The Effect of Viscous Dissipation on the DarcyBard Problem: Weakly Nonlinear Analysis and Strongly Nonlinear Computations
- Title
- The Effect of Viscous Dissipation on the DarcyBard Problem: Weakly Nonlinear Analysis and Strongly Nonlinear Computations
- Creator
- Rees, D. Andrew S.; Siddheshwar, P.G.
- Description
- We consider the effect of viscous dissipation on the onset and nonlinear development of two-dimensional convection in a unit enclosure heated from below. First, we show that the linear theory is unchanged from that which arises when viscous dissipation is absent. Second, a weakly nonlinear analysis shows that convection becomes weaker with increasing values of Ge~, a modified Gebhart number. In addition, the rate of heat transfer at the lower and upper sufaces differ from one another. Third, nonlinear convection is found to lose both up/down and left/right symmetry as both Ge~ and Ra (the DarcyRayleigh number) increase. It is also found that once viscous dissipation increases in strength to unphysically large amounts, then the maximum temperature migrates from the lower boundary to the interior of the enclosure. The Author(s) 2025.
- Source
- Transport in Porous Media;Volume;152;Issue;12;Article No.;111;
- Date
- 01-01-2025
- Publisher
- Springer Science and Business Media B.V.
- Subject
- Darcy-Benard; Porous; Stability; Strongly nonlinear; Viscous dissipation; Weakly nonlinear
- Coverage
- Rees D.A.S., Department of Mechanical Engineering, University of Bath, Bath, BA2 7AY, United Kingdom; Siddheshwar P.G., Department of Mathematics, Centre for Mathematical Needs, Christ University, Bengaluru, 560 029, India
- Rights
- All Open Access; Hybrid Gold Open Access
- Relation
- ISSN: 1693913; CODEN: TPMEE
- Format
- online
- Language
- English
- Type
- Article
Collection
Citation
Rees, D. Andrew S.; Siddheshwar, P.G., “The Effect of Viscous Dissipation on the DarcyBard Problem: Weakly Nonlinear Analysis and Strongly Nonlinear Computations,” CHRIST (Deemed To Be University) Institutional Repository, accessed June 19, 2026, https://archives.christuniversity.in/items/show/21952.