Receive a 20% Discount on All Purchases Directly Through IGI Global's Online Bookstore

DOI: 10.4018/978-1-68318-006-7.ch010

Top## Mathematical Formulations Of The Problem

### The Physical Problem

### Assumptions

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 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 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.

Search this Book:

Reset