Analytical solution of magnetohydrodynamic flow of Jeffrey fluid through a circular microchannel

The magnetohydrodynamic (MHD) flow of Jeffrey fluid in a circular microchannel is presented. Using the method of variable separation, the analytical solutions to both DC-operated MHD and AC-operated MHD micropumps are found. The flow is assumed to be laminar, unidirectional, one dimensional and driven by the Lorentz force. The Lorentz force can be taken as hydrostatic pressure gradient in the momentum equation of the MHD microchannel flow model. The effects of Hartmann number Ha, dimensionless relaxation time λ¯1 and retardation time λ¯2 on the velocity and volumetric flow rate are investigated. The velocity and volumetric flow rate grow and then reduce with Hartmann number Ha. There is a critical value of the Ha for MHD velocity and an optimum Ha for maximum volumetric flow rate. In addition, a comparison with previous works is also provided to confirm the validity of the present results.