Concept

Thermal resistance — where it appears

The temperature difference needed to drive a unit of heat flow through a layer, a gap or a path, by analogy with electrical resistance. Resistances in series add and those in parallel combine reciprocally, which is how insulation, radiation shields and heat sinks are designed.

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

Insulating a thin wire makes it lose more heat. The heat lost per metre from a wire 2 mm across held 40 K above the air, against the outer radius of the PVC insulation round it (k = 0.19 W/m K), with the surface losing 10 W/m²K to still air by convection and radiation, on a logarithmic radius axis; dashed, the bare wire. The first layers of insulation increase the loss, from 2.51 to a maximum of 12.11 W/m at an outer radius of 19 mm — the critical radius k/h — because they add surface faster than they add resistance. Beyond the critical radius the loss falls again, but so slowly — the resistance of the insulation grows only as the logarithm of its radius — that it does not get back down to the bare wire's until the PVC is 178 km thick. Any sheath a cable could carry makes it lose more heat, not less.

The insulation that makes a wire lose more heat

Wrap a hot water pipe in glass wool and it loses less heat. Wrap a thin electrical wire in PVC and it loses more — four times more, at the best thickness — and runs cooler for it. The insulation adds a resistance to heat flowing through it, but it also adds surface for the heat to leave from, and around a thin enough cylinder the surface wins. The crossover is a radius, k/h, set by the insulation and the air; below it, more insulation means more heat lost, and a small enough ball cannot be insulated by anything wrapped round it.

thermodynamics · Diffusion

Each foil divides the heat by one more. The radiant heat flowing from a wall at 293 K to one at 77 K — room temperature to liquid nitrogen — in watts per square metre on a logarithmic axis, against the number of thin shields placed between them, for walls and shields all black-painted, dull metal and aluminised film. With nothing between them, black walls exchange 340 W/m²; aluminised walls 6.3. Each shield adds one more equal resistance in series, so N shields divide the flux by N + 1: thirty aluminised foils bring it to 204 milliwatts per square metre. Between black walls a single aluminised foil passes 6.2 W/m², less than thirty black shields do, 11.0 W/m², because a shield's resistance is 2/ε − 1 and a shiny one is worth 54 black.

The thin foils that stop radiant heat

In a vacuum, heat can cross a gap only as radiation, and a single sheet of foil a few hundredths of a millimetre thick, hung in the gap and touching nothing, halves it. Two sheets cut it to a third, thirty to a thirty-first. The foil does not need to be thick or cold or clever; it needs only to be shiny, because a sheet that absorbs little also emits little, and each one becomes a radiator in its own right, floating at a temperature between its neighbours. The golden blankets on spacecraft and the silvering inside a vacuum flask are the same arithmetic of resistances in series.

thermodynamics · Blackbody

Named alongside it

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

Convection Critical radius of insulation Emissivity Heat conduction Heat transfer coefficient Kirchhoffs law Laplace equation Multilayer insulation Radiation shield Stefan boltzmann law Thermal conductivity Thermal radiation

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