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.