How do you derive a heat flux equation from the poisson equation for heat flow in a cylinder.?

Question

I have the poisson equation for steady state cylindrical co-ordinate system. Which is (1/r)*d(r*dT/dr)/dr + g/lambda = 0 (r= radius of cylinder, g=energy generation, lambda=heat transfer coefficient. I need to get the equation in terms of dT/dr so i can substitute it into the Fourier equation to calculate the heat flux. I suspect the equation needs to be integrated but im not sure how this would be done correctly.

Thanks in advance for any help.

supastremph · Answer

If you have no theta or z dependence (as you ve written), can't you just integrate your expression?  Otherwise you'll be looking at Bessel's functions to solve that bad boy.

Anonymous · Answer

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How do you derive a heat flux equation from the poisson equation for heat flow in a cylinder.?

2 Answers