In this paper, magneto-hydrodynamic blood flows through porous arteries are numerically simulated using a locally modified homogenous nanofluids model. Blood is taken into account as the third-grade non-Newtonian fluid containing nanoparticles. In the modified nanofluids model, the viscosity, density, and thermal conductivity of the solid-liquid mixture (nanofluids) which are commonly utilized as an effective value, are locally combined with the prevalent single-phase model. The modified governing equations are solved numerically using Newton's method and a block tridiagonal matrix solver. The results are compared to the prevalent nanofluids single-phase model. In addition, the efficacies of important physical parameters such as pressure gradient, Brownian motion parameter, thermophoresis parameter, magnetic-field parameter, porosity parameter, and etc. on temperature, velocity and nanoparticles concentration profiles are examined.
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