International Journal for Numerical Methods in Fluids · 2007 · 35 citations · 16 references
Natural SciencesMechanical EngineeringPhysicsComputational Fluid DynamicsFluid DynamicsHeat TransferHeat Transfer In FluidsIncompressible FlowNavier-stokes EquationsPartial Differential EquationsThermal Boundary LayersViscous FlowConvectionConvection RegimesFluid-thermal CouplingIncompressible Navier-stokes EquationsMixed ConvectionMixed Layer ConvectionTemperature Dependence Of FlowViscosity
Abstract In this first part we propose and analyse a model for the study of two‐dimensional incompressible Navier–Stokes equations with a temperature‐dependent viscosity. The flow is supposed in a mixed convection regime and considers an outflow region, leading to a strongly coupled problem between the Navier–Stokes and energy equations, which will be justified theoretically. The coupling in the continuous problem is treated by an outer temperature fixed point strategy. Existence results for a particular variational formulation follows from this study. Further, a particular uniqueness result for small data is also obtained. Copyright © 2007 John Wiley & Sons, Ltd.
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