Numerical treatment and Global Error Estimation of a MHD Flows of an Oldroyd 6-Constant Nano-Fluid through a non- Darcy Porous medium with Heat and Mass Transfer

Abstract— Explicit Finite-Difference method was used to obtain the solution of the system of the non-linear ordinary differential equations which transform from the non-linear partial differential equations. These equations describe the steady magneto-hydrodynamic flow of an oldroyd 6-constant non-Newtonian nano-fluid through a non-Darcy porous medium with heat and mass transfer. The numerical formula of the velocity, the temperature, the concentration, and the nanoparticles concentration distributions of the problem were illustrated graphically. The effect of Darcy number Da, Forchheimer number Fs, magnetic field parameter M, local temperature Grashof number Gr, local nanoparticle Grashof Br, Prandtl number Pr, Dufour number Nd, Brownian motion parameter Nb, Thermophoresis parameter Nt, Lewis number Le, Sort number Ld, Chemical reaction parameter Rc, and Chemical reaction order m on those formula were discussed at the values of material parameters ( specially in the case of pure Coutte flow. Then, the effects of modified pressure gradients on those formulas were discussed in the case of pure Poiseuille flow and the generalized Couette flow. Also, an estimation of the global error for the numerical values of the solutions is calculated by using Zadunaisky technique.