Thermal convection in a Brinkman–Darcy–Kelvin–Voigt fluid with a generalized Maxwell–Cattaneo law
Brian Straughan
Abstract
Abstract We investigate thoroughly a model for thermal convection of a class of viscoelastic fluids in a porous medium of Brinkman–Darcy type. The saturating fluids are of Kelvin–Voigt nature. The equations governing the temperature field arise from Maxwell–Cattaneo theory, although we include Guyer–Krumhansl terms, and we investigate the possibility of employing an objective derivative for the heat flux. The critical Rayleigh number for linear instability is calculated for both stationary and oscillatory convection. In addition a nonlinear stability analysis is carried out exactly.
Topics & Concepts
PhysicsConvectionMechanicsViscoelasticityHeat fluxClassical mechanicsPorous mediumThermodynamicsHeat transferMaterials sciencePorosityComposite materialNanofluid Flow and Heat TransferFluid Dynamics and Turbulent FlowsRheology and Fluid Dynamics Studies