Computational study of non-similar magneto-convection from an isothermal surface in saturated porous media with induction effects

Beg, OA; Vasu, B; Beg, TA; Leonard, HJ; Jouri, W; Kadir, A; Gorla, RSR

Abstract

We study theoretically and numerically the forced convection magnetohydrodynamic (MHD) boundary layer flow of an
electrically conducting fluid along a non-conducting isothermal wall adjacent to a porous medium, with magnetic field
aligned with the plate direction. Induced magnetic field effects are incorporated. The transformed hydrodynamic, thermal
and magnetic boundary layer equations are solved using the Chebyschev spectral collocation method with a MATLABbased code, MAGNASPEC. Super-Alfven flow is considered for which the magnetic force parameter () has values less
than unity, following the approach of Glauert [J. Fluid Mechanics, 10, 276-288 (1956)). The effects of Darcian porous drag
force parameter (ND), magnetic Prandtl number (Prm), magnetic force number (), Prandtl number (Pr) and also various
thermal boundary conditions at the wall, on the distribution of dimensionless velocity (f/), dimensionless induced
magnetic field (g/ i.e. gradient of the magnetic stream function, g), dimensionless temperature (), shear stress
function (
2
f/
2
), and wall temperature gradient function (/), are investigated. Increasing ND values decelerate the
flow and decrease temperatures through the boundary layer but increase the induced magnetic field values. Increasing
magnetic Prandtl number (Prm) slightly reduces the velocity in the boundary layer and similarly has a weak effect in
reducing the wall shear stress. No noticeable response is computed for the effect of magnetic Prandtl number on the
temperature distribution; however, increasing Prm values are found to reduce magnetic induction values near the plate
surface but enhance them further towards the freestream. An increase in the magnetic force number, (which expresses
the ratio of the square of the Alfven speed to the free stream velocity) is shown to fractionally reduce the shear stress but
considerably increases the induced magnetic field values along the entire plate length i.e. with -coordinate. Negligible
modification is witnessed for the surface temperature gradient (/) with a large increase in  from 0.01 to 0.5. The
present spectral solutions are also benchmarked with Sparrow-Quack-Boerner local non-similarity method (LNM) and
He’s variational iteration method (VIM) and furthermore demonstrate excellent correlation with steady state nonpermeable (purely fluid) finite difference solutions in the literature. Applications of the study arise in materials processing
and plasma aerodynamics.

Citation

Beg, O., Vasu, B., Beg, T., Leonard, H., Jouri, W., Kadir, A., & Gorla, R. (in press). Computational study of non-similar magneto-convection from an isothermal surface in saturated porous media with induction effects. Computational Thermal Sciences,

• Journal Article Type: Article
• Acceptance Date: Apr 29, 2021
• Deposit Date: Apr 29, 2021
• Journal: Computational Thermal Sciences
• Print ISSN: 1940-2503
• Electronic ISSN: 1940-2554
• Publisher: Begell House
• Publisher URL: https://www.begellhouse.com/journals/computational-thermal-sciences.html