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

Abstract

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.