This paper presents the results of exact solutions and numerical simulations of strongly-conductive and weakly-conductive magnetic fluid flows. The equations of magnetohydrodynamic (MHD) flows with different conductivity coefficients, which are independent of viscosity of fluids, are investigated in a horizontal rectangular channel under a magnetic field. The exact solutions are derived and the contours of exact solutions of the flow for magnetic induction modes are compared with numerical solutions. Also, two classes of variational functions on the flow and magnetic induction are discussed for different conductivity coefficients through the derived numerical solutions. The known results of the phenomenology of magnetohydrodynamics in a square channel with two perfectly conducting Hartmann-walls are just special cases of our results of magnetic fluid.
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