On the magnetohydrodynamic stability of channel flow of Navier-Stokes-Voigt fluid

The linear stability of a pressure-driven channel flow of an electrically conducting Navier-Stokes-Voigt type of the viscoelastic fluid subject to a transverse magnetic field is investigated. The validity of Squire's theorem is proved, and the generalized eigenvalue problem for two-dimensional modes is obtained by adopting the Galerkin method, which is subsequently solved using the QZ-algorithm. Although the base flow retains its Newtonian fluid characteristics, the noticeable influence of the Kelvin-Voigt parameter in conjunction with the Hartmann number on the stability of fluid flow is perceived. Instability is exclusively identified within a specific range of the Kelvin-Voigt parameter, markedly affected by the Hartmann number. Furthermore, closed neutral stability curves arise, indicating the requirement of two values of the Reynolds number to completely assess the linear stability criteria, in contrast to the typical single value observed in the case of Newtonian fluids.