Search results for " 35B27"

showing 2 items of 2 documents

Derivation of a Homogenized Two-Temperature Model from the Heat Equation

2014

This work studies the heat equation in a two-phase material with spherical inclusions. Under some appropriate scaling on the size, volume fraction and heat capacity of the inclusions, we derive a coupled system of partial differential equations governing the evolution of the temperature of each phase at a macroscopic level of description. The coupling terms describing the exchange of heat between the phases are obtained by using homogenization techniques originating from [D. Cioranescu, F. Murat: Coll\`ege de France Seminar vol. 2. (Paris 1979-1980) Res. Notes in Math. vol. 60, pp. 98-138. Pitman, Boston, London, 1982.]

01 natural sciencesHomogenization (chemistry)Heat capacity010305 fluids & plasmasTwo temperatureMathematics - Analysis of PDEsThermal nonequilibrium models0103 physical sciencesFOS: Mathematics[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]0101 mathematicsScalingMSC 35K05 35B2776T05 (35Q79 76M50)35K05 35B27 76T05 (35Q79 76M50)MathematicsNumerical AnalysisHomogenizationPartial differential equationInfinite diffusion limitApplied MathematicsHeat equationMathematical analysis010101 applied mathematicsComputational MathematicsThermal non-equilibrium modelsModeling and SimulationVolume fractionHeat equationAnalysisAnalysis of PDEs (math.AP)
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The Mean-Field Limit for Solid Particles in a Navier-Stokes Flow

2008

We propose a mathematical derivation of Brinkman's force for a cloud of particles immersed in an incompressible viscous fluid. Specifically, we consider the Stokes or steady Navier-Stokes equations in a bounded domain Omega subset of R-3 for the velocity field u of an incompressible fluid with kinematic viscosity v and density 1. Brinkman's force consists of a source term 6 pi rvj where j is the current density of the particles, and of a friction term 6 pi vpu where rho is the number density of particles. These additional terms in the motion equation for the fluid are obtained from the Stokes or steady Navier-Stokes equations set in Omega minus the disjoint union of N balls of radius epsilo…

Stokes equation01 natural sciencesHomogenization (chemistry)Navier-Stokes equationPhysics::Fluid DynamicsMathematics - Analysis of PDEsFOS: Mathematics[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]Boundary value problem0101 mathematicsMathematical Physics(MSC) 35Q30 35B27 76M50Particle systemPhysicsHomogenization010102 general mathematicsMathematical analysis35Q30 35B27 76M50Stokes equationsStatistical and Nonlinear Physics010101 applied mathematicsFlow velocityDragSuspension FlowsBounded functionCompressibilityBall (bearing)Navier-Stokes equationsAnalysis of PDEs (math.AP)
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