"There is no fan, so it is a simple problem" is one of the most expensive sentences in thermal analysis. In natural convection you do not supply the velocity; it arises from the buoyancy created by temperature differences. Temperature drives velocity, and velocity transports temperature. The two fields are locked together, which is why these solutions converge more slowly and depend more sensitively on the mesh than forced convection.
Establish the regime first
The Rayleigh number is the ratio of buoyancy to damping, and it dictates how the solution should be set up:
| Ra | Regime | Consequence |
|---|---|---|
| < 10⁸ | Laminar | A turbulence model is unnecessary, even harmful |
| 10⁸ – 10¹⁰ | Transitional | The hardest range; results depend on model choice |
| > 10¹⁰ | Turbulent | A turbulence model is required |
The characteristic length matters: height for a vertical plate, area over perimeter for a horizontal one, gap width in an enclosure. A Ra computed with the wrong length puts you in the wrong regime.
In electronics enclosures Ra usually falls in the transitional range. Solving it as laminar underpredicts heat transfer and solving it as fully turbulent overpredicts it; running both and reporting the spread as an uncertainty is the honest approach.
The limit of the Boussinesq approximation
Treating density as variable only in the buoyancy term makes the computation markedly cheaper. Its condition is that the temperature difference stays small relative to the absolute temperature — in practice ΔT / T < 0.1.
That holds for a 30 K difference at room temperature. It does not hold for a surface at 300 °C in a 20 °C environment; there, density has to be solved as a genuine function of temperature. Pushing past the limit and insisting on Boussinesq biases the flow rate systematically.
Mesh: the boundary layer is thicker here, and more critical
In natural convection the velocity boundary layer is slow and thick, yet all the heat transfer passes through the thin thermal layer inside it. Wall functions were not derived for this regime — resolve to the wall and target y+ < 1.
Resolution is also needed along the direction buoyancy drives: the layer thickens as it rises up a vertical surface, and refining only normal to the wall will not capture that development.
Convergence: oscillation is probably physics
Natural convection problems often refuse to converge in steady state. The reason is usually not numerical: the rising thermal plume genuinely oscillates, and cells in an enclosure exchange places. Suppressing that by lowering relaxation factors erases the physics.
The right approach is to solve transient and take a time average of the monitored quantity. See the note on convergence.
Do not forget radiation
Surface heat fluxes are low in natural convection, which makes radiation proportionally much more significant. In an enclosure at 60 °C, radiation can carry half the total heat rejection. Setting up a natural convection analysis without radiation usually produces a wrong answer from the start — the ratio test in the radiation note belongs here without exception.
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
- Modest, M. F. & Mazumder, S. (2021). Radiative Heat Transfer, 4th ed. Academic Press. ISBN 978-0-323-98406-5.