Akademik Veri Yönetim Sistemi
Communications in Nonlinear Science and Numerical Simulation, cilt.125, 2023 (SCI-Expanded)
In this article, we study the onset of convection in porous media with through flow based on Darcy formulation. Unlike the impermeable porous medium problems between horizontal two parallel plates frequently accessed in the literature, the thermal instability of convective cells under the influence of a uniform vertical flow is of the prime concern here in an aim to control the thermal instability onset. Three devised thermal boundary constraints representing external heat transfer with isothermal or isoflux lines across the walls are investigated fully taking into account the linear stability equations with small flow/heat wave disturbances with respect to the normal modes. In each case, the neutral stability response of the saturated porous layer separating the stable and unstable perturbation regimes are identified affected by a Peclet number manifesting itself as the through flow strength. The pre-analysis of the analytical solutions of thermal fields proves that the thermal layer thickness is lowered by the opposing through flow, otherwise an assisting through flow enhances the thickness. The critical Darcy–Rayleigh numbers and Benard cell wavenumbers of lateral fluctuating perturbations initiating the convective Darcy–Benard thermal rolls within the porous media for a prescribed Peclet number are ultimately worked out numerically, except an analytical expression is elaborated where the heating is supplied from the walls via varying heat fluxes. The well-documented thresholds of Rayleigh numbers 39.47, 27.09 and 12 with vanishing Peclet number (Barletta, 2019) corresponding to the three studied thermal cases are reproduced successfully. Further results clarified that both opposing and assisting through flows are sources of stabilization when the walls are thermally isothermal. On the other hand, the other thermally conducting porous walls lead to a more unstable convection with the assisting through flow having a thermal layer growth, otherwise stable convection occurs with the opposing through flow.