Tutorial 2: Heat transfer through extended surfaces (fins)
Question 1
A 2m2 hot plate has 2 cm-diameter, 15 cm long aluminium pin fins (k = 237 W/m.K) in an
aligned array at a distance of 4 cm between the pins. The environmental air is at 25 0C which
goes through the array, giving a heat transfer coefficient of 35 W/m2 K. The fins are assumed
to be insulated at the tip
1.1 If the plate is not to exceed a 75 0C operating temperature, what is the heat transfer
rate? [20.188 kW]
1.2 The efficiency of the fins [81.6 %]
1.3 The effectiveness of the fins [5.8]
Question 2
A brass rod (k=110 W/m 0C) 80 mm long and 6 mm in diameter extends horizontally from a
casting iron at 180 0C. The rod is insulated at the tip is in an air environment with
T∞
=25
℃
and
h
=20
W
/
m
2
.℃
. Calculate the temperature of the rod at 20mm, 45mm
and 80mm from the base. [Ans: 159.5 0C; 142.9 0C; 134.740C]
Question 3
An array of six Aluminium alloy fins, each 3mm wide, 0.4 mm thick, and 40 cm long, it is used to
cool a transistor, when the base is at 340K and the ambient air is at 300K. How much power do
they need if the combined convection and radiation heat transfer coefficient is estimated to be
8 W/m2K? The Aluminium alloy has a conductivity of 175 w/m.k. ( Note: the fin is infinitely long)
[Ans: 0.811 W]
Question 4
A plane wall with surface temperature of 350 0C is attached with straight rectangular fins ( k =
235 w/m.k). The fins are exposed to an ambient air condition of 25 0C and the convection heat
transfer coefficient is 154 w/m2.k. Each fin has a length of 50 mm, a base of 5 mm thick and a
width of 100 mm. (Note: Assume that the tip of the fin is insulated). Determine
a) Fin efficiency [81.3 %]
b) Heat transfer rate from the fin [427.25 W]
c) Fin effectiveness [17.07]
