Natural Convection in Enclosed Cavities
Theory: when trapped air starts to move
Overview
I assumed a thicker air gap in double glazing insulates better. Why are around 12 mm gaps so common?
Still air is a good insulator, but a thicker space lets it start moving. Air warmed at the warm pane rises and air cooled at the cold pane sinks, setting up a circulating flow, so heat travels by flow as well as conduction. While the gap is thin, thickening adds conductive resistance; beyond a certain thickness convection begins and cancels the gain. The Rayleigh number sets that threshold.
Rayleigh number
$L$ is the spacing between facing walls and $\Delta T$ their temperature difference. It scales with the cube of spacing, so doubling thickness multiplies Ra by eight. A horizontal layer heated from below starts convecting above about 1,708 (Rayleigh–Bénard convection). A vertical cavity has weak circulation even at low Ra, but heat transfer then stays close to pure conduction.
Tall-cavity correlation
$H$ is cavity height; larger height-to-spacing ratios reduce the relative influence of the top and bottom ends. Outside the valid range — especially Ra below 10,000 — the correlation doesn't apply and Nu is taken as about 1 (conduction only).
Bénard's hexagonal cells
In 1900 the French physicist Bénard observed neat hexagonal patterns — convection cells — in a thin layer of oil heated from below. In 1916 Lord Rayleigh explained it theoretically, showing flow begins once a combination of temperature difference and layer thickness exceeds a threshold; hence the Rayleigh number. It later emerged that many of Bénard's patterns were actually driven by temperature-dependent surface tension (Marangoni convection), yet the two names remain paired as the starting point of convection theory.
Worked example: the air gap in double glazing
Height 1 m, 15 K between panes, mean air temperature about 10 °C; gap conductance from conduction and convection, excluding radiation:
| Gap | Ra | Nu | Conductance | Conduction only |
|---|---|---|---|---|
| 6 mm | 395 | 1.00 | 4.17 W/(m²·K) | 4.17 |
| 12 mm | 3,160 | 1.00 | 2.08 W/(m²·K) | 2.08 |
| 16 mm | 7,500 | 1.13 | 1.76 W/(m²·K) | 1.56 |
| 20 mm | 14,600 | 1.42 | 1.78 W/(m²·K) | 1.25 |
| 30 mm | 49,400 | 2.18 | 1.82 W/(m²·K) | 0.83 |
Beyond 16 mm it barely improves.
Right. Conduction alone would reach 0.83 at 30 mm, but convection brings it back to 1.82. A thicker gap just adds weight and frame depth — which is why products sit around 12–16 mm. Note that 16 mm is at the edge of the correlation's range and the real curve changes gradually, so think of the minimum as lying somewhere in 12–20 mm. Larger temperature differences raise Ra and shift the optimum slightly thinner.
With argon fill
Filling the same 16 mm with argon lowers conductance from 1.76 to 1.31 W/(m²·K) thanks to its lower conductivity. Across the whole window, though, radiation between panes carries several W/(m²·K) too, so the gas makes a big difference only once a low-emissivity (low-E) coating suppresses radiation.
How to approach the analysis
CFD cautions
- Near-wall mesh: thin thermal and velocity boundary layers form at the walls; refine normal to them.
- Include radiation: in air-filled cavities it matches or exceeds conduction and convection.
- Possible unsteadiness: at high Ra the flow oscillates; if steady runs won't converge, run transient and average.
- End conditions: heat escaping through top, bottom and frame changes corner temperatures greatly — critical for condensation checks.
“It's hotter inside the box than expected”
Estimating board temperatures inside a sealed electronics box from the difference with outside air alone can come out too low. Air inside circulates by enclosed natural convection, but weakly, and hot air pools near the top — components placed high often run over 10 K hotter than those below. Analyses should resolve the internal air flow and check the vertical temperature spread across component placements.
Common mistakes
Mistakes and fixes
| Mistake | Effect | Fix |
|---|---|---|
| Assuming thicker always insulates better | Ineffective design | Judge by Ra |
| Using correlations out of range | Wrong heat transfer | Check validity |
| Excluding radiation | Heat loss badly underestimated | Solve radiation too |
| Ignoring oscillation in steady runs | Non-convergence, scatter | Transient averaging |
| Uniform air inside a box | Upper components underestimated | Resolve internal flow |
I'd like to try natural convection calculations myself.
Try the natural convection simulator and Grashof number calculator for dimensionless groups and heat transfer, and the convection cell simulator for convection cells. Related geometries are covered in natural convection on vertical plates, Rayleigh–Bénard convection and natural convection in vertical channels, and the meaning of the groups in Grashof and Rayleigh numbers.
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