Slip boundary conditions effect on bidispersive convection with local thermal non-equilibrium: Significant findings

We examine a theory concerning heat convection within a porous material characterized by a skeletal structure comprising macropores and, additionally, cracks or fissures leading to a network of micro pores. Brinkman theory and slip conditions were considered applicable within the macropores, while exclusively Darcy theory was applied within the micropores. This represents a scenario of thermal convection within a double-porosity porous medium. The theory accommodates non-equilibrium thermal conditions, allowing for the possibility that the temperature of the solid skeleton differs from that of the fluid present in either the macro or micro pores. Importantly, the model permits independent fluid velocities and pressures within both the macro and micro pores. We conducted both linear and nonlinear stability assessments, with a specific focus on assessing how slip boundary conditions affect the stability of the system. Once we pinpointed the onset of instability, we calculated the critical Rayleigh number as a variable dependent on the slip coefficient. Additionally, we provided numerical results that outline the thresholds for stability and instability.