Freon 12 at -40C flows through a copper pipe (K = 386W / m * K) with inner and outer diameters of 4.09 and 4.83 m, respectively. It is desired to insulate the pipe with polystyrene foam (K = 0.04W / m K) to protect the personnel and reduce the heat transfer from the ambient air at 25C. The individual indoor and outdoor heat transfer coefficients are 500 and 5 W / (m ^ 2) * k . respectively. Calculate the thickness of the insulation required to reduce heat transfer by 50%, compared to the value that would be obtained if the pipe were bare.