# At the Speed of Heat

Many analogies exist relating heat flow to fluid flow. Oops, there’s one. A good electronics thermal design is one that gets the heat out from the heat sources quickly and the cold in to quench them quickly. Before I scoot off to sunny (though heavy rain is forecast) Devon for a family holiday I thought I’d leave you with this…

Thermal power dissipation is measured in Watts (W)

A Watt is a Joule/second (J/s)

A Joule is a Newton meter (Nm)

So Power = m/s x N

A speed multiplied by a force.

Does this mean that there is a concept of a (steady state) ‘speed of heat’? If so what is it? These aren’t rhetorical questions by the way

31st July Hampton Court

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Posted July 31st, 2009, by **Robin Bornoff**

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power dissipation, temperature

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## About Robin Bornoff's blog

Views and insights into the concepts behind electronics cooling with a specific focus on the application of FloTHERM to the thermal simulation of electronic systems. Investigations into the application of FloVENT to HVAC simulation. Plus the odd foray into CFD, non-linear dynamic systems and cider making. Robin Bornoff's blog

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Commented on August 17, 2009 at 8:55 am

By Johannes

Dear Robin,

a really nice idea, but I don’t think it will come to a result because the equations of motion (Newton’s m*a=F) and heat transfer (Fourier + heat exchange term) are quite different in nature. Even if we consider as a mechanical counterpart a 3D air flow, we are comparing a hyperbolic with a parabolic partial differential equation. In simpler words, heat transfer is always tending to smooth gradients instead of “transporting a thermal signature” at some speed.

What we can do is to speak about time scales, i.e. the characteristic time where some temperature changes happen. AND we would have to include words about boundary conditions.

To make a simple example, let us consider a bar of some length L (to get meters into the game), feed in some heat signal on one side and watch the time when the heat is arriving at the other (cold) end. All circumferal planes shall be insulated to prevent other heat losses. In any case, the time(scale) at which the temperature signal arrives is always proportional to the square of the length of the bar: time=(density*specific heat)/(conductivity*length**2). This means that speed=length/time does not behave as it does in mechanics: double time = double distance at constant speed, but depends on geometry. Should that be another sort of relativity? (Joke)