The analytical solution of the MHD equations via Minkowski 2-D space continuum of liquid metals through a square duct under multiple transport effects

Abstract

The problem of mass, heat transfer due the steady, laminar for mercury and gallium liquids flow in to a square duct in the presence of transverse magnetic field and ultrasonic fields, is tackled analytically resorting to the wave-position ansatz as the unique independent variable in the 2-D Minkowskiinner product space. The MHD system of partial differential equations is solved by assuming the absence of slip boundary conditions. Each of duct wall is electrically insulated, and have a constant temperature and, the fluid is under a constant pressure gradient. The resulting solutions are visualized graphically for the velocity, temperature distribution, induced magnetic field, entropy generation rate and Bejan numbers, which are illustrated according to different suggested values corresponding to the affected fields. Good agreements are found with previous studies.