Problem 3. (6 pts)

A 2 inch, schedule-40 steel pipe carries saturated steam at 60 psia through a laboratory that is 60

ft long.

(a) Use the shell-balance approach to derive the differential equation that governs heat

conduction through the insulated pipe. Derive two equations, one in terms of heat flux

(q) and the other in terms of temperature (T). (3 pts)

(b) The pipe is insulated with 1.5 inches of 85% magnesia that costs $0.75 per foot. How

long must the steam line be in service to justify the insulation cost if the heating cost for

the steam is $0.68 per 105 Btu? The outside surface convective heat-transfer coefficient

may be taken as 5 Btu/hr ft² °F. (3 pts)