naturalConvection

Heat flow from a surface to the air q = Ac|dT|^(4/3) (Buildings natural convection), smooth at dT = 0

FastSmoothBuildings.Utilities.naturalConvection, function (source)

Purpose

Heat flow rate from a surface to the air by natural convection, Q = A c |ΔT|^1/3 ΔT as in Buildings, regularised at small temperature differences so that it is infinitely differentiable.

Equations

With ΔT = dT, the surface minus the air temperature, and ΔT₀ = dT0,

Q = A ((c₊ + c₋)/2 + (c₊ − c₋)/2 ΔT/√(ΔT² + ΔT₀²)) ΔT (ΔT² + ΔT₀²)^1/6.

For |ΔT| >> ΔT₀, Q tends to A c₊ ΔT^4/3 when the surface is warmer (cPos) and to −A c₋ |ΔT|^4/3 when it is colder (cNeg). At ΔT = 0 the conductance is A (c₊ + c₋)/2 ΔT₀^1/3 instead of 0, and the switch between the two coefficients is spread over a few ΔT₀. C-infinity for ΔT₀ > 0.

Use

dT0 = 0.1 K by default. The coefficients come from convectionCoefficient; the interior convection and the exterior exchange of the surfaces call this function when no fixed coefficient is given.

Revisions

• October 2026: moved from trano's FastModel.Utilities.