2.2. Governing Equation
2D steady convective flow of nanofluid in a porous media is considered in existence of constant magnetic field. The PDEs equations are:
(1)(2)(3)(4)and are defined as:
(5)(6)(7)The KKL (Koo-Kleinstreuer-Li) correlation has been utilized for viscosity of nanofluid
(8)The related coefficient and properties of Cuo-water nanofluid is presented in Table 1 and 2. Maxwell model and Hamilton–Crosser model for irregular particle geometries by introducing a shape factor can be expressed as
(9) in which
and
are the conductivities of the particle material and the base fluid. In this equation
“m” is shaper factor. Table 3 shows the different values of shape factors for various shapes of nanoparticles. Vorticity and stream function should be used to eliminate pressure source terms:
(10)Introducing dimensionless quantities:
(11)The final formulae are:
(12)(13)(14) where dimensionless and constants parameters are illustrated as:
(15) and boundary conditions are:
on bottom wall
on other walls
on all walls
(16)Local and average Nusselt over the hot wall can calculate as:
(17)(18)