DC MHD Micropump

The X component of the momentum equation under negligible inertia force assumption is given by 

This equation describes the balance between the pressure gradient, the viscous diffusion, and the Lorentz force. 

Using the fully developed flow solution in a rectangular cross-sectional channel (White, 2006), the following analytical solutions for MHD flow may be assumed as 

A2 is only a function of the aspect ratio b/a of the microchannel. Substituting the assumed velocity profile, u(y, z), into the momentum equation and taking the volume integration of the equation for the domain, -L/2 x Ljl, -a y a, and -b z b, wt get 

7 = 7 X x // is the electric current. The infinite series in the above equation can be simplified as 

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