The Horton–Rogers–Lapwood problem in a Jeffrey fluid influenced by a vertical magnetic field

Abstract

In this work, the impact of a magnetic field on the onset of the Jeffrey fluid convection through a porous medium is investigated theoretically. The layer of Jeffrey fluid is heated from below and is operated by a consistent upright magnetic field. Using the normal mode procedure, a dispersion equation is obtained analytically and this dispersion relation is utilized to derive the critical conditions for the onset of stationary and oscillatory patterns of convection. The results reveal that the stability of the system diminished with the augmentation of the Jeffrey parameter, while an opposite result is obtained with magnetic field parameters (magnetic Chandrasekhar–Darcy number and magnetic Prandtl number). The size of convective cells decreases with Jeffrey and magnetic field parameters. It is also found that the existence of a magnetic field indicates the possibility of the survival of the oscillatory mode of convection.

Magnetohydrodynamics Solver for a Two-Phase Free Surface Flow Developed in OpenFOAM

“…Here F o corresponds to the value of the initial central shaft current I shaft and pressure is assumed to be constant and equal to p o . Substituting Equation (24) into Equation ( 23) leads to a specific form of Grad-Shafranov equation:…”

“…Magnetic target configuration has been calculated by solving Grad-Shafranov equation for the curved shape of the cavity. As in the previous tests, magnetic configuration has been defined by Equation (24), with F o = 0.4 T m (I shaft = 2 MA) and ψ max = 0.1 Wb/rad. Injected magnetic target are shown by ψ contours with the last closed ψ surface emphasized with the green color.…”

“…One of the main messages coming out of those works is that the approach of extending existing solvers within OpenFOAM toward MHD solvers is promising. We also hope that the new solver has a potential in the future to be applied and complement other theoretical and reduced-order studies which include magentic fields, such as in recent works [23,24], for example. The rest of the paper is organized as follows.…”

Numerical simulation of 3D Darcy–Forchheimer fluid flow with the energy and mass transfer over an irregular permeable surface

“…Kumar et al 23 discussed the influence of an applied magnetics flux on an irregular 2D Jeffrey fluid flow. A theoretical investigation is carried out by Yadav et al 24 to determine the upshot of a magnetic flux and mixed convection on the Jeffrey fluid flow. The results show that increasing the Jeffrey fluid parameter reduces system stability while increasing magnetic field parameters has the reverse effect.…”

Casson nanofluid performance on MHD convective flow past a semi‐infinite inclined permeable moving plate in presence of heat and mass transfer

“…Yadav 37 studied the impact of chemical reactions on the convective heat transport in nanofluid occupying in porous enclosures. Yadav et al 38 have studied the impact of a magnetic field on the onset of the Jeffrey fluid convection through a porous medium investigated theoretically. Yadav et al 39 have studied Hybrid nanomaterial and instability analysis of convective flow in permeable media.…”