On the irreversible thermodynamics of an electron gas in the vicinity of a suddenly moving rigid plate
Department of Mathematics, Faculty of Science, Monoufiya University, 32511, Shebin-Elkom, Egypt
Published online: 28 May 2012
The Rayleigh flow problem is studied in the framework of the Bhatnager-Gross-Krook (BGK) approximation to the Boltzmann equation supplemented by Maxwell’s equations. The behavior of a rarefied electron gas extracted from noble gases is investigated, considering the method of moments with a two-sided distribution function of Liu and Lees type. Exact solutions of the fourth-order linear homogeneous differential equations, based on the method of the separation of variables for both the mean flow velocity and the shear stress are obtained in terms of the coordinate y and time t with suitable boundary conditions. The advantage of dealing with the Boltzmann equation permits to consider the principles of the irreversible thermodynamics near-equilibrium, by substituting the calculated distribution functions in the formulae of Boltzmann’s H-theorem to evaluate entropy and entropy production. The different contributions of the forces exerted on the system change its internal energies. They are expressed via the Gibbs formula within which the diamagnetic properties of the system are predicted.
© Società Italiana di Fisica and Springer-Verlag Berlin Heidelberg, 2012