The onset of penetrative convection in an inclined porous layer

Arnone, Giuseppe; Cantini, Giulio; Capone, Florinda; Carnevale, Mauro

doi:10.1016/j.ijheatmasstransfer.2023.124532

Cited by 5 publications

(3 citation statements)

References 34 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…paying attention first to transforming the definition interval of the unknown fields from (0, 1) to (−1, 1) with a suitable transformation [5]. We can now substitute equation (A 1) into (3.15) and then profit from the orthogonality of Chebyshev polynomials with respect to the scalar product…”

Section: Appendix a (A) Numerical Proceduresmentioning

confidence: 99%

“…This is a well-recognized problem in the literature (see [38,[41][42][43]) but a valuable solution is found thanks to boundary conditions. We will not go through this, but we refer the reader to a very detailed explanation in [5]. Once the new eigenvalue problem involves non-singular matrices, eigenvalues can be determined safely.…”

Section: Appendix a (A) Numerical Proceduresmentioning

confidence: 99%

“…Since his pioneering piece of work appeared, considerable attention has been devoted to penetrative convection, see e.g. [3][4][5][6], in particular because of its applications in geophysics in whose context the patterned ground genesis was explained as a type of stability phenomenon [7,8]. In these papers, the penetrative convection phenomenon in porous media is modelled under the hypothesis of local thermal equilibrium (LTE), by defining a single temperature for both fluid and solid phases, which are in thermal equilibrium.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Stability of penetrative convective currents in local thermal non-equilibrium

Arnone,

Capone,

Gianfrani

2024

Proc. R. Soc. A.

Self Cite

View full text Add to dashboard Cite

The aim of this paper is to investigate the onset of penetrative convection in a Darcy–Brinkman porous medium under the hypothesis of local thermal non-equilibrium. For the problem at stake, the strong form of the principle of exchange of stabilities has been proved, i.e. convective motions can occur only through secondary stationary motions. We perform linear and nonlinear stability analyses of the basic state, with particular regard to the behaviour of stability thresholds with respect to the relevant physical parameters characterizing the problem. The Chebyshev- τ method and the shooting method are employed and accurately implemented to solve the differential eigenvalue problems arising from linear and nonlinear analyses to determine critical Rayleigh numbers. Via numerical simulations, the stabilizing effect of the upper bounding plane temperature, of the Darcy number and of the interaction coefficient for the heat exchange, is demonstrated.

show abstract

Section: Appendix a (A) Numerical Proceduresmentioning

confidence: 99%