6533b85efe1ef96bd12bfc77
RESEARCH PRODUCT
Application of a non linear local analysis method for the problem of mixed convection instability
Christophe GuilletCong Tam NguyenThierry Marésubject
Dynamical systems theoryApplied MathematicsMechanical EngineeringMathematical analysisPrandtl numberReynolds numberLaminar flowRayleigh numberPhysics::Fluid DynamicsNonlinear systemsymbols.namesakePitchfork bifurcationMechanics of MaterialsCombined forced and natural convectionPhysical SciencessymbolsComputingMilieux_MISCELLANEOUSMathematicsdescription
Abstract We consider the problem of laminar mixed convection flow between parallel, vertical and uniformly heated plates where the governing dimensionless parameters are the Prandtl, Rayleigh and Reynolds numbers. Using the method based on the centre manifold theorem which was derived from the general theory of dynamical systems, we reduce a three-dimensional simplified model of ordinary differential amplitude equations emanating from the original Navier-Stokes system of the problem in the vicinity of a trivial stationary solution. We have found that when the forcing parameter, the Rayleigh number, increases beyond the critical value Ra s , the stationary solution is a pitchfork bifurcation point of the system.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2007-10-09 |