Numerical study of magnetohydrodynamic natural convection in a non-Darcian porous enclosure filled with electrically conducting helium gas

Abstract

A theoretical and computational study of MHD natural convection in an isotropic non-Darcian porous medium saturated with electrically conducting helium gas in an enclosure in the presence of heat generation is presented. A Brinkman extended Darcy-Forchheimer model is employed and the working fluid is assumed to be incompressible. The model is non-dimensionalised and converted into pressure-velocity form. The Harlow-Welch marker and cell (MAC) finite difference technique is employed to solve the nonlinear boundary value problem via pressure-vorticity coupling. A parametric investigation of the influence of Grashof number ( Gr), Hartmann magnetic number ( Ha), Darcy number ( Da), and the internal heat generation parameter ( Γ) on streamline and isotherm distributions with Prandtl number ( Pr) is 0.71 (Helium) is conducted. The variation in local Nusselt number along the left and right walls of the computational 2 D enclosure is also studied. Validation house-computational numerical MATLAB code is tests are included. Local Nusselt number is elevated at both left and right walls with greater Darcy number (higher medium permeability) and Grashof number. However, with greater internal heat generation, local Nusselt number magnitudes are enhanced at the left (cold) wall only but suppressed at the right (hot) wall. Increasing magnetic field reduces local Nusselt number at both left and right walls. With increasing magnetic field, the single vortex is strongly distorted and skewed towards the top left and lower right corners of the enclosure. Temperature contours at the left and right wall are however less intense with greater magnetic field effect. The simulations are of relevance to hybrid electromagnetic gaseous fuel cells, magnetic field control of filtration processes and porous media materials processing systems.

Magneto-convective flow through a porous enclosure with Hall current and thermal radiation effects: numerical study

“…The above studies on MHD convection in enclosures generally neglected the inclusion of porous media. Although porous media enclosure flows have been studied previously in the presence of magnetohydrodynamic effects [23][24][25]. Sankar et al [30] presented detailed analysis on impacts of various key parameters on flow and thermal behaviour of three different nanofluids in the annular geometry having finite thickness at the inner cylinder.…”

Conductive Heat Transfer in Materials under Intense Heat Flows

“…In practical calculations, one should limit oneself to the number of members of the series in expressions Equation (32) or (35) sufficient to ensure the required accuracy:…”

“…Methods for creating and using various models of the generalized theory of thermal conductivity can be found in publications [30][31][32][33][34]. A numerical approach to the study of such problems is demonstrated in the article [35].…”

Radiative magneto‐thermogravitational flow in a porous square cavity with viscous heating and Hall current effects: A numerical study of ψ–v scheme

“…The above studies on MHD convection in enclosures generally neglected the inclusion of porous media. Although porous media enclosure flows have been studied previously in the presence of MHD effects, [23][24][25][26][27][28][29] they have not considered the simultaneous presence of Hall currents, viscous dissipation, and radiative transfer. The present numerical investigation is focused on Hall current, viscous dissipation, and thermal radiation effects on laminar 2D MHD flow in a square enclosure embedded with porous.…”