Numerical solutions for the MHD mixed convection flow of non-Newtonian nanofluid in a U-shaped enclosure

Abstract

In this article, the mixed convection (natural and forced) heat transfer of non-Newtonian nanofluid (\({\text{Fe}}_{3}{\text{O}}_{4}\)-water) steady-state, \(2\text{D}\) flow, laminar, with the influence of a magnetic field in a baffled, U-shaped lid-driven cavity has been analyzed. The problem is modeled mathematically, and the resulting nonlinear partial differential equations are solved numerically using FEM. The cavity is heated by the baffles and cooled by the vertical walls (moving walls), while the other walls are adiabatic. Where Prandtl number \((Pr=6)\) and Grashof number (\(Gr=10000\)) are assumed to be fixed. While the Richardson number is taken in the range of \(0.01<Ri<100\), the Hartmann number is taken in the range of 0 < Ha < 400, with an angle of inclination 0 < γ < π/2, and the power law index varies in the range of \(0.6<n<1.4\). The results are presented in terms of streamlines, isotherms and in line graphs, it is investigated that, the force convection is dominating the natural convection at low value of \(Ri\) while natural convection is dominating mechanism of heat transfer at higher values of \(Ri\) and a detailed study has been conducted for the various effects of \(Ha,\) \(\gamma \) and power law index on fluid flow and heat transfer. Also, it is observed that as the power-law index increases, the Nusselt number increases. For the convergence and validation of results, an artificial neural network is used and discussed.