As per previous post the magnetic field results in a Lorentz force opposing the fluid flow, it doesn't not change the viscosity at least in standard incompressible Hartmann flow. The ratio between the Lorentz force due to the magnetic field and the viscous forces is THE Hartmann number. Look up Hartmann flow between parallel plates and see the derivation. One needs a good understanding of both Emag and fluid mechanics to understand it. A lot of material on the subject online.


Google search the below words and look say on the 5th hit, that is a pdf called 4.pdf from ijpam which explains it all:

hartmann flow between parallel plates