Another Method of Estimating h c for Water

Another Method of Estimating h c for Water

t c V = 7 037 199 6 ( . + . 2 79 ) 02 .† (B.4a)

V is the water velocity in m/s t is the temperature in °C

d i the tube inner diameter in m

( V 150 + . 1 55

t ) 02 . (B.4b)

where

h c , Btu/ft 2 h °F t, °F

V, ft/s

d i , in.

Example B.3

If 6.3 kg/s (50,000 lb/h) of water at 121°C (250°F) flows inside a pipe of inside diameter 73.6 mm (2.9 in.), determine h c .

Solution

First one has to estimate the water velocity V. V is given by the simple formula in Table B.1.

In SI units, V = 1 246 .

wv

(B.5a)

V-m/s; w = flow in kg/s; v = specific volume of water from steam tables = 0.0010625

m 3 /kg (0.017 ft 3 /lb); d = tube ID in m. V = 1.246 × 6.3 × 0.0010625/0.07366/0.07366 = 1.54 m/s

In British units V , = 0 05 . wv

d 2 i (B.5b)

V, ft/s; w, flow in lb/h; v, specific volume in ft 3 /lb; . 0 017

V = . 0 05 50 000 × , ×

ft/s

Appendix B: Tube-Side Heat Transfer Coefficients and Pressure Drop 383

Then using (B.4), we have

h c = . 0 7 37 × ( 199 6 . + . 2 79 121 × ) × . 1 54

= 8996 W/m K 15 2 8 0 8 Btu/ft h F 7737 kcal/m h C 2 ° 2

(As discussed earlier, the performance of an economizer is impacted mainly by the gas-

side heat transfer coefficient, and hence, small variations in h c of water will not affect the

overall heat transfer coefficient U; hence, will not cause significant error in evaluating

their thermal performance or duty. However, h c is important for evaluating tube wall temperature that suggests the possibility of low-temperature corrosion.)

Example B.4

0.5 kg/s (3967 lb/h) of saturated steam at 35 bara (507 psia) flows inside a superheater

tube of inner diameter 38 mm (1.5 in.). What is h c ?

Solution

C value from Table B.4 for saturated steam at 3500 kPa or 35 bara is 354.6. Using (B.4),

h c = 0.0278 × 354.6 × 0.50 0.8 /0.038 1.8 = 2038 W/m 2 K In British units, C = 0.0011343 × 354.6 = 0.4022. h c = 2.44 × 3967 0.8 × 0.4022/1.5 1.8 = 358

Btu/ft 2 h °F. In Metric units, C = 0.001229 × 354.6 = 0.4358.

h c = 00278 . × 04358 . × 180008 . = 1753 kcal/m h C 2 ° 003818 . .

Example B.5

In this case, if the steam temperature is 400°C, what is h c ?

Solution

C = 281; h c = 0.0278 × 281 × 0.50 0.8 /0.038 1.8 = 1615 W/m 2 K.

In British units, C = 0.001229 × 281 = 0.3187. h c = 2.44 × 0.3187 × 3967 0.8 /1.5 1.8 = 284 Btu/ft 2 h °F. In Metric units, C = 0.001229 × 281 = 0.3453. hc = 0.0278 × 18000.8/0.0381.8 = 1389

kcal/m 2 h °C. By performing such calculations manually, plant engineers can understand how h c values change with the temperature and pressure of steam. We note that h c for super-

heated steam in the preceding example is lower than that of saturated steam. Also one may note that C decreases first and then increases at low pressures. Hence, depending on pressure and temperature, the tube-side coefficient will vary and affect the tube wall temperature. At very high pressures (>7000 kPa), the heat transfer coefficient decreases as steam temperature increases, while at lower pressure, a dip in the value is seen.

Figure B.3 shows the trend at 30–70 kg/cm 2 a steam pressures as a function of tempera- ture for a flow of 1500 kg/h inside 38 mm tube.

384 Appendix B: Tube-Side Heat Transfer Coefficients and Pressure Drop

1300 2 h °C m

1250 eff., kcal/

at transfer co 1150

Temperature, °C

FIGURE B.3

Heat transfer coefficient of steam inside tubes from 30 to 70 kg/cm 2 a.