Computer simulation of MHD blood conveying gold nanoparticles as a third grade non-Newtonian nanofluid in a hollow porous vessel

In this paper, heat transfer and flow analysis for a non-Newtonian third grade nanofluid flow in porous medium of a hollow vessel in presence of magnetic field are simulated analytically and numerically. Blood is considered as the base third grade non-Newtonian fluid and gold (Au) as nanoparticles are added to it. The viscosity of nanofluid is considered a function of temperature as Vogel's model. Least Square Method (LSM), Galerkin method (GM) and fourth-order Runge–Kutta numerical method (NUM) are used to solve the present problem. The influences of the some physical parameters such as Brownian motion and thermophoresis parameters on non-dimensional velocity and temperature profiles are considered. The results show that increasing the thermophoresis parameter (Nt) caused an increase in temperature values in whole domain and an increase in nanoparticles concentration just near the inner wall of vessel. Furthermore by increasing the MHD parameter, velocity profiles decreased due to magnetic field effect.