The addition of aluminum fins has been suggested to increase the rate of heat dissipation from one side of an electronic device 1-m-wide and 1-m-tall. The fins are to be rectangular in cross section, 2.5-cm-long and 0.25-cm-thick. There are to be 100 fins per meter. The convective heat transfer coefficient, both for the wall and the fins, is estimated at 35 W/(m2 K). With this information, determine the per cent increase in the rate of heat transfer of the finned wall compared to the bare wall.

Question

GIVEN

Aluminum fins with a rectangular cross section

Dimensions: 2.5-cm-long and 0.25-mm-thick

Number of fins per meter = 100



FIND

The per cent increase in the rate of heat transfer of the finned wall compared to the bare wall

ASSUMPTIONS

Steady state heat transfer

SKETCH

Answer 1

Since the fins are of uniform cross section, can be used to calculate the heat transfer rate from a

single fin with convection at the tip





Therefore, the rate of heat transfer from one fin, 1-meter-wide is:



In 1 m2 of wall area there are 100 fins covering 100 tw = 100 (0.0025 m) (1 m) = 0.25 m2 of wall area leaving 0.75 m2 of bare wall. The total rate of heat transfer from the wall with fins is the sum of the heat transfer from the bare wall and the heat transfer from 100 fins.



The rate of heat transfer from the wall without fins is



The percent increase due to the addition of fins is