## 7.4 HEAT LOSS FROM AN UNINSULATED SURFACE TO AIR

A steam line with a diameter of 3.5 in (0.089 m) and a length of 50 ft (15.2 m) transports steam at 320 F (433 K). The carbon steel pipe [thermal conductivity of 25 Btu/(h)(ft)( F) or 142 W/(m 2)(K)] is not insulated. Its emissivity is 0.8. Calculate the heat loss for calm air and also for a wind velocity of 15 mi/h (24 km/h), if the air temperature is 68 F (293 K).

### Calculation Procedure

1. Calculate the heat loss due to radiation. Because the coefficient for heat transfer from the outside of the pipe as a result of radiation and convection is much less than all other heat-transfer coefficients involved in this example, the surface temperature of the pipe can be assumed to be that of the steam. To calculate the heat loss, use the straightforward radiation formula

where Q is heat loss in British thermal units per hour, A is heat-transfer area in square feet, T s is absolute temperature of the surface in degrees Rankine, T a is absolute temperature of the air, and is the emissivity of the pipe. (Note that in this version of the formula, the 10 ?8 portion of the Stefan-Boltzmann constant is built into the temperature terms.)

Thus,

2. Calculate the heat loss as a result of natural convection in calm air. Use the formula

where ? T= T s ? T

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