Heat transfer investigation of the fourth-grade non-Newtonian MHD fluid flow in a plane duct considering the viscous dissipation, joule heating and forced convection on the walls

Abstract

The present study aims to investigate the heat transfer of the fourth-grade non-Newtonian MHD fluid flow in a plane duct analytically. The applied angular magnetic field is exerted on the channel walls and fluid flow. The effects of the viscous dissipation and joule heating, as well as forced convection heat transfer boundary conditions on the duct walls, are considered. The governing equations including momentum and energy are transformed into dimensionless forms; afterward, solved using the analytical method. As a novelty, the full energy equation is solved using the least squared method and the results are validated by the numerical 4th order Runge–Kutta (RK4) method. The results revealed since the Hartmann number increases, the bulk temperature inside the duct reduces about 20%, and the absolute value of the heat transfer rate on the duct wall decreases by about 40%. Besides, it was observed as the magnetic field angle reduces, the dimensionless temperature and absolute value of the temperature gradient decrease between 30 and 40%. When the Eckert number and Prandtl number decrease, the dimensionless temperature distribution becomes flattened; likewise, the heat transfer rate is reducing on the duct wall more than tripled. The increase of Biot number leads to a reduction of the dimensionless temperature inside the channel about three-time; however, the heat transfer rate increases first and then declines.