Influence of Couple Stresses and Magnetic Field on Thermal Convection in Darcy–Brinkman–Kelvin–Voigt Fluid

Abstract This study investigates the influence of couple stresses and an applied magnetic field on thermal convection in a Darcy–Brinkman–Kelvin–Voigt fluid layer heated from below. The model incorporates viscoelastic effects through the Kelvin–Voigt framework, porous medium interactions via the Darcy–Brinkman law, and microstructural effects using couple stress theory. Linear stability analysis is conducted using the normal mode technique, while the energy method provides the nonlinear stability criterion. The findings reveal that both couple stresses and the magnetic field enhance thermal stability by delaying the onset of convection, whereas increased permeability of the porous medium has a destabilizing effect. The viscoelastic parameter alters energy dissipation and influences the stability threshold. Among the boundary configurations, rigid–rigid surfaces yield the highest stability. These results contribute to understanding convection regulation in complex fluids and have potential applications in geophysical flows, polymer and industrial processing, energy systems, and bioengineering.