Page 418 - Handbook of Energy Engineering Calculations

bulb temperature met in summer is 90°F (32.2°C). Use this as the air inlet
temperature.
Before the required surface area can be determined, the air outlet
temperature from the radiator must be known. This outlet temperature cannot
be computed directly. Hence, it must be assumed and a trial calculation made.

If the area obtained is too large, a higher outlet air temperature must be
assumed and the calculation redone. Assume an outlet air temperature of
150°F (65.6°C).

4. Compute the LMTD for the radiator

The largest temperature difference for this exchanger is 160 – 90 = 70°F
(38.9°C), and the smallest temperature difference is 150 – 140 = 10°F
(5.6°C). In the smallest temperature difference expression, 140°F (77.8°C) =
water discharge temperature from the engine – cooling-water temperature rise

during passage through the engine, or 160 – 20 = 140°F (77.8°C). Then
LMTD = (70 – 10)/[ln (70/10)] = 30°F (16.7°C). (Figure 4 could also be used
to compute the LMTD.)

5. Compute the required exchanger surface area
2
Use the relation A = Q/U × LMTD, where A = surface area required, ft ; Q =
rate of heat transfer, Btu/h; U = overall coefficient of heat transfer, Btu/(h ·
2
ft · °F). To solve this equation, U must be known.
Table 1 in the first calculation procedure in this section shows that U
2
2
ranges from 2 to 10 Btu/(h · ft · °F) [56.8 W/(m · °C)] in the usual internal-
combustion-engine finned-tube radiator. Using a value of 5 for U, we get A =
2
2
2,200,000[(5)(30)] = 14,650 ft (1361.0 m ).

6. Determine the length of finned tubing required
The total area of a finned tube is the sum of the tube and fin area per unit
length. The tube area is a function of the tube diameter, whereas the finned

area is a function of the number of fins per inch of tube length and the tube
diameter.
Assume that 1-in (2.5-cm) tubes having 4 fins per inch (6.35 mm per fin)
are used in this radiator. A tube manufacturer’s engineering data show that a

2
2
finned tube of these dimensions has 5.8 ft of area per linear foot (1.8 m /lin
m) of tube.