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3-201 Steam in a heating system flows through tubes whose outer diameter is 3 cm and whose walls are maintained at a temperature of 120°C. Circular aluminum alloy fins (k = 180 W/m K) of outerdiameter 6 cm and constant thickness t = 2 mm are attached to the tube, as shown in Fig. P3-201. The space between the fins is 3 mm, and thus there are 200 fins per meter length of the tube. Heat istransferred to the surrounding air at 25°C, with a combined heat transfer coefficient of 60 W/m2-K. Determine the increase in heat transfer from the tube per meter of its lengthas a result of adding fins.page 245FIGURE P3-201r= 1.5 cm2-3 cmt=2 mmS 3 mm

Question
3-201 Steam in a heating system flows through tubes whose outer diameter is 3 cm and whose walls are maintained at a temperature of 120°C. Circular aluminum alloy fins (k = 180 W/m K) of outer
diameter 6 cm and constant thickness t = 2 mm are attached to the tube, as shown in Fig. P3-201. The space between the fins is 3 mm, and thus there are 200 fins per meter length of the tube. Heat is
transferred to the surrounding air at 25°C, with a combined heat transfer coefficient of 60 W/m2-K. Determine the increase in heat transfer from the tube per meter of its length
as a result of adding fins.
page 245
FIGURE P3-201
r= 1.5 cm
2-3 cm
t=2 mm
S 3 mm
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3-201 Steam in a heating system flows through tubes whose outer diameter is 3 cm and whose walls are maintained at a temperature of 120°C. Circular aluminum alloy fins (k = 180 W/m K) of outer diameter 6 cm and constant thickness t = 2 mm are attached to the tube, as shown in Fig. P3-201. The space between the fins is 3 mm, and thus there are 200 fins per meter length of the tube. Heat is transferred to the surrounding air at 25°C, with a combined heat transfer coefficient of 60 W/m2-K. Determine the increase in heat transfer from the tube per meter of its length as a result of adding fins. page 245 FIGURE P3-201 r= 1.5 cm 2-3 cm t=2 mm S 3 mm

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Step 1

Write all the given variables in the problem along with their proper notations.

Outer radius of pipe,
= 1.5 cm
Thickness of fin, t = 2 mm
Thermal conductivity of fin material, k = 180 W/m K
Outer radius of the fin, r, = 3 cm
Temperature of the outer surface of pipe, T (120+273) K = 393 K
Ambient temperature, T(25+273) K 298 K
Heat transfer coefficient of ambient air, h = 60 W/m2 K
Number of fins per meter length of the tube, n = 200
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Outer radius of pipe, = 1.5 cm Thickness of fin, t = 2 mm Thermal conductivity of fin material, k = 180 W/m K Outer radius of the fin, r, = 3 cm Temperature of the outer surface of pipe, T (120+273) K = 393 K Ambient temperature, T(25+273) K 298 K Heat transfer coefficient of ambient air, h = 60 W/m2 K Number of fins per meter length of the tube, n = 200

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Step 2

Write the expressions for corrected radius of the fin and simultaneously substitute the suitable values to obtain the same.

2
1 m
1
(2 mm) 1000 mm
1m
=3 cm
100 cm
= 0.031 m
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2 1 m 1 (2 mm) 1000 mm 1m =3 cm 100 cm = 0.031 m

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Step 3

Write the expression for the corrected length of the fin and simult...

L = L-
2
2
1 m
1
(2 mm
2
1m
1 m
-1.5 cm
3 cm
1000 mm
100 cm
100 cm
=0.016 m
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L = L- 2 2 1 m 1 (2 mm 2 1m 1 m -1.5 cm 3 cm 1000 mm 100 cm 100 cm =0.016 m

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