Thermo-Fluid Coupling — Buoyancy, Mixed Convection & Stratification
Density-temperature coupling, Boussinesq approximation, Richardson number, mixed convection regimes, thermally stratified flows, and thermal-hydraulic safety analysis.
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Quick Explainer
What is the Boussinesq approximation and when is it valid?
Boussinesq treats fluid as incompressible everywhere except in the buoyancy term, where rho = rho0*(1 - beta*dT). This captures buoyancy-driven flow while avoiding full compressibility. Valid when temperature differences are small relative to absolute temperature (dT/T0 << 1) and density variations are primarily thermal rather than from compressibility.
What distinguishes mixed convection from purely forced or natural convection?
Mixed convection occurs when both forced flow (fan, pump) and buoyancy forces are significant. The Richardson number Ri = Gr/Re^2 quantifies the ratio: Ri >> 1 is natural, Ri << 1 is forced, Ri ~ 1 is mixed. In electronics cooling with a failing fan, the transition to mixed convection creates complex flow patterns where buoyancy either aids or opposes forced flow depending on geometry.