Abstract
In the present article, a model for penetrative convection in a fluid-saturated inclined porous medium is analyzed. Penetrative convection occurs when an unstably stratified fluid moves into a stably stratified region. In this study, it will be shown that the inclination of the layer plays a relevant role for the penetrative thermal convection of a fluid-saturated porous medium. The results reported in the literature for the limiting case of horizontal layer are recovered and the numerical results for the linear instability, obtained via the Chebyshev-τ method, show that the most destabilizing perturbations are the longitudinal and, as expected, the transverse ones destabilize only up to a certain critical inclination angle of the layer. Moreover, in the numerical analysis of the three-dimensional perturbations, we show that the longitudinal perturbations are the most destabilizing not only with respect to the transverse but also with respect to any general perturbation. We also give nonlinear stability results for the longitudinal perturbations via the weighted energy method.
| Original language | English |
|---|---|
| Article number | 124532 |
| Journal | International Journal of Heat and Mass Transfer |
| Volume | 216 |
| Early online date | 3 Aug 2023 |
| DOIs | |
| Publication status | Published - 1 Dec 2023 |
Bibliographical note
Funding Information:This paper has been performed under the auspices of the National Group of Mathematical Physics (GNFM-INdAM). G. Arnone would like to thank Progetto Giovani GNFM 2023: “Modelli per la propagazione termica governati dalla legge di Darcy frazionaria”, CUP_E53C22001930001. The authors want to thank Simon Vella for his expertise in helping them to present the 3D numerical simulations with high-quality images and Jacopo Gianfrani for his helpful suggestions. The authors kindly thank the anonymous Referees, whose suggestions and comments led to significant improvements in the manuscript.
Funding
This paper has been performed under the auspices of the National Group of Mathematical Physics (GNFM-INdAM). G. Arnone would like to thank Progetto Giovani GNFM 2023: “Modelli per la propagazione termica governati dalla legge di Darcy frazionaria”, CUP_E53C22001930001. The authors want to thank Simon Vella for his expertise in helping them to present the 3D numerical simulations with high-quality images and Jacopo Gianfrani for his helpful suggestions. The authors kindly thank the anonymous Referees, whose suggestions and comments led to significant improvements in the manuscript.
Keywords
- Chebyshev-tau method
- Inclined layer
- Instability analysis
- Nonlinear stability
- Penetrative convection
- Porous media
ASJC Scopus subject areas
- Condensed Matter Physics
- Mechanical Engineering
- Fluid Flow and Transfer Processes