Inclined convection in a porous Brinkman layer: linear instability and nonlinear stability

Area of Science:

• Fluid Dynamics
• Heat Transfer
• Porous Media Convection

Background:

• Extends previous models of thermal convection in inclined porous layers by incorporating inertial effects and rigid boundary conditions.
• Builds upon Darcy's Law models by utilizing the Brinkman Law for a more comprehensive analysis.
• Addresses limitations of prior studies that excluded inertial terms or used stress-free boundaries.

Purpose of the Study:

• To investigate thermal convection in an inclined porous layer under the Brinkman Law with inertial effects and rigid boundaries.
• To analyze three-dimensional perturbations and provide critical surfaces for linear and nonlinear stability.
• To compute critical nonlinear Rayleigh regions and estimate global nonlinear asymptotical stability.

Main Methods:

• Employs the Brinkman Law to model fluid flow in the porous layer.
• Analyzes linear and nonlinear stability using three-dimensional perturbations.
• Applies the Lyapunov method for nonlinear stability analysis and solves a variational maximum problem.

Main Results:

• Provides critical surfaces for linear and nonlinear stability analyses.
• Computes critical nonlinear Rayleigh regions for inclined layers, a novel contribution.
• Offers estimates of global nonlinear asymptotical stability, including the influence of the inertial term (finite Va).

Conclusions:

• The inclusion of inertial effects and rigid boundaries significantly impacts thermal convection dynamics in inclined porous layers.
• The study provides a more complete understanding of stability criteria, extending beyond linear analysis.
• This research offers valuable benchmarks for future studies on convective heat and mass transfer in porous media.