Numerical analysis of Poiseuille and thermal transpiration flows of a real gas confined between two parallel plates

The Poiseuille and thermal transpiration flows of a real gas confined between two parallel plates are investigated based on the Enskog–Vlasov kinetic equation under the diffuse reflection boundary condition. In contrast to an ideal gas, the gradients of pressure and normal stress components in the flow direction, as well as the density, are nonuniform in the direction normal to the plates. The net mass flows and the profiles of flow velocity and heat flow are obtained for various Knudsen numbers, molecular sizes, and magnitudes of the long-range intermolecular attractive force. Depending on the magnitude of the attractive force, the nondimensional net mass flow of the thermal transpiration flow exhibits a local minimum at an intermediate Knudsen number, analogous to the Knudsen minimum known for the Poiseuille flow. Both in the Poiseuille and thermal transpiration flows, the flow velocity and heat flow are enhanced due to the intermolecular attractive force, compared to the case of the Enskog equation for a purely repulsive hard-sphere dense gas. Unless the molecular diameter is sufficiently small compared to the distance between the plates, the enhancement is observed even at high Knudsen numbers, where the volume fraction of molecules is small. This occurs because, although the attractive force itself is small at high Knudsen numbers, its influence on molecules with small velocity components normal to the boundary remains significant. Due to the effect of intermolecular attractive force, the velocity distribution function of gas molecules becomes discontinuous not only on the boundary but also in the gas.