Unsteady MHD heat and mass transfer of a non-Newtonian nanofluid flow of a two-phase model over a permeable stretching wall with heat generation/absorption

The combined effects of magnetic field and heat generation or absorption on unsteady boundary-layer convective heat and mass transfer of a non-Newtonian nanofluid over a permeable stretching wall have been addressed. A power-law model includes Brownian motion and thermophoresis influences are utilized for non-Newtonian nanofluids with a convective boundary condition. The non-linear governing equations are reduced into ODEs by similarity transformations and solved numerically by using Runge-Kutta-Fehlberg 4th–5th order numerical method (RKF45) with shooting technique. The different physical parameters effects such as the magnetic parameter $(M)$, the heat source/sink parameters $(\lambda )$, the unsteadiness parameter $(A)$, the generalized Prandtl and Lewis numbers on the dimensionless velocity, temperature and nanoparticles volume fraction, in addition to the skin friction, local Nusselt and Sherwood numbers are analyzed. It is reached that the thermal and concentration boundary-layer thickness has higher values with the increasing of magnetic field and heat generation in the case of a pseudo-plastic nanofluid than others.