Thermal Convection in a Layer of Maxwellian Visco-Elastic Nanofluid in the Presence of Vertical Magnetic Field

The Physical Problem

In this chapter we shall investigate the effect of magnetic field on the onset of thermal convection in a horizontal layer Maxwellian visco-elastic nanofluid. The physical configuration of the problem to be considered as

Consider an infinite horizontal layer of Maxwellian visco-elastic nanofluid of thickness ‘d’ bounded by horizontal boundaries z = 0 and z = d. A Cartesian coordinate system (x, y, z) is chosen with the origin at the bottom of the fluid layer and the z- axis normal to the fluid layer. Fluid layer is acted upon by a uniform vertical magnetic field H(0, 0, H) and is acted upon by a gravity force g(0, 0,-g). Fluid layer is heated from below in such a way that horizontal boundaries z = 0 and z = d respectively maintained at a uniform temperature T₀ and T₁ (T₀ > T₁). The normal component of the nanoparticles flux has to vanish at an impermeable boundary and the temperature T is taken to be T₀ at z = 0 and T₁ at z = d (T₀ > T₁) as shown in Figure 1. The reference scale for temperature and nanoparticles fraction is taken to be T₁ and φ₀ respectively_.

Figure 1.

Physical configuration of the problem