# Physics Of A Non Linear Pdes

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This work presents a system of a non-linear PDEs, which governing the MHD flow of a Homann nanofluid with heat and mass transfer through a porous medium. The problem is solved numerically by making use of the finite difference method. The formulas of the velocity components, temperature and concentration are obtained as functions of the problem physical parameters. The effects of these parameters on the solutions are illustrated numerically and graphically through a set of figures to reinforce the parametric study of the fluid flow.
Fig.(2) depicts the Variation of the velocity fields f(η) & f '(η) , the temperature θ(η) and the nanoparticles concentration ϕ(η) for different values of the suction parameter S. The velocities f(η) and f '(η) increase; while, the temperature θ(η) and the nanoparticles concentration ϕ(η) decrease as S increases. Moreover, increasing the Hartmann number Ha increases f(η), f '(η)), θ(η) and the ambient nanoparticles concentration far from the wall; otherwise, ϕ(η) decreases near the wall as Ha increases as illustrated in Fig.(3).
The results included in Fig.(4) clarify that increasing the permeability parameter β has a marked effect on decreasing the velocity fields and increasing the temperature values; as a consequence of the increase in the resistive force on the velocity due to the porosity of the medium. Whereas, the nanoparticles concentration near the wall decreases and the ambient nanoparticles concentration far