Rarefied gas flow between moving plates with heat transfer

Abstract

The state of a single-species monatomic gas under rarefied conditions remains a fundamental research problem with important applications. The most powerful approaches to handle this type of flows is the Direct Simulation Monte Carlo method and the kinetic theory. Here, we apply the latter one. In particular, we apply the non-linear Bhatnagar-Gross-Krook (BGK) and Shakhov (S) kinetic model equations, subject to Maxwell diffuse boundary conditions, to solve the one dimensional compressible Couette flow problem coupled with heat transfer. The intermolecular collisions are modeled by the inverse power law model. The computational scheme is based on finite differencing in the physical space and on the discrete velocity method in the molecular velocity space.. The numerical solution is valid in the whole range of the Knudsen number. Its accuracy has been tested in several ways including the recovery of the corresponding analytical solutions at the free molecular and hydrodynamic regimes and the successful comparison with previous results. In all cases excellent agreement has been demonstrated. In addition, a detailed comparison between the simple BGK model with the more sophisticated Shakhov model, clearly indicates that the BGK model remains a reliable choice at least for engineering purposes. Also, the application of the hard sphere and Maxwell molecular models for intermolecular interaction shows that the intermolecular potential model does not significantly influence the flow properties and characteristics. Results for the bulk quantities of velocity, temperature, vertical and horizontal heat flux, density, pressure and shear stress have been presented in terms of the three dimensionless parameters describing the flow configuration, namely the rarefaction parameter, the temperature ratio and the relative velocity of the plates. Several interesting issues related to the combined momentum and heat transfer effects have been studied. It has been found that the velocity slip and the temperature jump are larger at the hot plate compared to the ones at the cold plate. Moreover, the pressure distribution is a function of the spatial variable in the transition regime. This is also due to the rarefaction of the flow. Even more, the flow is characterized by the presence of an horizontal axial heat flux, which increases as the rarefaction of the gas is increased and which is present only when both velocity and temperature gradients exist in the flow. This is a non-equilibrium cross effect and it vanishes at the hydrodynamic limit.