TY  - EJOU
AU  - Shubenkov, Ivan 
AU  - Lyubimova, Tatyana 
AU  - Sadilov, Evgeny 

TI  - Three-Dimensional Convection in an Inclined Porous Layer Subjected to a Vertical Temperature Gradient
T2  - Fluid Dynamics \& Materials Processing

PY  - 2024
VL  - 20
IS  - 9
SN  - 1555-2578

AB  - In this paper, we study the onset and development of three-dimensional convection in a tilted porous layer saturated with a liquid. The layer is subjected to a gravitational field and a strictly vertical temperature gradient. Typically, problems of thermal convection in tilted porous media saturated with a liquid are studied by assuming constant different temperatures at the boundaries of the layer, which prevent these systems from supporting conductive (non-convective) states. The boundary conditions considered in the present work allow a conductive state and are representative of typical geological applications. In an earlier work, we carried out a linear stability analysis of the conductive state. It was shown that at any layer tilt angles, the most dangerous type of disturbances are longitudinal rolls. Moreover, a non-zero velocity component exists in -direction. In the present work, three-dimensional non-linear convection regimes are studied. The original three-dimensional problem is reduced to two-dimensional one with an analytical expression for the velocity -component . It is shown that the critical Rayleigh number values obtained through numerical solutions of the obtained 2D problem by a finite difference method for different layer inclination angles, are in a good agreement with those predicted by the linear theory. The number of convective rolls realized in nonlinear calculations also fits the linear theory predictions for a given cavity geometry. Calculations carried out at low supercriticalities show that a direct bifurcation takes place. With increasing supercriticality, no transitions to other convective regimes are detected. The situation studied in this problem can be observed in oil-bearing rock formations under the influence of a geothermal temperature gradient, where the ensuing fluid convection can affect the distribution of oil throughout the layer.
KW  - Thermal convection; inclined layer; porous media; vertical temperature gradient

DO  - 10.32604/fdmp.2024.050167