Kinetic Theory Analysis of Temperature Jump in a Polyatomic Gas

Abstract

A kinetic theory analysis of the temperature jump at the wall and the temperature distribution near the wall in polyatomic gases has been made. The collision term in the Boltzmann equation is represented by a classical (BGK-type) polyatomic model. The problem is linearized by considering small temperature and density variations over their respective mean values, which leads to three simultaneous singular linear integral equations. For the solution of the problem, a direct numerical method is used. The integral equations are reduced to a set of simultaneous linear equations for discrete values of the dependent variables by approximating the integrals with suitable quadrature formulas. This analysis shows that the temperature jump can be expressed as ΔT = (1/Pr)λ(dT/dy′)∞χ(l, β, αt, αi) , where l denotes the effective number of internal degrees of freedom, and αt and αi are the thermal accommodation coefficients for the translational and internal energy transfers, respectively. The parameter β is inversely proportional to N, the number of collisions to achieve equilibrium between the translational and internal modes of molecular motion. The results show that the temperature jump coefficient is, to good approximation, the same as that for the monatomic case only if αi = αt = α. In this case ΔT = [(2.0−0.83α)/α][2γ/(γ+1)](λ/Pr) (dT/dy′)∞.