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

TL;DR

This paper presents a numerical simulation of steady natural convection in an H-form cavity using finite-element methods, analyzing effects of Rayleigh number and cavity aspect ratios on flow and heat transfer.

Contribution

It introduces a validated finite-element simulation approach for H-form cavities and explores the impact of aspect ratio and Rayleigh number on convection and heat transfer.

Findings

Flow and heat transfer depend on Rayleigh number and cavity aspect ratio.

Numerical results agree with previous studies for validation.

Heat transfer rate varies significantly with cavity geometry and Rayleigh number.

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.