Exact Solutions Corresponding to the Viscous Incompressible and Conducting Fluid Flow Due to a Porous Rotating Disk

Abstract

A study is pursued in this paper for the evaluation of the exact solution of the steady Navier–Stokes equation, governing the incompressible viscous Newtonian, electrically conducting fluid flow motion over a porous disk, rotating at a constant angular speed. The three-dimensional equations of motion are treated analytically yielding to the derivation of exact solutions. The effects of the magnetic pressure number on the permeable flow field are better conceived from the exact velocity and induced magnetic field obtained. Making use of this solution, analytical formulas for the angular velocity and current density components, as well as for the magnetic wall shear stresses, are extracted. Interaction of the resolved flow field with the surrounding temperature is then analyzed via energy equation. The temperature field is shown to accord with the convection, viscous dissipation, and Joule heating. As a result, exact formulas are obtained for the temperature field, which takes different forms, depending on whether isothermal and adiabatic wall conditions or suction and blowing are considered.