Combined Effect of Rotation and Magnetic Field on the Thermal Convection in a Layer of Maxwellian Visco-Elastic Nanofluid

Combined Effect of Rotation and Magnetic Field on the Thermal Convection in a Layer of Maxwellian Visco-Elastic Nanofluid

Copyright: © 2017 |Pages: 19
DOI: 10.4018/978-1-68318-006-7.ch004
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Mathematical Formulations Of The Problem

The Physical Problem

In this chapter we shall investigate the combined effect of rotation and 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:

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 rotating uniform about z-axis with angular velocity Ω(0, 0,Ω) and is acted upon by a uniform vertical magnetic field H(0, 0, H). Fluid layer also acted upon by a gravity force g(0, 0,-g) and 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

The following analysis is confined to a narrow and very long fluid layer. Since the significance of the centrifugal acceleration depends on the offset distance from the centre of rotation therefore for the layer which is adjacent to the rotation axis (i.e. x = 0, y = 0), the impact of the centrifugal acceleration to be zero. Due to the fact that here a narrow and very long fluid layer is considered, centrifugal effects can be neglected in the momentum equation.

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