gas for definite radiation field intensity corresponding to the plate temperature. Graphics illustrating the calculated variables are drawn to predict their behavior and the results are discussed.

Keywords: Rarefied gas dynamics; Heat transfer; Thermal radiation field; Boltzmann kinetic equation; BGK model; Entropy production; Onsager’s reciprocity relation; Gibb's formula.