Question

An overhead 25m-long, uninsulated industrial steam pipe of 100-mm diameter, is routed through a building whose walls and air are at25C. pressurized steam matains a pipe surface temperature of 150C and the coeff of nature convection h = 10W/m^2K. the surface emissivity e= 0.8
1. what is the rate of heat loss from the steam line?
2.if the steam is gernerated in a gas-fired boiler operating at efficenty of 0.9, and natural gas is priced at C=0.02 per MJ, what is the annual cost of heat loss from line?

Answer 1

Answer:

1) q=18414.93 W

2) C=12920$

Explanation:

Given data:

pipe length L=25m

pipe diameter D=100mm =0.1 m

air temperature $T_{s1}$=$T_{\infty1} }$=25 °C.....= 298.15k

pipe surface temp $T_{s2}$=150 °C.....=423.15k

surface emissivity e= 0.8

boiler efficiency η=0.90

natural gas price Cg=$0.02 per MJ

1) Total heat loss and radiation heat loss combined

          q=$q_{conv} +q_{rad}$

          q=$A[h(T_{s2}-T_{s1})+e$б($T_{s2}$^4-$T_{s1}$^4)]....... (1)

б=5.67×10^-8 W/m^2K^4 (boltzmann constant)

area A =L.Dπ=25×0.1π=7.85 m^2

putting all these values in eq (1)

q=18414.93 W

2) suppose boiler is operating non stop annual energy loss will be

               E=q.t

                  =18414.93.3600.24.365

                  =5.81×10^11 J

   to find furnace energy consumption

               Ef =E/η

                  =6.46×10^5 MJ

   annual cost

                  C=Cg. Ef

                    =12920$