Thermal convection in a Brinkman–Darcy and Kelvin–Voigt fluid of order one with coupled stresses effect

Abstract Our paper thoroughly examines a model for the thermal convection of specific viscoelastic fluids within a porous medium characterized by Brinkman–Darcy properties. These fluids demonstrate first‐order Kelvin–Voigt behavior as they permeate the medium. This investigation considers the influence of couple stresses on the system. We calculate the critical Rayleigh number required for linear instability theory, focusing on both stationary and oscillatory types of convection. Additionally, we conduct the nonlinear stability theory. In the latter cases, it is demonstrated that oscillatory convection can occur. A detailed investigation is conducted into the characteristics of both stationary and oscillatory convection branches, including the points at which the transition occurs.