Thermal Convection in a Layer of Maxwellian Visco-Elastic Nanofluid with Hall Current

The Physical Problem

The physical configuration of the problem to be considered as:

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 gravity force g(0, 0,-g) and a uniform vertical magnetic field H (0, 0, H). 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