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Question 5

The aluminum plate has rectangular fins on one side in contact with air at 38°C and a heat transfer coefficient of 8.5 W/m2K. Water at 13°C flows on the other side with a heat transfer coefficient of 83.1 W/m2K. (1) The fin efficiency is calculated to be 0.707. (2) The rate of heat transfer per unit area of wall is calculated to be 116 W/m2. (3) Fins would be less effective on the water side due to the higher heat transfer coefficient, so the current design with fins on the air side is better.

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Muhammad Aliff
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459 views4 pages

Question 5

The aluminum plate has rectangular fins on one side in contact with air at 38°C and a heat transfer coefficient of 8.5 W/m2K. Water at 13°C flows on the other side with a heat transfer coefficient of 83.1 W/m2K. (1) The fin efficiency is calculated to be 0.707. (2) The rate of heat transfer per unit area of wall is calculated to be 116 W/m2. (3) Fins would be less effective on the water side due to the higher heat transfer coefficient, so the current design with fins on the air side is better.

Uploaded by

Muhammad Aliff
Copyright
© Attribution Non-Commercial (BY-NC)
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as DOC, PDF, TXT or read online on Scribd
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A 0.3-cm thick aluminum plate has rectangular fins on one side, 0.16 0.6 cm, spaced 0.6 cm apart.

. The finned side is in contact with low pressure air at 38 ! and the a"erage heat transfer coefficient is #8.$ %&'m# (). *n the unfinned side water flows at +3 ! and the heat transfer coefficient is #83., %&'m# (). 'a) !alculate the efficienc- of the fins '.) calculate the rate of heat transfer per unit area of wall and 'c) comment on the design if the water and air were interchanged. GIVEN Aluminum plate with rectangular fins on one side /late thickness '0) 1 0.3 cm 1 0.003 m 2in dimensions 't 3) 1 0.0016 m 0.006 m 2in spacing 's) 1 0.006 m apart 2inned side Air temperature 'Ta) 1 38 ! 4eat transfer coefficient ' ha ) 1 #8.$ %&'m# () 5nfinned side %ater temperature 'Tw) 1 +3 ! 4eat transfer coefficient ' hw ) 1 #83., %&'m# ()

ASSUMPTIONS The aluminum is pure %idth of fins is much longer than their thickness The s-stem has reached stead- state The thermal conducti"it- of the aluminum is constant

SOLUTION: 'a) The fin efficienc- is defined as the actual heat transfer rate di"ided .- the rate of heat transfer if the entire fin were at the wall temperature. 6ince the fin is of uniform cross section, Ta.le #.1 can .e used to find an e7pression for the heat transfer from a fin with a con"ection from the tip

8f the entire fin were at the wall temperature 'Tsa) the rate of heat transfer would .e

The fin efficienc- is

'.) The heat transfer to the air is e9ual to the sum of heat transfer from the fins and the heat transfer from the wall area not co"ered .- fins. The num.er of fins per meter height is

The wall area not co"ered .- fins per m# of total wall area is A.are 1 1 m# : '131. 6 fins) '0.0016 m&fin) '1 m width) 1 0.,8+ m# The surface area of the fins per m# of wall area is Afins 1 131.6 fins '#'0.006 m) ; 0.0016 m) '1 m width) 1 1.,+ m# The rate of heat transfer to the air is

Therefore, the resistance to heat transfer on the air side '<=) is

The thermal circuit for the wall is shown .elow

The indi"idual resistance .ased on 1 m# of wall area are

The rate of heat transfer through the wall is

'c) >ote that the air side con"ecti"e resistance is .- far the dominant resistance in the pro.lem. Therefore, the fins will enhance the o"erall heat transfer much less on the water side. 2or fins on the water side

The fins are most effecti"e in the medium with the lowest heat transfer coefficient. %ith no fins, the rate of heat transfer would .e 1$1+ %&m #. 2ins on the water side increase the rate of heat transfer 6?. 2ins on the air side increase the rate of heat transfer 116?. Therefore, installing fins on the water side would .e a poor design.

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