A Computational Simulation of Steady Natural Convection in an H-Form Cavity

Abstract

The simulation of natural convection problem based on the Galerkin finite-element method, with the penalty finite-element formulation of the momentum balance equation, is exploited for accurate solutions of equations describing the problem of H-Form cavity differentially heated side walls. The cavity is occupied by the air whose Prandtl number is Pr=0.71, the fluid is assumed to be steady, viscous and incompressible within thermal convection. A numerical investigation has been made for Rayleigh numbers ranging from 10 to 10 6 for three cases of total internal height aspects of H-Form cavity: 0%, 50%, and 85%. Firstly, the goal is to validate the numerical code used to resolve the equations governing the problem of this work. For that, we present a comparison between the profiles at the point (0.5, 0) for the u-component, and u-component obtained in previous work for simple square cavity. Further, a comparison of the averaged Nusselt number with previous works for simple square cavity is realized in order to ensure the numerical accuracy, and the validity of our considered numerical tool. Secondly, the objective is to investigate on the hydrodynamic effects of Rayleigh number for different total internal height aspects of H-Form cavity on the dynamics of natural convection. Shortly after, the ambition is to assess the heat transfer rate for different Rayleigh number for three cases of internal height aspects.

MHD free convection with Joule heating and entropy generation inside an H-shaped hollow structure

“…Similar research was conducted by Keramat et al [ 19 ] regarding free convection in an H -shaped chamber filled with air and containing porous fins. Loukili et al [ 20 ] studied the free convective flow of air within an H -shaped chamber using the Galerkin finite element approach. They demonstrated that higher interior heights resulted in less efficient heat transmission.…”

“…The applications of H -shaped chambers in thermal and fluid engineering have garnered significant attention in the existing literature, as evidenced by numerous studies [ [16] , [17] , [18] , [19] , [20] , [21] ]. Despite the extensive research on H -shaped chambers, a critical gap exists in exploring entropy production resulting from MHD free convection within such chambers, particularly when considering the variable dimensions and the impact of Joule heating.…”

The Numerical Diffusion Effect on the CFD Simulation Accuracy of Velocity and Temperature Field for the Application of Sustainable Architecture Methodology

“…However, the optimal states (parallel flow) can only be achieved by calculating straight sections of pipeline without the obstacles using the hexahedral cells [30]. The direction of the flow is always in the general direction with respect to the cell walls (hexahedral, tetrahedral, and polyhedral) in the most flows [31].…”