Thermal Convection in a Rotating Anisotropic Fluid Saturated Darcy Porous Medium

• Main Author: Shatha Haddad
• Format: Article
• Language: English
• Published: MDPI AG 2017-08-01
• Series: Fluids
• Subjects: thermal convection; nonlinear stability; anisotropy; rotation; linear instability
• Online Access: https://www.mdpi.com/2311-5521/2/3/44

The stability of the thermal convection in a fluid-saturated rotating anisotropic porous material is investigated. We take into account the rotation of a layer of saturated porous medium about an axis orthogonal to the planes bounding the layer. The permeability is allowed to be an anisotropic tensor. In particular, we restrict our attention to the case where the permeability in the vertical direction is different to that in the horizontal plane. The linear instability and nonlinear stability analysis, in the case where the inertial term vanishes, are performed. It is shown, by using an energy method, that the nonlinear critical Rayleigh numbers coincide with those of the linear analysis. The results reveal that the system becomes more stable when the rotation is present.