Effect of Vertical Magnetic Field on the Onset of Double Diffusive Convection in a Horizontal Porous Layer with Concentration Based Internal Heat Source

Abstract

This study considers the effects of concentration based internal heat and vertical magnetic field on the onset of double diffusive convection in a horizontal porous layer using normal mode analysis. The normal mode analysis is used to find solutions for the fluid variables, the critical wave number and the critical Rayleigh number for the onset of convection with free-free boundaries. The results obtained are displayed graphically and in tables. The results show that the concentration based internal heat, , hastens the onset of instability while the magnetic field, , and solutal Rayleigh number, , delays the onset of instability in the system for stationary and oscillatory convections. The influence of Lewis number, , and porosity, , is also presented.

Effect of Vadasz Number on Magnetoconvection in a Darcy Porous Layer with Concentration Based Internal Heating

“…where is the reference density Following many researchers [16,21] and [22] and the assumptions made, the governing equations become…”

“…Substituting Equation (19) into Equations (13) - (16) and the boundary condition (17) and (18) yield the equations governing the basic state as…”

“…where ⃗, , and are the perturbed quantities over their equilibrium counterparts and are assumed small. On substituting Equation 28into Equations (13)−(16) and the boundary condition (17) and 18, and then using Equation (28), we obtain the linearized equations as ∇ ⃗ . ⃗ = 0 (29)…”

“…Thermal instability in a porous medium that is heated and salted from below under various conditions has equally received significant attention. The work of Israel-Cookey et al [16] is a classic example, where the effect of vertical magnetic field on the onset of double diffusion convection in a horizontal porous layer with convection based internal heat source is studied. Soret and magnetic field effect on thermosolutal convection in a porous medium with concentration based internal heat was considered by Isreal-Cookey et al [17].…”

“…The work of Israel-Cookey et al [16] is a classic example, where the effect of vertical magnetic field on the onset of double diffusion convection in a horizontal porous layer with convection based internal heat source is studied. Soret and magnetic field effect on thermosolutal convection in a porous medium with concentration based internal heat was considered by Isreal-Cookey et al [17]. Cross-diffusion and reaction effect on double diffusive convection in a porous medium with concentration based internal heat source was studied by many researchers [18,19,20].…”