Kelvin–Voigt Fluid Models in Double-Diffusive Porous Convection

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.