Thermal Lattice Boltzmann Model for Nonisothermal Gas Flow in a Two-Dimensional Microchannel
Youssef Elguennouni, Mohamed Hssikou, Jamal Baliti, Mohammed Alaoui
Abstract
In this paper, the Thermal Lattice Boltzmann Method (TLBM) is used for the simulation of a gas microflow. A 2D heated microchannel flow driven by a constant inlet velocity profile <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:msub><mml:mrow><mml:mi>U</mml:mi></mml:mrow><mml:mrow><mml:mtext>in</mml:mtext></mml:mrow></mml:msub></mml:mrow></mml:math> and nonisothermal walls is investigated numerically. Two cases of micro-Poiseuille flow are considered in the present study. In the first case, the temperature of the walls is kept uniform, equal to zero; therefore, the gas is driven along the channel under the inlet parameters of velocity and temperature. However, in the second one, the gas flow is also induced by the effect of temperature decreasing applied on the walls. For consistent results, velocity slip and temperature jump boundary conditions are used to capture the nonequilibrium effects near the walls. The rarefaction effects described by the Knudsen number, on the velocity and temperature profiles are evaluated. The aim of this study is to prove the efficiency of the TLBM method to simulate Poiseuille flow in case of nonisothermal walls, based on the average value of the Nusselt number and by comparing the results obtained from the TLBM with those obtained using the Finite Difference Method (FDM). The results also show an interesting sensitivity of velocity and temperature profiles with the rarefaction degree and the imposed temperature gradient of the walls.