Heat transfer between parallel plates with arbitrary surface accommodation

Elementary solutions of the coupled pair of integrodifferential equations arising from the decomposition of the linearized BGK equation in the kinetic theory of gases are used to solve the problem of heat transfer between parallel plates with arbitrary surface accommodation. A coupled pair of Fredholm equations is derived, and rapidly convergent iterative solutions are constructed. These solutions are then used to obtain accurate values of the heat flux between the plates and the temperature and density profiles, for various values of the accommodation coefficient and inverse Knudsen number. Numerical results for the heat flux are presented and compared to existing variational solutions. Also, explicit results for the temperature and density profiles are given.