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DOI: 10.4018/978-1-68318-006-7.ch002

Top## Mathematical Formulations Of The Problem

### The Physical Problem

In this chapter we shall investigate the effect of rotation 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 Maxwell 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 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 T_{0} and T_{1} (T_{0} > T_{1}). The normal component of the nanoparticles flux has to vanish at an impermeable boundary and the temperature T is taken to be T_{0} at z = 0 and T_{1} at z = d, (T_{0} > T_{1}) as shown in Figure 1. The reference scale for temperature and nanoparticles fraction is taken to be T_{1} and φ_{0} respectively_{.}

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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