(66,878) (0.18) (575-565) " 4.79 - 0.52 " 4.27

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STEP 5. Calculate the thickness. Assume that ts =

Example. A 48-in.-diameter duct 90 ft long in a 60°F ambient temperature has gas entering at 575°F and 15,000 cfm. The gas density standard conditions is 0.178 lb/ft3 and the gas outlet must not be below 555°F. Cp = 0.18 Btu/lb °F. Determine the thickness of calcium silicate required to keep the outlet temperature above 565°F, giving a 10°F buffer to account for the interior film coefficient. A more sophisticated approach calculates an interior film resistance Rs (interior) instead of using a 10°F or larger buffer. The resulting equation for Qp would be

0.45 for calcium silicate from Appendix Figure 15.A1.

This equation, however, will not be used.

STEP 1. Determine th the average gas temperature, = (575 + 565)/2 = 570°F. (A logarithmic mean could be calculated for more accuracy, but it is usually not necessary.)

STEP 2. Determine M lb/hr. The flow rate is 15,000 cfm of hot gas (570°F). At standard conditions 1 atm, 70°F), the flow rate must be determined by the absolute temperature ratio:

= 6262 cfm std. gas (or scfm) M = 6262 cfm x 0.178 lb/ft3 x 60 min/hr = 66,878 lb/hr

STEP 3. Determine Rs from Table 15.4 assuming ts = 80°F and a dull surface R = 0.5.

STEP 6. The thickness required for this application is 2 in. of calcium silicate. Again, a more conservative recommendation would be 2-1/2 in.

Note: The foregoing calculation is quite complex. It is, however, the basis for many process control and freeze-prevention calculations. The two equations for Q, can be manipulated to solve for the following:

Temperature drop, based on a given thickness and flow rate.

Minimum flow rate, based on given thickness and temperature drop.

Minimum length, based on thickness, flow rate, and temperature drop.

Freeze Protection. Four different calculations can be performed with regard to water-line freezing (or the unacceptable thickening of any fluid).

1. Determine the time required for a stagnant, insulated water line to reach 32°F.

2. Determine the amount of heat tracing required to prevent freezing.

3. Determine the flow rate required to prevent freezing of an insulated line.

4. Determine the insulation required to prevent freezing of a line with a given flow rate.

Calculations 1 and 2 relate to Section 15.4.5, where we dealt with stationary media. To apply the same principles to the freeze problems, the following modifications should be made.

In calculation 1, the heat transfer should be based on the average water temperature between the starting temperature and freezing:

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