Boundary Equation for Water Cooled Cylinder

[sangy]

There is a cylinder which is water cooled from outside.I want to know what would be the boundary equation for water cooled boundary.

 

[Dr.D]

How about r = const?

You really need to say what sort of problem you are trying to solve here if you want anything more than this.

 

[sangy]

Sir,
Ya its a concentric cylinder.
Last cylinder has water following through it.
the inner cylinder has gas in it, which has high temperature. The water is flowed through this cylinder boundary as it should not melt the cylinder (Quartz tube).
Please let me know the boundary condition for outermost boundary of the cylinder.

 

[minger]

If the outer wall is being cooled, then that's the boundary condition, heat convection at r=r_o. If its a cylinder, then there is no r=0 boundary condition. The solution is a Bessel function which at zero you can simply cancel one of them out...man I worded that poorly.

At zero, you have (IIRC) something like T(r) = I(r) + J(r). I believe one of those functions goes to infinity at zero, so you can cancel it out.