# 12. The temperature at the inner and outer surfaces of a hollow cylindrical pipe with wall...

###### Question:

12. The temperature at the inner and outer surfaces of a hollow cylindrical pipe with wall thickness L are held at constant values of T and T, respectively, where T, <To. The wall material has thermal conductivity that varies linearly according to k = k,(1 +BT), where k, and ß are constants. Draw a schematic of the system. Define and label a coordinate system. State assumptions and boundary conditions. b. Derive the governing differential equation for the heat transport and solve for the temperature profile by applying the boundary conditions. c. At what point will the actual temperature differ most from that which would exist is the case of constant thermal conductivity?

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