Consider a 10.0 m long pipe, of diameter 0.6m, wall thickness 0.7 m, and a thermal conductivity k = 2.5 w/m k. the inside of the pipe is maintained at a constant temperature of 500°k while it is subjected to a constant external wall temperature of 100 °k. evaluate (a) the temperature profile within the pipe wall, and (b) the total heat transfer rate leaving at the pipe outer surface.