A 0.3-cm-thick aluminum plate has rectangular fins 0.16 x 0.6 cm, on one side, spaced 0.6 cm apart. The finned side is in contact with low pressure air at 38°C and the average heat transfer coefficient is 28.4 W/(m2 K). On the unfinned side water flows at 93°C and the heat transfer coefficient is 284 W/(m2 K). (a) Calculate the efficiency of the fins (b) 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
FIND
(a) The fin efficiency (?f)
(b) Rate of heat transfer per unit wall area (q/Aw)
(c) Comment on the design if the water and air were interchanged
ASSUMPTIONS
Width of fins is much longer than their thickness
The system has reached steady state
The thermal conductivity of the aluminum is constant
SKETCH
(a) The fin efficiency is defined as the actual heat transfer rate divided by the rate of heat transfer if the entire fin were at the wall temperature. Since the fin is of uniform cross section,
can be used to find an expression for the heat transfer from a fin with a convection from the tip
If the entire fin were at the wall temperature (Tsa) the rate of heat transfer would be
(b) The heat transfer to the air is equal to the sum of heat transfer from the fins and the heat transfer from the wall area not covered by fins.
The number of fins per meter height is
1m (0.076 m/fin) = 131.6 fins
The wall area not covered by fins per m2 of total wall area is
The surface area of the fins per m2 of wall area is
The rate of heat transfer to the air is
Therefore, the resistance to heat transfer on the air side (Ra) is
The thermal circuit for the wall is shown below
The individual resistance based on 1 m2 of wall area are
The rate of heat transfer through the wall is
(c) Note that the air side convective resistance is by far the dominant resistance in the problem. Therefore, the fins will enhance the overall heat transfer much less on the water side.
For fins on the water side
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