Water at 50°c is routed from one building in which it is generated to an adjoining building in which it is used for space heating. transfer between the buildings occurs in a steel pipe (k = 60 w/m-k) of 100-mm outside diameter and 8-mm wall thickness. during the winter representative environmental conditions involve air at t[infinity] = -5°c and v = 3 m/s in cross flow over the pipe.

a) if the cost of producing the hot water is $0.05 per kw-hr, what is the representative daily cost of heat loss from an uninsulated pipe to the air per meter of pipe length? the convection resistance associated with water flow in the pipe may be neglected.
b) determine the savings associated with application of a 10-mm-thick coating of urethane insulation (k = 0.026 w/m-k) to the outer surface of the pipe.

A3-mm-thick panel of aluminum alloy (k 177 w/m-k, c 875 j/kg-k and ? = 2770 kg/m) is finished on both sides with an epoxy coating that must be cured at or above t,-150°c for at least 5 min. the production line for the curing operation involves two steps: (1) heating in a large oven with air at ts,0-175°c and a convection coefficient of h, 40 w/m2. k, and (2) cooling in a large chamber with air at 25°c and a con- vection coefficient of he 10 w/m2.k. the heating portion of the process is conducted over a time interval te which exceeds the ime required to reach 150°c by 5 min (h = r + 300 s). the coating has an emissivity of ? = 0.8, and the temperatures of the oven and chamber walls are 175 and 25°c, respectively. if the panel is placed in the oven at an initial temperature of 25°c and removed from the chamber at a safe-to-touch tempera ture of 37°c, what is the total elapsed time for the two-step curing operation?