Effects of a Magnetic Field and Couple Stresses on the Onset of Convection in Navier-Stokes-Voigt Fluid

This study investigates the influence of a magnetic field and couple stresses on the initiation of thermal convection in a viscoelastic fluid described by the Navier-Stokes-Voigt (NSV) model, subjected to heating from below. The study is motivated by applications in polymer processing, crystal growth, and magnetohydrodynamic heat transfer. The analysis examines three types of boundary conditions using both linear (normal mode) and nonlinear (energy method) techniques. The energy method incorporates an energy decay framework to evaluate the impact of viscoelasticity, while a variational principle is applied to formulate the eigenvalue problem. Critical Rayleigh numbers obtained from both methods consistently predict the onset of convection.It is observed that convection occurs solely through stationary modes, in agreement with the principle of exchange of stabilities. The findings indicate that the presence of a magnetic field and couple stresses stabilizes the fluid layer by postponing the onset of convection. These insights are valuable for enhancing thermal stability and optimizing heat-transfer processes in engineering applications involving viscoelastic and magnetized fluid systems.