Abstract
Hydrodynamic stability of plane Couette flow of an upper convected Maxwell fluid is investigated in presence of a transverse magnetic field assuming that the magnetic Prandtl number is sufficiently small. The resulting equation is a modified Orr-Sommerfeld equation. The equations of stability are solved numerically using Chebyshev collocation method with QZ algorithm. The critical values of Reynolds number, wave number and wave speed are computed and the results are shown through the neutral curves. By increasing the amount of elasticity to a certain value, it is shown that, as the Hartmann number increases, the minimum critical Reynolds number decreases and it does not increase again in contrast to the Newtonian case.
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