#3 parts (a) , (b) , (c)

Question \#3: (30 pts) A metal steam pipe having an outside diameter of 60mm contains saturated steam at 200C(473K). The pipe is to be insulated with an insulation having a thickness of 40mm and a thermal conductivity (kins) of 0.182W/(m.K). The length of the pipe is 30m. The pipe is exposed to air at 27C(300K) and a convective heat-transfer coefficient of 30 W/(m2K) (a) Estimate the critical thickness of the insulation in mm by calculating the critical radius for insulation. Based on the estimated value, do you expect the rate of heat loss for bare pipe is to be smaller or greater than that for the insulated pipe? Hint: Note that if outer radius (r2)=critical radius (r2)c, adding more insulation will decrease the rate of heat loss. (r2)cr=k/h0. (b) Calculate the rate of heat loss (W=J/s) for both the bare pipe and the insulated pipe by assuming that the surface temperature of the pipe remains constant over the insulation. Compare your results. (c) Calculate the kg of steam condensed per hour in the insulated pipe due to the heat loss. (Saturated Steam @ 200C : Latent Heat of Condensation, Hcond=1940.75 kJ/kg)(1hr=3600s)