Effects of a Non-uniform Magnetic Field-Dependent Viscosity on the Ferroconvective Flow in an Inclined U-Shaped Enclosure

Abstract

A case of variable dynamic viscosity that is a function of a non-uniform electromagnetic force has been examined. This variable electromagnetic force is resulting from a magnetic wire near the bottom wall of an inclined U-shaped enclosure. The working fluid is a ferrofluid resulting from water as abased fluid and iron oxide as nanoparticles. The mathematical formulations of the governing equations are depending on the basic concepts of the magnetohydrodynamics and the ferrohydrodynamics. The finite volume solver is used to solve the system of equations, and the results display tools are the contour maps for the streamlines and isotherms, graphical illustrations for the local Nusselt number and the average Nusselt number. A parametric study is conducted and effects of pertinent parameters such as the Hartmann number, the aspect ratio of the U-shaped enclosure, the inclination angle, and the volume fraction of the Fe3O4 nanoparticles on the flow, the temperature fields and rate of the heat transfer inside the enclosure are investigated. The results showed that the stream function is diminished by 74.89%, 72.32%, and 78.04% at $$A = 0.2, 0.4$$ and 0.6, respectively as the Hartmann number enhances from 0 to 50. In addition in case of the vertical enclosure, the increase in $$\phi$$ by 6% makes the averaged Nusselt number is enhanced by 1.09%.