Research Article ThermalLatticeBoltzmannModelforNonisothermalGasFlowin a Two-Dimensional Microchannel YoussefElguennouni , 1 MohamedHssikou , 2 JamalBaliti , 3 andMohammedAlaoui 1 1 Moulay Ismail University of Meknes, Faculty of Sciences, Morocco 2 University of Ibn Zohr, Faculty of Sciences, Agadir, Morocco 3 University of Sultan Moulay Slimane, Polydisciplinary Faculty, Beni Mellal, Morocco Correspondence should be addressed to Youssef Elguennouni; y.elguennouni@edu.umi.ac.ma Received 23 July 2019; Revised 31 December 2019; Accepted 31 January 2020; Published 19 March 2020 Academic Editor: Miguel Cerrolaza Copyright © 2020 Youssef Elguennouni et al. is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. In this paper, the ermal 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 U in 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. e rarefaction eﬀects described by the Knudsen number, on the velocity and temperature proﬁles are evaluated. e 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). e results also show an interesting sensitivity of velocity and temperature proﬁles with the rarefaction degree and the imposed temperature gradient of the walls. 1.Introduction Microdevice technology has shown an interesting growth in the last few decades. In order to understand the behavior and the physics of gas ﬂows in such micro-electro-mechanical systems (MEMS) better, researchers are focused on several approaches. Kinetically, such ﬂows are governed by the Boltzmann equation, in which the solution is better ap- proximated by direct simulation of Monte Carlo (DSMC) [1] and dynamic molecular (MD) [2]. To save the computation time, other alternatives have been used mainly in the slip regime such as moment equations [3]. To combine the advantages of both approaches, the lattice Boltzmann method (LBM) becomes recently a powerful tool of such applications, and this approach is a hybrid method which combines the kinetic description given by the Boltzmann equation and the classical computational ﬂuid dynamics (CFD), mesoscopic approach. Several attempts are made by scientists to improve the LBM approach and extend its ability to simulate more complex geometry ﬂows [4–6]. is method is used to simulate diﬀerent types of ﬂows: the Rayleigh-Benard convection [7], micro-Poiseuille ﬂow [8–12], micro-Couette ﬂow [11, 12], Lid-driven cavity [4, 12], etc. However, the study of such ﬂow needs a good choice and implementation of the boundary conditions (BC), which is a crucial step in the LBM simulation. In this context, diﬀerent BC are tested in the literature for diﬀerent problems. Nie et al. [13] used the bounce-back boundary conditions, which is compared with the DSMC method [14]. Lim et al. [15] employed specular reﬂection and a second-order extrapolation scheme to capture the slip Hindawi Mathematical Problems in Engineering Volume 2020, Article ID 8638494, 13 pages https://doi.org/10.1155/2020/8638494