Nonlinear density and temperature variation’s role (NDT) on the magnetohydrodynamic (MHD) natural convective flow of couple stress fluid with nanoparticles through a vertical porous channel modeled as Darcy-Forchheimer flow is the purpose of our work. The nanoparticles volume fraction is taken into consideration (Buongiorno model). The nonlinear partial differential equations governing this flow were transformed into ordinary differential equations via the similarity technique and simulated numerically using Matlab, following boundary value problem (BVP4c) code. Graphical illustrations, including non-dimensional velocity, temperature, concentration, nanoparticle’s concentration and numerical results containing Nusselt and Sherwood numbers were presented for different values of the non-linear part of the Boussinesq approximation; couple stress parameter, and the Biot number on the walls.
This paper looks at the MHD natural convection flow through a vertical porous channel of couple stress fluid nanoparticles under convective heat conditions at the wall of the channel. Incorporated Soret and Dufour effects lead to strong coupled and highly nonlinear differential systems. To describe accurately all the physical phenomenon, the nanoparticle's volume fraction is taken into account. The useful technical of the similarity transformations is used to produce an ordinary system which is numerically solved. Graphical illustrations containing non-dimensional velocity, temperature, concentration and concentration of nanoparticles are extensively presented for different values of various thermophysical parameters. Main quantities of interest as Nusselt and Sherwood numbers at both the walls are tabulated.
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