MHD flow of Newtonian fluid in a permeable tubule

The magnetohydrodynamic flow of an incompressible Newtonian fluid in a small diameter permeable tube with an application to the flow in the renal tubule is presented. The fluid absorption at the tube wall is taken as a function of the wall permeability and pressure gradient across the tube wall. Using suitable physical approximations, the equations of motion are transformed into a simpler form and the exact solution of the reduced equation is obtained. Expressions for radial and axial velocity profiles, pressure distribution, volume flow rate, wall shear stress, fractional reabsorption and streamlines are presented. Effects of the wall permeability coefficient and Hartmann number on flow variables are studied. The results indicate that the increase in strength of the magnetic field considerably reduces fluid reabsorption at the permeable wall, while the increase in magnitude of the wall permeability coefficient increases fluid reabsorption at the permeable wall.