SNJB’S LATE SAU K. B.

JAIN COLLEGE OF ENGINEERING CHANDWAD

Unit 2 ASSIGNMENT NO. 2

Autonomy 2017 Pattern

Unit II – One dimensional steady state heat conduction with Uniform

heat generation and Heat conduction through Extended Surfaces – Fins

Q.1) List two examples of heat conduction with heat generation.

Q.2)

Q.3)

Q.4)

Q.5)

Q.6)

Q.7) Explain the criteria for selection of fins.

Q.8) Derive the general heat conduction equation in Cartesian co-ordinates.
Under what condition does this get reduced to Poisson equation; Laplace
equation and Fourier equation.
Q.9) Write only “Three dimensional general differential equation of
conduction in cylindrical and spherical geometry.” Don’t derive.
Q.10) What is the purpose of insulation? Explain significance of critical

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radius of insulation with sketch.

Q.11) Derive an expression for critical radius of insulation of cylinder using
usual notations.
Q.12) Write minimum three applications of conduction with heat generation.

Numerical on all types of fins

Q.1) A very long 25 mm diameter copper (k = 380 W/m.K) rod extends from
a surface at 120°C.
The temperature of surrounding air is 25°C and the heat transfer coefficient
over the rod is 10 W/m2.K. Calculate:
(i) Heat loss from the rod,
(ii) How long the rod should be in order to be considered infinite?

Q.2) One end of a long rod 3 cm in diameter is inserted into a furnace with
the outer end projecting into the outside air. Once the steady state is
reached the temperature of the rod is measured at two points, 15 cm apart
and found to be 140°C and 100°C, when the atmospheric air is at 30°C with
convection coefficient of 20 W/m2.K. Calculate the thermal conductivity of
the rod material.

Q.3) Three rods of copper, aluminium and stainless steel are coated with
wax all around and are
dipped vertically in a water bath at 85°C. The length of each rod projecting
outside the bath is 300 mm. Diameter of each rod is 20 mm and length is
400 mm. Convective heat transfer coefficient at the surface of each rod is 11
W/m2.K.
Thermal conductivity of
(i) Copper rod = 380 W/m.K
(ii) Aluminium rod = 206 W/m.K

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 SNJB’S LATE SAU K. B. JAIN COLLEGE OF ENGINEERING CHANDWAD

(iii) Steel rod = 17 W/m.K

Q.4) An electric motor is to be connected by a horizontal steel shaft (k =

42.56 W/m.K), 25 mm in diameter to an impeller of a pump, circulating liquid
metal at a temperature of 540°C. If the temperature of electric motor is
limited to a maximum value of 52°C with the ambient air at 27°C and heat
transfer coefficient of 40.7 W/m2.K, what length of shaft should be specified
between the motor and pump?

Q.5) The handle of a saucepan, 30 cm long and 2 cm in diameter is partially

immersed in boiling water at 100°C. The average unit conductance over the
handle surface is 7.35 W/m2.K in the kitchen air at 24°C. The cook is likely
to grasp the last 10 cm of the handle and hence, the temperature of this
portion should not exceed 32°C. What should be the material conductivity of
handle? The handle may be treated as a fin of insulated tip.

Q.6) A steel fin (k = 54 W/m.K) with a cross section of an equilateral

triangle, 5 mm in side is 80 mm long. It is attached to a plane wall
maintained at 400°C. The ambient air temperature is 50°C and unit surface
conductance is 90 W/m2.K. Calculate the heat dissipation rate from the rod.

Q.7) The handle of a ladle used for pouring molten metal at 327°C is 30 cm
long and is made of 2.5 cm × 1.5 cm mild steel bar stock (k = 43 W/m.K). In
order to reduce the grip temperature, it is proposed to make a hollow handle
of mild steel plate 0.15 cm thick to the same rectangular shape. If the
surface heat transfer coefficient is 14.5 W/m2.K and the ambient
temperature is at 27°C, estimate the reduction in the temperature of grip.
Neglect the heat transfers from inner surface of the hollow shape.

Q.8) One end of a copper rod (k = 380 W/m.K), 300 mm long is connected
to a wall which is maintained at 300°C. The other end is firmly connected to
other wall at 100°C. The air is blown across the rod so that the heat transfer
coefficient of 20 W/m2.K is maintained. The diameter of the rod is 15 mm

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 SNJB’S LATE SAU K. B. JAIN COLLEGE OF ENGINEERING CHANDWAD

and temperature of air is 40°C. Determine:

(i) Net heat transfer rate to air,
(ii) The heat conducted to other end which is at 100°C.

Fin Performance: Fin Effectiveness, Fin Efficiency

Q.1) It is better to use 10 fins of 5 cm length than 5 fins of 10 cm length.
State and prove correctness of the statement. Take properties as follows:
Diameter of fin = 10 mm Thermal conductivity = 45 W/m.K, Heat transfer
coefficient = 95 W/m2.K.

Q.2) Three identical straight fins, 10 mm in diameter and 120 mm long are
exposed to an ambient with convective heat transfer coefficient of 32
W/m2.K. Compare their efficiency and relative heat flow performance. The
three fin materials and their thermal conductivities are:
Copper: 380 W/m.K, Aluminium : 210 W/m.K, Mild steel : 45 W/m.K.

Q.3) An electronic semiconductor device has a rating of 60 mW. In order to

keep its proper operation, the inside temperature should not exceed 70°C.
The device can dissipate about 20 mW of heat on its own when placed in an
environment at 40°C with heat transfer coefficient of 12.5 W/m2.K. To avoid
overheating of the device, it is proposed to install aluminium (k = 190
W/m.K) square fins 0.6 mm side, 10 mm long, to provide additional cooling.
Find the number of fins required. Assume no heat loss from the tip of fins.

Q.4) A 1 m long, 5 cm diameter, cylinder placed in an atmosphere of 40°C is

provided with 12 longitudinal straight fins (k = 75 W/m.K), 0.75 mm thick.
The fins protrude 2.5 cm from the cylinder surface. The heat transfer
coefficient is 23.3 W/m2.K. Calculate the rate of heat transfer, if the surface
temperature of cylinder is at 150°C.

Q.5) The cylinder barrel of a motorcycle is constructed of aluminium alloy (k

= 186 W/m.K), 0.15 m high and 50 mm in diameter. Under typical operating
conditions, the outer surface of the cylinder is at a temperature of 500 K and

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 SNJB’S LATE SAU K. B. JAIN COLLEGE OF ENGINEERING CHANDWAD

is exposed to the ambient air at 300 K with convection coefficient of 50

W/m2.K. Annular fins of rectangular profiles are typically added to increase
the heat transfer rate to the surroundings.
Assume that the five such fins, 6 mm thick, 20 mm long and equally spaced
are added. What is the increase in heat transfer rate due to addition of fins ?
Take fin efficiency as 0.95.

Q.6) A hot surface at 100°C is to be cooled by attaching 3 cm long, 0.25 cm

diameter aluminium fins (k = 237 W/m.K) to it, with a center to center
distance of 0.6 cm. The temperature of surrounding air is 30°C and heat
transfer coefficient on surface is 35 W/m2.K. Calculate the rate of heat
transfer from the surface for a 1 m × 1 m section of the plate. Also
determine the overall effectiveness of the fins.

Design Considerations for Fins

Q.1) The 4 mm thick fins of Mild Steel are used to transfer heat from water
to air. Decide the utility of fin on either side. The heat transfer coefficient of
air is 80 W/m2K while that of water is 5600 W/m2K. Take thermal
conductivity of mild steel as 45 W/mk.

Q.2) A steel fin having 8 mm diameter and 100 mm long is exposed to

boiling water having h= 4000 W/m2K. The thermal conductivity of steel as 17
W/mk. Show by calculation how much heat dissipation is achieved and is it
advisable to use the fin?
How the heat dissipation performance will change, if a material with k = 45
W/mK is used? All other conditions are same.

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 SNJB’S LATE SAU K. B. JAIN COLLEGE OF ENGINEERING CHANDWAD

GATE Syllabus
Heat transfer through fins

GATE Questions

Q.1) On heat transfer surface, fins are provided [IES-2010]

(a) To increase temperature gradient so as to enhance heat transfer
(b) To increase turbulence in flow for enhancing heat transfer
(c) To increase surface are to promote the rate of heat transfer
(d) To decrease the pressure drop of the fluid

Q.2) Which one of the following is correct? [IES-2008]

The effectiveness of a fin will be maximum in an environment with
(a) Free convection (b) Forced convection
(c) Radiation (d) Convection and radiation
Q.3)

Q.4) Fins are made as thin as possible to: [IES-2010]

(a) Reduce the total weight
(b) Accommodate more number of fins
(c) Increase the width for the same profile area
(d) Improve flow of coolant around the fin

Q.5) A finned surface consists of root or base area of 1 m2 and fin surface
area of 2 m2. The average heat transfer coefficient for finned surface is
20 W/m2K. Effectiveness of fins provided is 0.75. If finned surface with
root or base temperature of 50°C is transferring heat to a fluid at 30°C,

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then rate of heat transfer is: [IES-2003]

(a) 400 W (b) 800 W (c) 1000 W (d) 1200 W

Q.6) Consider the following statements pertaining to large heat transfer

rate using fins: [IES-2002]
1. Fins should be used on the side where heat transfer coefficient is
small
2. Long and thick fins should be used
3. Short and thin fins should be used
4. Thermal conductivity of fin material should be large
Which of the above statements are correct?
(a) 1, 2 and 3 (b) 1, 2 and 4 (c) 2, 3 and 4 (d) 1, 3 and 4

PBL Questions on Fins

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