Hydromagnetic flow of a second-grade fluid in a channel - Some applications to physiological systems

An asymptotic series solution for steady flow of an incompressible, second- grade electrically conducting fluid in a channel permeated by a uniform tra nsverse magnetic field is presented. The depth of the channel is assumed to vary slowly in the axial direction. Analytical expressions are derived for the vorticity and pressure drop along the channel as well as the wall shea r stress. It is found that for fixed Values of the Reynolds number R and th e non-Newtonian parameter K-1, the wall shear stress increases with increas ing value of magnetic parameter M. Numerical computations carried out for a specific slowly varying channel show that flow separation occurs for both second-grade (K-1 < 0) and second-order (K-1 > 0) fluids when \K-1\ < 0.15. The analysis also reveals the interesting result that while how separation takes place for a second-order fluid for K-1 greater than or equal to 0.15 , no separation occurs at all for \K-1\ greater than or equal to 0.15 for a second-grade fluid.