Equation Of Volumetric Nanoparticle Fractions

Because of the static configuration is a stable one, in the absence of streaming, the density of the upper fluid be lighter than the density of the lower one. The basic unperturbed flows have uniform velocities and . The two fluids are dielectrics and having the uniform dielectric constants and . The two fluids are influenced by an oblique electric field at the interface between the two media, according to:

(2.1) where is the unit vector along the direction, and is the inclination angle between the fields and the axis.
We shall assume that there are no volumes charges present in the bulk of the two fluids. Also, there are no surface charges exist at the surface …show more content…
(2.3)
The equations of motion, heat and volumetric nanoparticle fraction are written in both regions as follows [22]:
1- In the Porous Region (1):
The incompressibility condition yields . (2.4)
The conservation of momentum requires . (2.5)
The conservation of energy yields (2.6)
The equation of the volumetric nanoparticle fraction is given …show more content…
the fluid temperature, is the nanoparticle volume fraction, is the Brownian diffusion coefficient, is the thermophoretic diffusion coefficient, is the specific heat of the nanoparticle material, is the fluid thermal diffusivity, is the fluid temperature at the initial state , is the velocity vector components in the and directions and is the time.
The overall density of the nanofluid is given by [22] . (2.12) where, is the thermal volumetric expansion and is the fluid’s density at the reference temperature .
The Cauchy stress tensor of the Walters B' viscoelastic model may be described by the following equation [23]: ,