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## Main Question or Discussion Point

hi, I met a problem about heat transfer in cylinder, if you can help, I will appreciate it.

The question is simple. I want to know the

the governing equation:

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

The question is simple. I want to know the

**transient heat distribution**in a cylinder with**internal 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 havethe governing equation:

**dT/dt=k(d**

rw<r<∞

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

b.c.: r(∞, t) = t0

r(rw ,t) = t1^{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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