  Citation: Baliti, J.; Elguennouni, Y.; Hssikou, M.; Alaoui, M. Simulation of Natural Convection by Multirelaxation Time Lattice Boltzmann Method in a Triangular Enclosure. Fluids 2022, 7, 74. https://doi.org/10.3390/ fluids7020074 Academic Editor: Mehrdad Massoudi Received: 17 December 2021 Accepted: 25 January 2022 Published: 10 February 2022 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affil- iations. Copyright: © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). fluids Article Simulation of Natural Convection by Multirelaxation Time Lattice Boltzmann Method in a Triangular Enclosure Jamal Baliti 1, * , Youssef Elguennouni 2 , Mohamed Hssikou 3 and Mohammed Alaoui 2 1 Polydisciplinary Faculty, Sultan Moulay Slimane University, Beni Mellal 23000, Morocco 2 Faculty of Sciences, Moulay Ismail University, Meknes 50000, Morocco; y.elguennouni@edu.umi.ac.ma (Y.E.); m.alaoui@fs.umi.ac.ma (M.A.) 3 TE Laboratory, Faculty of Sciences, Ibn Zohr University, Agadir 80000, Morocco; m.hssikou@uiz.ac.ma * Correspondence: jamal.baliti@usms.ma Abstract: The natural convection of incompressible flow confined within an enclosed right-angled triangular and isosceles cavity was investigated numerically using the multirelaxation time lattice Boltzmann method (MRT-LBM). According to the left and inclined walls thermal boundary conditions, two cases were considered in this study. In the first case, the inclined side of the enclosure was adiabatic, and the horizontal wall was heated, while the left one was kept at a cold temperature. However, the states of the left and inclined walls were interchanged in the second case. As the flow is only transported under the convection force, this study was carried out for the Rayleigh number ranging from Ra = 10 3 to 10 6 . The effects of the Rayleigh number on velocity and temperature profiles, streamlines, isotherms, and average Nusselt number were investigated. The position of cold and adiabatic walls had a great effect on the results. The results obtained are in good agreement with those of the literature and show the robustness of the MRT-LBM approach. In both cases, the heat-transfer rate increases with the increase in the Rayleigh number. Keywords: lattice Boltzmann; MRT; convection; triangular cavity; Rayleigh number; Nusselt number 1. Introduction Natural convection in enclosed cavities in two-dimensional [ 1, 2] or in three-dimensional [ 3, 4] continues to captivate researchers’ interest, owing to its large number of engineering appli- cations. By understanding this phenomenon, the energy transfer can be well controlled, and the energy overload can be removed in time to protect the equipment. The heat removal must be in case of the use of electrical and electronic equipment, solar collec- tors, and nuclear reactor design [5,6]. The books of Bejan [7] and Yang [8] summarize a significant portion of the literature on this topic, and they have dealt extensively with heat-transfer convection in the cases of external/internal natural convection in laminar, turbulent, and free flow regimes. Numerous of the previous researches on natural convection have focused on rectan- gular enclosures with a vertical (Rayleigh–Benard convection) or a horizontal gradient of temperature [9,10], while others have studied rectangular cavities partially heated or cooled [11,12]. Natural convection in triangular enclosures [13–15] has been treated also due to its widespread use in many industrial and domestic systems such as building roofs and solar power, etc. Yesiloz et al. [16] and Oztop et al. [17] have studied experimentally the natural convection of water and air, respectively, in a right-angled triangular cavity. Both papers compared their experimental results with numerical solutions. Yesiloz et al. used the FLUENT software, while Oztop et al. used the governing equations based on a stream function–vorticity and solved them with the finite-difference method. The single relaxation time lattice Boltzmann method (SRT) has been used as an alternative CFD approach to study the natural convection of air and water in a triangular cavity [18,19]. The results are shown for different inclination angles of the cavity. Ridouane et al. [20] treated turbulent Fluids 2022, 7, 74. https://doi.org/10.3390/fluids7020074 https://www.mdpi.com/journal/fluids