Concept

Thermal boundary layer — where it appears

The thin layer next to a surface through which heat is conducted between the surface and the fluid beyond, much as a velocity boundary layer carries momentum. Its thickness grows as the square root of the time or distance over which heat has had to diffuse.

Named by 2 essays across 2 fields — each of them below, with the objects they name alongside it.

The number a duct settles at is an eigenvalue. The local Nusselt number against x⁺ = x/(D·Re·Pr), from a Crank–Nicolson march that contains no eigenvalue anywhere. It settles at 3.6568, which is λ₀²/2 for the Graetz eigenvalue problem — a completely separate calculation. The mark at x⁺ = 0.05 is the entry length every textbook quotes: it delivers a Nusselt number 1.45 per cent above the developed value, which is a perfectly reasonable tolerance and is never the one stated.

How far before the heat arrives

A duct's thermal entry length is quoted everywhere as x/(D·Re·Pr) = 0.05, with no tolerance attached. Working out what it delivers gives a Nusselt number 1.45 per cent above the developed value — and the developed value itself is not a term ratio at all but an eigenvalue, 3.6568, which is also the rate at which the duct forgets its inlet.

regimes · Peclet

A travelling bubble's B-factor grows as the square root of its age, and the bubble turns heat-limited when it reaches B*. The vapour a growing bubble has made over the liquid it has cooled, against its age, in water at 80 °C under a tension 10 kPa below the vapour pressure, while inertia limits its growth; the dashed line is B, at which the cooling would use up the whole tension. B is 4.3 at a microsecond and 136 at a millisecond, and meets B = 31.6 at 53.8 µs, when its radius is 0.141 mm.

A bubble is throttled by its age, and a sheet by its length

A cavity cools the liquid it boils, and the cooling lowers the vapour pressure it needed. Whether that matters was a question about one number, the B-factor — vapour made over liquid cooled — and no real cavity's was known. Computed, the two kinds a pump has are nothing alike. A travelling bubble cools a thin shell that thins further as it stretches, so its B grows as the square root of its age and reaches the critical value at Brennen's thermal time: a millisecond in water at 60 °C, four microseconds at the boiling point. An attached sheet keeps renewing the liquid it cools, so its B is a few, fixed by its length and speed. In warm water the bubbles are suppressed forty degrees before the sheet.

applied · Cavitation

Named alongside it

The objects these essays reach for when they reach for this one.

Peclet number Cavitation Convergence Dimensionless Eigenvalue Entry length Graetz Heat transfer Latent heat Model limit Nusselt number Similarity solution

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