Kelvin–Voigt Fluid Models in Double-Diffusive Porous Convection

Straughan, Brian

Abstract

We investigate problems of convection with double diffusion in a saturated porous medium, where the saturating fluid is one of viscoelastic type, being specifically a Navier–Stokes–Voigt fluid, or a Kelvin–Voigt fluid. The double diffusion problem is analysed for a porous medium with Darcy and Brinkman terms, for a Navier–Stokes–Voigt fluid, and then for a general Kelvin–Voigt fluid of order N. The case where N has the value one is analysed in detail. We also propose a theory where the fluid and solid temperatures may be different, i.e. a local thermal non-equilibrium (LTNE) theory for a porous medium saturated by a Kelvin–Voigt fluid. A further generalization to include heat transfer by a model due to C. I. Christov is analysed in the context of Kelvin–Voigt fluids in porous media. Finally, we examine the question of whether a Navier–Stokes–Voigt theory should be used for nonlinear flows, or whether a suitable objective derivative is required.

Citation

Straughan, B. (2025). Kelvin–Voigt Fluid Models in Double-Diffusive Porous Convection. Transport in Porous Media, 152(1), Article 11. https://doi.org/10.1007/s11242-024-02147-z

• Journal Article Type: Article
• Acceptance Date: Dec 4, 2024
• Online Publication Date: Dec 21, 2024
• Publication Date: 2025-01
• Deposit Date: Jan 10, 2025
• Publicly Available Date: Jan 10, 2025
• Journal: Transport in Porous Media
• Print ISSN: 0169-3913
• Electronic ISSN: 1573-1634
• Publisher: Springer
• Peer Reviewed: Peer Reviewed
• Volume: 152
• Issue: 1
• Article Number: 11
• DOI: https://doi.org/10.1007/s11242-024-02147-z
• Public URL: https://durham-repository.worktribe.com/output/3329482