Parabolic Temperature Profile Through A Pipe Wall
Parabolic Temperature Profile Through A Pipe Wall
(OP)
Hey Folks,
Was wondering if anyone knew of any good textbooks or journals which could help me with some theory involving parabolic heat transfer in a pipe wall. I've tried looking through a few textbooks but get a bit lost.
Thanks
Was wondering if anyone knew of any good textbooks or journals which could help me with some theory involving parabolic heat transfer in a pipe wall. I've tried looking through a few textbooks but get a bit lost.
Thanks





RE: Parabolic Temperature Profile Through A Pipe Wall
Apart from during a short heat-cool-heat transience, I struggle to understand how else one would achieve it.
RE: Parabolic Temperature Profile Through A Pipe Wall
RE: Parabolic Temperature Profile Through A Pipe Wall
I'm looking into a forming process for pipes called Induction Bending. It's where you heat a small section (20-40mm) of pipe (in this case super duplex stainless steel) to around 1100C using an induction coil around the outside of the pipe which puts the material into the super plastic region and is able to be bent.
After doing an experiment with a thick-walled pipe and some thermocouples it turns out that the inside wall of the pipe is approximately 1150C, the centre of the wall is 1200C and the outside wall is 1100C.
This is the main reason for me too look into conduction and the theory of a parabolic temperature profile. I'm not really looking at convection or radiation.
Hope this is clearer.
Thanks
RE: Parabolic Temperature Profile Through A Pipe Wall
One can certainly argue that the heat being generated by the induction coil is leaving from both sides of the wall, and is therefore showing a lower temperature than the middle of the wall.
TTFN
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RE: Parabolic Temperature Profile Through A Pipe Wall
RE: Parabolic Temperature Profile Through A Pipe Wall
q'''/k +d^2T/dx^2 =0 wwhere q''' is heat generated per unit volume. Integration with constant q''' will give parabolic profile.
Regards
RE: Parabolic Temperature Profile Through A Pipe Wall
I am actually more concerned about the particulars of measuring the mid-plane temperature
RE: Parabolic Temperature Profile Through A Pipe Wall
I was trying to answer the original question, however
With q""", the heat generation per unit volume a function of spaceual coordinate and time, I would use an approximate model of one dimension and time
If thermal diffusivity is constant, solve
1/alpha*dT/d time= q'''/k+ d^2T/dx^2----were d means partial derivative.
Regards