Stability of Viscoelastic Fluid Flowing Through Porous Medium Down Non-uniformly Heated Inclined Plane

Abstract

The stability of a thin layer of viscoelastic fluid flowing through a porous medium down a non-uniformly heated inclined plane with a constant temperature gradient along the plane is considered. The film flow system is influenced by gravity, mean surface tension, thermocapillary forces, viscoelastic forces, porosity, and permeability of porous medium. We seek a solution of the stability problem in a series in small wave numbers, and the obtained results, when the plane is heated in the downstream direction, show that the Marangoni, Galileo, Biot numbers, porosity, and permeability of the porous medium have dual roles in the stability of the flow system, while the viscoelastic parameter and angle of inclination have stabilizing effects, and the Prandtl number has a destabilizing effect. The effects of these physical parameters are also discussed in the case when the plane is cooled in the downstream direction, and we found that their effects are opposite to those of the previous case.

Anisotropic Rock Poroelasticity Evolution in Ultra‐low Permeability Sandstones under Pore Pressure, Confining Pressure, and Temperature: Experiments with Biot's Coefficient

“…For this paper, we selected typical reservoir rock samples from the study area in the Songliao Basin. We drilled three small samples from the x, y, and z axes in order to determine the parameters of rock mechanics under conditions of changing pore pressure, confining pressure or temperature to analyze the role and influence of Biot's coefficient with respect to microscopic anisotropy (Wu et al, 2014;El-Sayed et al, 2015;Garrido et al, 2015;Grassl et al, 2015;Lu et al, 2015).…”

Effect of anisotropic permeability on double‐diffusive bidisperse porous medium

“…They found that the linear instability threshold coincides with the nonlinear stability one. It is worth noting that the stability theory of thermal convection in a fluid‐saturated porous medium has been employed by many authors, for instance, Gaikwad and Dhanraj, 26 El‐Sayed et al, 27 Haddad, 28,29 and Attia et al 30 Other recent work that is employing stability theory in the context of a bidispersive porous medium is due to Franchi 31,32 and Straughan 33,34 …”