Abstract
We derive the linear instability and nonlinear stability thresholds for a problem of thermal convection in a tridispersive porous medium with a single temperature. Importantly we demonstrate that the nonlinear stability threshold is the same as the linear instability one. The significance of this is that the linear theory is capturing completely the physics of the onset of thermal convection. This result is different to the general theory of thermal convection in a tridispersive porous material where the temperatures in the macropores, mesopores and micropores are allowed to be different. In that case the coincidence of the nonlinear stability and linear instability boundaries has not been proved.
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