LAUSR

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 $$G_{c}$$Gc and the corresponding wave number $$\alpha_{c}$$αc and wave speed $$c_{c}$$cc are computed for a wide range of couple stress parameter $$\varLambda_{c}$$Λc, Prandtl number $$Pr$$Pr and Hartmann number $$M$$M. It is found that the value of $$Pr$$Pr at which the instability switches over from stationary to travelling-wave mode increases with increasing $$M$$M and decreasing $$\varLambda_{c}$$Λc. The effect of magnetic field is to delay the onset of instability while an opposite kind of behavior is observed with increasing $$\varLambda_{c}$$Λc. The streamlines presented herein demonstrate the development of complex dynamics at the transition mode.