Effect of magnetic field on the onset of thermal convection in a Jeffery nanofluid layer saturated by a porous medium: free-free, rigid-rigid and rigid-free boundary conditions

Abstract

The effect of the magnetic field on the onset of thermal convection in a porous layer saturated by Jeffrey nanofluid is studied. Three distinct boundary conditions are considered to be free-free, rigid-rigid and rigid-free boundaries. The model used for Jeffrey nanofluid includes the effect of Brownian motion and thermophoresis. The normal mode analysis as well as the Galerkin first approximation technique is used. The effects of the Rayleigh number of nanoparticles, Lewis number, modified diffusivity ratio, Jeffery parameter, porosity and Chandrasekhar number are investigated analytically and graphically. It is discovered that the Chandrasekhar number, Lewis number and modified diffusivity ratio have a stabilizing effect while the Jeffery parameter, nanoparticles Rayleigh number and porosity have a destabilizing effect. This study induces the effect of Chandrasekhar number and Jeffrey nanofluid. We have analyzed that Chandrasekhar number produces a stabilizing effect on the onset of convection i.e. it delays the onset of convection whereas the Jeffrey parameter which comes from Jeffrey nanofluid shows the destabilizing effect on the onset of convection i.e. it accelerates the onset of convection. The influence of a magnetic field on the commencement of nanofluid convection is significant in magnetohydrodynamic power generators, electrical equipment, petroleum reservoirs, nuclear reactors, biochemical engineering, chemical engineering and geophysics.

Keywords

• Magnetic field; thermal convection; Jeffery nanofluid; normal mode technique