3D simulation using the lattice Boltzmann method of heat transfer in a local with different door positions

¹ LabSIPE, National School of Applied Sciences of El Jadida, Chouaib Doukkali University, El Jadida, Morocco
² LPMAT Laboratory, Physics Department, Faculty of Sciences Ain Chock, Hassan II University, Casablanca, Morocco

^* Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Published online: 22 May 2026

Abstract

This study numerically examines three-dimensional natural convection in a bottom-heated, closed cubic cavity using the lattice Boltzmann method. The computational approach relies on a D3Q15 lattice scheme coupled with a single-time relaxation (SRT) collision operator. The cavity's lateral and top walls are treated as adiabatic surfaces, while two specific areas on the front wall, representing a window and a door, are treated as cold regions. Simulations are performed for a Rayleigh number of 10⁷ and a Prandtl number of 0.71. Key results include the time evolution of the temperature field, temperature profiles along the x, y, and z axes, three-dimensional velocity vector maps, calculations of the local and mean Nusselt numbers on the heated surface, and graphical representations of isothermal contours on different cross-sectional planes. This research provides a robust dataset for the study of three-dimensional natural convection phenomena in a fully enclosed structure with bottom heating.