THE ONSET OF BUOYANCY-DRIVEN CONVECTION IN A FLUID-SATURATED POROUS LAYER SUBJECTED TO RAMP HEATING TEMPERATURE
The onset of thermal convection in a time-dependent temperature field is investigated theoretically. An initially motionless, fluid-saturated porous layer placed between the two infinite horizontal plates is heated from below with a fixed temporal rate φ, i.e. ramp heating. The main objective is to find the critical time, τc to mark the onset of the fastest growing convective instability. For stability analysis, the propagation theory and also the numerical simulation are used. The former model is based on the assumption that temperature disturbances at the marginal state are confined mainly within the thermal penetration depth in the conduction state. The self-similar stability equations are enforced under linear theory. The numerical simulation employs the finite volume method. The temporal growth rates of mean temperature and its fluctuations are traced with time. A newly developed stability criterion is suggested: at the marginal state the growth rate of the conduction temperature field (r0,T) is equal to that of temperature disturbances (r1,T). The present numerical results for non-porous fluid layers are found very reasonable in comparison with extant experimental results.