Stability of natural convection in a vertical non-Newtonian fluid layer with an imposed magnetic field

A numerical study has been conducted to analyze the influence of a uniform horizontal magnetic field on the stability of buoyancy driven parallel shear flow in a differentially heated vertical layer of an electrically conducting couple stress fluid; a type of non-Newtonian fluid. Within the framework of linear stability theory, the resulting complex generalized eigenvalue problem is solved numerically using the Chebyshev collocation method with QZ algorithm. The critical Grashof number \(G_{c}\) and the corresponding wave number \(\alpha_{c}\) and wave speed \(c_{c}\) are computed for a wide range of couple stress parameter \(\varLambda_{c}\), Prandtl number \(Pr\) and Hartmann number \(M\). It is found that the value of \(Pr\) at which the instability switches over from stationary to travelling-wave mode increases with increasing \(M\) and decreasing \(\varLambda_{c}\). The effect of magnetic field is to delay the onset of instability while an opposite kind of behavior is observed with increasing \(\varLambda_{c}\). The streamlines presented herein demonstrate the development of complex dynamics at the transition mode.