An asymptotic series solution for steady flow of an incompressible, second-grade electrically conducting fluid in a channel permeated by a uniform transverse 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 shear stress. It is found that for fixed values of the Reynolds number R and the non-Newtonian parameter K1, the wall shear stress increases with increasing value of magnetic parameter M. Numerical computations carried out for a specific slowly varying channel show that flow separation occurs for both second-grade (K1<0) and second-order (K1>0) fluids when |K1|<0.15. The analysis also reveals the interesting result that while flow separation takes place for a second-order fluid for K1≥0.15, no separation occurs at all for |K1|≥0.15 for a second-grade fluid.

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