2. Hot water at 80C is carried through a long insulation pipe (average thermal conductivity, k=0.15W/mK ) with an inner diameter 2cm and outer diameter 4cm. Convection heat transfer coefficient of hot water and outside air ( at 20C) is 150W/m2K and 12W/m2K, respectively). (a) Write down the energy balance equation and initial and boundary conditions during initial transient period. [10pts] (b) solve the equation during steady state operation and find the temperature 1.5cm from the center of the pipe (halfway between inner and outer surface). [20 pts]