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

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

Copyright: © 2017 |Pages: 19
DOI: 10.4018/978-1-68318-006-7.ch003
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Mathematical Formulations Of The Problem

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

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