A thin-walled copper tube of radius ri is used to transport a low-temperature refrigerant and is at a temperature Ti that is less than that of the ambient air at To around the tube. There is an insulation material around the tube which has the outer radius of r. Formulate the resistance to heat transfer in this system. What will happen to the conductive contribution by increasing the insulation? How about the convective part? Is there an optimum insulation thickness? (hint: the first and second derivatives can help your analysis!) T T Air -Insulation, k Figure 3: A thin-walled copper tube