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Old 13th December 2010 | 12:35
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mathy
 
Joined: Mar 2008
Posts: 76
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From: London
enthalpy and Newton's Law of Cooling

You have demonstrated two key points. Firstly it is not temperature alone that is the determining factor but enthalpy usually written as H = U + pV where U is the total internal energy, p is the boundary pressure and V is the volume.

Clearly the tanks you refer to are not identical so the enthalpy in each is different.

The tanks being constructed differently and housed differently will not have the same heat transfer coefficient “k”. If you measure a time interval from t1 to t2 and calculate enthalpies H1 and H2 and the ambient enthalpy Ha then according to Newton's Law of Cooling

k(t1 - t2) = - natural logarithm[(H1 - Ha)/(H2 - Ha)]

Of course in a simple situation where the total internal energy of each tank is constant it is sufficiently accurate to substitute temperatures T1 and T2 for enthalpies H1 and H2. For example the aircraft is now on the ground and you simply want to know how long it will be before the fuel temperature rises to a certain temperature.

You can use the same formula for brakes.
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