Double Diffusive Convection in a Layer of Maxwellian Visco-Elastic Nanofluid

Double Diffusive Convection in a Layer of Maxwellian Visco-Elastic Nanofluid

Copyright: © 2017 |Pages: 20
DOI: 10.4018/978-1-68318-006-7.ch010
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Mathematical Formulations Of The Problem

The Physical Problem

In this chapter we shall investigate the double diffusive 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 acted upon by 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

Assumptions

The mathematical equations describing the physical model are based upon the following assumptions:

  • 1.

    Thermophysical properties of fluid expect for density in the buoyancy force (Boussinesq Hypothesis) are constant,

  • 2.

    The fluid phase and nanoparticles are in thermal equilibrium state and thus, the heat flow has been described using one equation model,

  • 3.

    Dilute mixture,

  • 4.

    Nanoparticles are spherical,

  • 5.

    Nanoparticles are non-magnetic,

  • 6.

    No chemical reactions take place in fluid layer,

  • 7.

    Negligible viscous dissipation,

  • 8.

    Radiative heat transfer between the sides of wall is negligible when compared with other modes of the heat transfer,

  • 9.

    Nanofluid is incompressible, electrically conducting, Newtonian and laminar flow,

  • 10.

    Each boundary wall is assumed to be impermeable and perfectly thermal conducting,

  • 11.

    The nanoparticles do not affect the transport of the solute.

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