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.