Modified lattice Boltzmann solution for non-isothermal rarefied gas flow through microchannel utilizing BSR and second-order implicit schemes

Thermal microscale gas flow was simulated into a coplanar microchannel was simulated at a broad range of Knudsen numbers. Attempts were made to improve the accuracy of slip velocity on walls using a modified model with two relaxation times based upon the mesoscopic method. The temperature jump of fluid flow at the wall was captured by a model with a single relaxation time using a second-order implicit method. The Zou–He boundary conditions were employed at both inlet and outlet boundaries, and bounce-back/specular reflection distribution functions were applied to the impermeable walls. The non-equilibrium distribution functions were also used as the inlet temperature boundary condition. A fully developed temperature profile was considered at the microchannel outlet. A pressure ratio of 2 was considered in the simulations, and various parameters such as dimensionless pressure, pressure deviation from the linear pressure, dimensionless velocity at various Knudsen numbers, centerline velocity and slip velocity of the fluid, centerline temperature and fluid temperature on the wall, Nusselt number with changing Knudsen and Prandtl numbers, parameter k along the microchannel length and Cf·Re values were evaluated in the slip and transition flow regimes. The results of the direct simulation Monte Carlo were used to evaluate the correctness of the numerical model. The consistency of the two methods indicated the accuracy of the proposed method.