A model for thermal convection of a fluid saturating an inclined layer of porous medium with a Brinkman law and stress-free boundary conditions is studied. When the Darcy number (Formula presented.) is zero, this problem has been studied by Rees and Bassom (Acta Mech 144(1–2):103–118, 2000). When the Brinkman term is present in the model ((Formula presented.)) the basic motion is a combination of hyperbolic and polynomial functions. With the Chebyshev collocation method we study the linear instability of the basic motion for three-dimensional perturbations. We also give nonlinear stability conditions and, for longitudinal perturbations, we prove the coincidence of linear and nonlinear critical Rayleigh numbers.

Thermal convection in an inclined porous layer with Brinkman law

Falsaperla, Paolo
;
Mulone, Giuseppe
2018-01-01

Abstract

A model for thermal convection of a fluid saturating an inclined layer of porous medium with a Brinkman law and stress-free boundary conditions is studied. When the Darcy number (Formula presented.) is zero, this problem has been studied by Rees and Bassom (Acta Mech 144(1–2):103–118, 2000). When the Brinkman term is present in the model ((Formula presented.)) the basic motion is a combination of hyperbolic and polynomial functions. With the Chebyshev collocation method we study the linear instability of the basic motion for three-dimensional perturbations. We also give nonlinear stability conditions and, for longitudinal perturbations, we prove the coincidence of linear and nonlinear critical Rayleigh numbers.
2018
Brinkman law; Inclined layer; Linear instability; Nonlinear stability; Porous Media; Mathematics (all); Applied Mathematics
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11769/325923
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