MHD instability of pressure-driven flow of a non-Newtonian fluid

Abstract

The effect of a uniform vertical magnetic field on the stability of pressure-driven flow of an electrically conducting non-Newtonian fluid in an isothermal channel is numerically investigated using the Chebyshev collocation method. The non-Newtonian fluid is modeled by the couple stress fluid theory, which permits for polar effects and encountered regularly in liquids with very large molecules. It is established that Squire’s theorem is valid and the modified Orr–Sommerfeld equation is derived by considering the fact that the magnetic Prandtl number Pm, for recognized electrically conducting liquids is too small. The triplets (Rc, αc, cc), where Rc is the critical Reynolds number, αc is the critical wave number and cc is the critical wave speed, are obtained for different values of couple stress parameter Λ and the Hartman number M. It is found that increasing M has a stabilizing effect on the system while an increase in the couple stress parameter shows twofold deeds. Individual aspects of the kinetic energy spectrum are observed and presented for different parametric values to obtain comprehensive information at the critical state of fluid flow.