Superheated steam at an average temperature 200 C is transported through a steel pipe (k=50 W/mK, D_0=8.0 cm, D_i=6.0 cm, and L=20.0 m). The pipe is insulated with a 4-cm thick layer of gypsum plaster (k=0.5 W/mK). The insulated pipe is placed horizontally inside a warehouse where the average air temperature is 10 C. The steam and the air heat transfer coefficients are estimated to be 800 and 200 W/m^2 K, respectively. Calculate (a) the daily rate of heat transfer from the superheated steam, and (b) the temperature on the outside surface of the gypsum plaster insulation.

The total amount of daily heat transfer is 1382.38 M w.

The temperature on the outside surface of the gypsum plaster insulation is 17.96 ° C.

Explanation:

Given data,

= 10° C

= 250 w/ k

Pipe length = 20 m

Inner diameter = 6 cm, = 3 cm

Outer diameter = 8 cm, = 4 cm

The thickness of insulation is 4 cm.

= + 4

= 4+4

= 8 cm

is the heat transfer coefficient of  convection inside, is the heat transfer coefficient of  convection outside.

The heat transfer rate between ambient and steam is

watt

=   watt

= watt

q = 15999.86 watt

The total amount of daily heat transfer = 15999.86 × 86400

= 1382.387904 watt

= 1382.38 M w

The total amount of daily heat transfer is 1382.38 M w.

b) The temperature on the outside surface of the gypsum plaster insulation.

q =

15999.86  

- 10 = 7.96

= 17.96 ° C.

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