hi, I met a problem about heat transfer in cylinder, if you can help, I will appreciate it.(adsbygoogle = window.adsbygoogle || []).push({});

The question is simple. I want to know thetransient heat distributionin a cylinder withinternal heating(constant temperature not constant flux). The boundary conditions comprises two constant temperature, inner and outer surface. we assume the cylinder radius is infinite. therefore, we have

the governing equation:

dT/dt=k(d^{2}T/dr^{2}+(1/r)*dT/dr)

rw<r<∞

i.c. : r(r,0)=t0

b.c.: r(∞, t) = t0

r(rw ,t) = t1

It looks like a hollow cylinder problem. But unfortunately, with surprise, I failed to find a solution for the heat transfer with two constant temperature in literatures. In Carslaw and Jaeger, I only found one solution for constant heat flux internal heating. So I derived the solution by Laplace Transform and that gives me a solution with Bessel function , here, I just want to find a example to verify my solution.

Thank you very much in advance !!

Bruce

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# Transient heat transfer in a cylinder with internal heating

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