Journal of Fluid Mechanics · 1983 · 192 citations · 23 references
Numerical AnalysisEngineeringPorous Medium EquationsMechanical EngineeringFluid MechanicsComputational MechanicsPorous MediumBoundary LayerConvective Heat TransferHeat Transfer ProcessFluid PropertiesRigid BoundariesMixed ConvectionNumerical SimulationThermodynamicsNatural ConvectionBoundary Element MethodMethod Of Fundamental SolutionFree Boundary ProblemBeavers–joseph Boundary ConditionHeat TransferBoundary CorrectionNumerical Method For Partial Differential EquationRayleigh-darcy ProblemPorothermoelasticityBrinkman EquationThermal EngineeringThermo-fluid Systems
The no-slip condition on rigid boundaries necessitates a correction to the critical value of the Rayleigh–Darcy number for the onset of convection in a horizontal layer of a saturated porous medium uniformly heated from below. It is shown that the use of the Brinkman equation to obtain this correction is not justified, because of the limitations of that equation. These limitations are discussed in detail. An alternative procedure, based on a model in which the porous medium is sandwiched between two fluid layers, and the Beavers–Joseph boundary condition is applied at the interfaces, is described, and an expression for the correction is obtained. It is found that the correction can be of either sign, depending on the relative magnitudes of the parameters involved.
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