Fins
Q1. One end of long rod of diameter 10 mm is inserted into a furnace. The temperatures measured
at two points A and B, 39.3 mm apart gave 265°C and 147.5°C respectively. If the convection
coefficient is 35 W/m2K, when exposed to air at 30°C, determine the conductivity of the material.
Ans: 45 W/mK
Q2. Two rods of diameter D mm and length L mm have one of the ends at 120°C and are exposed
to air at 30°C. The conductivity of the material of one rod is 45 W/mK and the temperature of the
rod at the end is measured as 80°C, while the end temperature of the other rod was 60°C. Determine
the conductivity of the other material.
Hint: Short fin end insulated condition suits the problem Ans: 20.62 W/mK
Q3. A rod of 12 mm dia is used as a fin of length 0.08 m. The material conductivity is 15.5 W/mK.
The convection coefficient is 25 W/m 2K. Compare the heat flow if the same volume is used for
two fins of same length. Assuming short fin end insulated condition. Ans: 22% increase
Q4. Frying requires oil to be heated to about 350°C. A laddle is used in the frying. The section of
the handle is 4 mm × 15 mm. The surroundings are at 35°C. The conductivity of the material is
210 W/mK. If the temperature at a distance of 40 cm from the oil should not reach 45°C, determine
the convection heat transfer coefficient required. Solve the problem for both Aluminum and steel
as the ladle material and justify your answer. Ans:Al: 24.67 W/m2K, Steel: 2.58 W/m2K
Q5. A volume of 5 cm3 is available for a circular pin fin. Determine the optimum diameter.
Conductivity = 200 W/mK, convection coefficient = 200 W/m 2K. Assume end insulated fin. Ans:
10 mm.
Q6. A copper fin 12 mm dia and 200 mm long spans two walls one at 200°C and the other at
120°C. The thermal conductivity of the material is 330 W/mK. Air at 30°C flows between the
walls and the convection coefficient over the rod was 56.8 W/m 2K. Determine the heat flow
through the rod. Also find the temperature at the mid-section and the location and value of the
minimum temperature. Ans: 47 W , mid point temp = 1300C, min temp = 1117.610C
Q7. A fin in the form of a ring of 0.25 mm thickness and 15 mm OD and 15 mm long is used on
an electric device to dissipate heat. Consider the outer surface alone to be effective and exposed to
air at 25°C with a convection coefficient of 40 W/m2K. The conductivity of the material is 340
W/mK. If the heat output is 0.25 W and if the device is also of the same OD, determine the device
temperature with and without the fin. Ans: 60.380C (W/o fin), 34.160C with fin
Q8. A handle fixed to chemical process equipment is as shown in Fig. The handle is exposed to
air at 37°C with a convection coefficient of 15 W/m2K. The conductivity of the material is 20
W/mK. Determine the heat lost and also the temperature at the mid location. Ans:4.01 W, 57.7 0C.
Hint: You can assume the whole handle as one fin with dirichlet condition at two ends or two
different fins with half the length and insulated tip condition.
Q9. A plane wall exposed to a fluid with a convection coefficient is found insufficient to dissipate
the heat. One mm thick plate fins of 40 mm length are added with a pitch of 10 mm. The addition
of the fins causes a reduction in the convection coefficient to 30 W/m 2K from the original value
of 40 W/m2K. If the conductivity of the material is 210 W/mK determine the percentage increase
in heat dissipation. Ans: The increase is about 855%.
Q10. Circumferential fins of constant thickness of 1 mm are fixed on a 50 mm pipe at a pitch of 4
mm. The fin length is 20 mm. The wall temperature is 130°C. The thermal conductivity of the
material is 210 W/mK. The convection coefficient is 50W/m 2K. Determine the heat flow and
effectiveness. Ans: 45.85 W, 14.
