I need help with the heat equation-specifically, I am confused about the Boundary Conditions for an insulated pipe. I need to know what the temperature profile (vs. radius) would look like for an insulated pipe with a refrigerated liquid on the inside and atmosphere (temperature higher than the liquid) on the outside. I am thinking that if R1 was the inside surface of the pipe and R2 was the surface of the insulation, the Boundary Condition would be dT/dt at r=R2 =0.

Question

I need help with the heat equation-specifically, I am confused about the Boundary Conditions for an insulated pipe.  I need to know  what the temperature profile (vs. radius) would look like for an insulated pipe with a refrigerated liquid on the inside and atmosphere (temperature higher than the liquid) on the outside.  I am thinking that if R1 was the inside surface of the pipe and R2 was the surface of the insulation, the Boundary Condition would be dT/dt at r=R2 =0.

kainui · Answer

It might help to draw a picture. I think this accurately describes the scenario since dT/dt=0 at r=R2 means that there is a constant temperature at the outside of the pipe. We know the outside is the atmosphere, so we can fairly safely assume that taking heat out of the atmosphere is negligible and the temperature of the atmosphere will continue to remain constant no matter how much our pipe sucks out of it. So far so good it seems. =)