# Q = mcpdT - what am I doing wrong here?

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Thread starter 2 years ago
#1
In identifying the heat transfer of a U-tube pipe buried under ground given a measured inlet and outlet temperature, is the equation Q = mdot*cp*dT always true?

At which conditions does this equation not hold true? Assuming that the surrounding ground is homogeneous and that the only moving "object" is the fluid flowing in the pipe.

I'm trying to identify the heat transfer of a U-tube pipe buried under ground. It has a slightly complex geometry of having the pipe surrounded with grout (to fill up the void during the excavation of the borehole).

In an attempt to calculate the heat transfer, I calculated the respective thermal resistances of the pipe, fluid flowing in the pipe, the surrounding grout and the surrounding soil.Then, I used an equation to identify the temperature evolution of the fluid through the pipe (see image below).

I took the average of the inlet and outlet temperature, call this T_HTFmean. Let's call the temperature of the surrounding soil as T_soil.

So I've set the heat transfer to Q = (T_HTFmean - T_soil) / (sum of thermal resistances * depth of U-tube) .

(see image above for thermal resistances)

Since I know the inlet and outlet temperatures, surely the calculated heat transfer above should match the heat transfer obtained from Q = mdot*cp*dT.... but it does not... so, I am trying to figure out if the way I have calculated the heat transfer above using the thermal resistances is incorrect or if Q = mdot*cp*dT is not necessarily always true in this specific question. Thanks
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Thread starter 2 years ago
#2
Alternatively, can someone try to derive how they got to the temperature evolution equation -- T(z,t) equation in the image
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