An enclosure ventilated by a low-speed fan, a slow flow over a hot surface, a stack assisted by natural draught — in all of these, buoyancy and forced flow are of the same order. This is the range where the simplifications of both regimes fail.
The number that sets the regime
The Richardson number is the ratio of buoyancy to inertial forces (Gr/Re²):
| Ri | Regime | Consequence |
|---|---|---|
| ≪ 1 | Forced convection dominant | Buoyancy can be neglected |
| ~ 1 | Mixed convection | Both must be solved together |
| ≫ 1 | Natural convection dominant | Forced flow is secondary |
The calculation is a few lines and settles the modelling decision up front. Skipped, an analysis run with gravity switched off gets heat transfer systematically wrong.
Aiding or opposing?
The particular trap of mixed convection is its directional dependence:
Aiding flow. Buoyancy and forced flow in the same direction. Heat transfer is somewhat higher than the sum of the two.
Opposing flow. In opposite directions. Near the wall the flow slows and may even reverse; the boundary layer thickens and heat transfer can be lower than in either pure regime. This is counter-intuitive and is frequently overlooked in vertical channels.
Modelling
Gravity and the density-temperature relation must be defined. If the temperature difference is small, Boussinesq is sufficient; if not, density must be a genuine function of temperature. See the natural convection note.
Care is needed on the turbulence side too: standard models may not include the buoyancy production term, and without it they exaggerate mixing in stratified regions.
References
- Churchill, S. W. & Chu, H. H. S. (1975). Correlating equations for laminar and turbulent free convection from a vertical plate. International Journal of Heat and Mass Transfer, 18(11), 1323–1329. DOI: 10.1016/0017-9310(75)90243-4
- Ferziger, J. H., Perić, M. & Street, R. L. (2020). Computational Methods for Fluid Dynamics, 4th ed. Springer. DOI: 10.1007/978-3-319-99693-6