Code No: V3114
R07
Set No: 1
III B.Tech. I Semester Supplementary Examinations, December - 2013
HEAT TRANSFER
(Common to Mechanical Engineering and Automobile Engineering)
Time: 3 Hours
Max Marks: 80
Answer any FIVE Questions
All Questions carry equal marks
**
1. a) What are different modes of heat transfer? Explain briefly giving governing equations and
at least two examples to each.
b) A furnace wall consists of three layers. The inner layer of 10 cm thickness is made of fire
brick (k = 1 W/m0C), intermediate layer of 20 cm thickness is made of masonry brick (k =
0.7 W/m0C) followed by a 5 cm thick concrete wall (k = 1.5 W/ m0C). The inner and outer
surface temperatures are 8000C and 500C. Calculate the rate of heat loss per unit area of the
wall and the intermediate temperatures.
2.
a) What is overall heat transfer coefficient and where do you use it?
b) What is meant by lumped capacity and when can it be applied in heat transfer problems?
c) A steel pipe line (k = 50 W/mK) of I.D 100 mm and O.D 110 mm is to be covered with
two layers of insulation each having a thickness of 50 mm. The thermal conductivity of the
first insulation material is 0.06 W/mK and that of the second is 0.12 W/mK. Calculate the
loss of heat per meter length of pipe and the interface temperatures between the two layers of
insulation when the temperature of the inside tube surface is 300 0C and that of the
outside surface of the insulation is 700C.
3.
a) Show different types of fins with the help of simple sketches and give their applications.
b) What is the significance of Biot and Fourier numbers?
c) Derive an expression for temperature distribution for a cylinder with heat sources.
4.
a) Sketch and explain temperature and velocity profiles in free convection on a vertical wall.
b) A 30 cm long glass plate is hung vertically in the air at 25 0C while its temperature is
maintained at 750C. Calculate the boundary layer thickness at the trailing edge of the plate. If
a similar plate is placed in a wind tunnel and air is blown over it at a velocity of 4 m/s,
estimate the boundary layer thickness at its trailing edge.
5.
a) Describe the relationship between fluid friction and heat transfer.
b) A vertical cylinder having a length of 30 cm is maintained at 1000C and exposed to room air
at 150C. Calculate the minimum diameter the cylinder can have in order to behave as a
vertical plate and also calculate the heat lost by free convection.
**
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Code No: V3114
R07
Set No: 1
6. a) Derive an expression for LMTD of a counter flow heat exchanger. State the assumptions
you have made.
b) Water at the rate of 65 kg / min is heated from 30 0C to 700C by oil having a specific heat
of 2 kJ/ kg.K. The fluids are used in counter flow double - pipe heat exchanger, and the oil
enter the exchanger at 1000C and leaves at 700C. Taking U as 300 W/m2K, calculate the heat
exchanger area. Instead of the double pipe arrangement in the above problem, it is desired to
use a shell and tube exchanger with the water making one shell pass and the oil making tow
tube passes. Calculate the area required for this exchanger.
7. a) What are different regimes of pool boiling?. Explain with the help of a neat sketch.
b) A heated vertical plate at a temperature of 1050C is immersed in a tank of water exposed
to atmospheric pressure. The temperature of the water is 100 0C, and boiling occurs at the
surface of the plate. What is the heat loss rate from the plate for an area of 0.3 m2?
8. a) What is radiation shape factor?
b) Derive an expression for radiation heat exchange between two large parallel planes.
c) Emissivities of two large parallel plates maintained at 8500C and 3500C are 0.35 and 0.55
respectively. Find the percentage reduction in heat transfer when a polished aluminum
radiation shield of emissivity 0.05 is placed between them. Also find the temperature of the
shield.
**
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Code No: V3114
R07
Set No: 2
III B.Tech. I Semester Supplementary Examinations, December - 2013
HEAT TRANSFER
(Common to Mechanical Engineering and Automobile Engineering)
Time: 3 Hours
Max Marks: 80
Answer any FIVE Questions
All Questions carry equal marks
**
1. a) Derive, starting from the fundamentals, general conduction equation in spherical
coordinates.
b) Explain briefly the concept of driving potential in heat transfer.
2.
a) What is critical thickness of insulation on a pipe? Explain its physical significance and
derive an expression for the same. State the assumptions you have made.
b) Calculate the critical radius of insulation for asbestos surrounding a pipe and exposed to
room air at 300C with h = 3 W/m2K. Calculate the heat loss from a 250 0C, 5 cm diameter
pipe when covered with critical radius of insulation and also without insulation.
3.
a) Define the terms efficiency and effectiveness as applied to fins.
b) What are the boundary conditions for three cases of rectangular plate fins - very long,
finite length with and without ends insulated?
c) An aluminum fin (k = 200 W/mK) 3.0 mm thick and 7.5 cm long protrudes from a wall.
The base is maintained at 3000C, and the ambient temperature is 500C with h = 10 W/m2K.
Calculate i) the heat loss from the fin per unit depth of material ii) temperature of the fin at
its end iii) efficiency and effectiveness of the fin.
4.
a) Explain how velocity boundary layer is formed over a flat plate in forced convection.
b) Air at 20 0C is flowing along a heated flat plate at 130 0C at a velocity of 3 m/s. The plate
is 2 m long and 1.5 m wide. Calculate i) the thickness of velocity boundary layer at 50 cm
from leading edge ii) Skin friction coefficient at 50 cm from leading edge iii) Average
friction coefficient over the entire length of the plate iv) Total drag force experienced by the
plate v) Heat transfer coefficient at 50 cm from leading edge vi) Heat transferred from the
entire plate
5.
a) What is the hydraulic diameter and when is it used?
b) How do laminar and turbulent flows influence heat transfer rates? Explain briefly
c) A large vertical plate 3 m high is maintained at 50 0C and exposed to atmospheric air at
100C. Calculate the heat transfer if the plate is 10 m wide.
6.
a) How are heat exchangers classified?
b) Derive an expression for LMTD of a parallel flow heat exchanger. State the assumptions
you have made.
c) Water at the rate of 4 kg/s is heated from 40 0C to 550C in a shell-and-tube type heat
exchanger. The water is to flow inside tubes of 2 cm diameter with an average velocity of 35
cm/s. Hot water available at 970C and at the rate of 2 kg/s is used as the heating medium on
the shell side. If the length of tubes must not be more than 2 m calculate the number of tube
passes, the number of tubes per pass and the length of the tubes for one pass shell, assuming
overall heat transfer coefficient based on outside area as 1500 W/m2 K.
**
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Code No: V3114
R07
Set No: 2
7. a) Distinguish between i) Film and drop wise condensation ii) nucleate and film boiling
b) A vertical plate 30 cm wide and 1.2 m high is maintained at 80 0C and exposed to
saturated steam at 1 atm. Calculate the heat transfer and the total mass of steam condensed
per hour.
8. a) State and prove Kirchhoff’s law of radiation.
b) Emissivities of two large parallel plates maintained at 9000C and 4000C are 0.4 and 0.6
respectively. Find i) The percentage reduction in heat transfer when a polished aluminum
radiation shield of emissivity 0.05 is placed between them. ii) Temperature of the shield. iii)
The number of shields to be placed between the two plates to reduce radiation heat transfer by
50 times, assuming all the shields have the same emissivity of 0.05.
**
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R07
Set No: 3
Code No: V3114
III B.Tech. I Semester Supplementary Examinations, December - 2013
HEAT TRANSFER
(Common to Mechanical Engineering and Automobile Engineering)
Time: 3 Hours
Max Marks: 80
Answer any FIVE Questions
All Questions carry equal marks
**
1. A furnace wall consists of three layers- an outer brick work of 20 cm thickness and inner
wooden panel of 2 cm thickness. The intermediate layer is made of an insulating material 10
cm thick. The thermal conductivities of the brick and wood used are 1.04 W/m°K and 0.69
W/m°K respectively. The inside and outside temperatures of the composite wall are 800 ° C
and 50 °C respectively. If the layer of insulation offers twice the thermal resistance of the
brick wall, calculate the rate of heat loss per unit area of the wall and the thermal
conductivity of insulating material.
2.
a) What is overall heat transfer coefficient and where do you use it?
b) What is meant by lumped capacity and when can it be applied in heat transfer problems?
3.
a) A wall of a house is constructed from a 11 cm layer of common brick (k = 0.7 W/mK)
followed by a 4 cm layer of plaster (k = 0.48 W/mK). What thickness of loosely packed
rockwool insulation (k = 0.065 W/mK) should be added to reduce the heat loss through the
wall by 50 %?
b) A current of 200 A is passed through a stainless steel wire 3 mm in diameter. The
resistivity of the steel may be taken as 70 µΩ -cm, and the length of the wire is 1 m. The
wire is submerged in a liquid at 1000C and experiences a convective heat transfer coefficient
of 4 kW/m2K. Taking k for wire as 20 W/mK, Calculate the central temperature of the wire.
4.
a) Distinguish between free and forced convection.
b) Air flow through a long rectangular air conditioning duct of 30 cm height and 60 cm
width maintains the outer duct surface temperature at 15 0C. If the duct is un insulated and
exposed to air at 250C, calculate the heat gained by the duct per meter length, assuming it to
be horizontal.
5.
a) What is the significance of Reynolds, Prandtl, Grashof and Nusselt numbers?
b) Engine oil enters a 5 mm diameter tube at 120 0C. The tube wall is maintained at 500C,
and the inlet Reynolds number is 1000. Calculate the heat transfer, average heat transfer
coefficient and exit oil temperature if the length of the tube is 20 cm.
6.
a) What are the advantages of NTU method over the LMTD method ?
b) What are fouling factors? Explain briefly.
c) Water enters a cross flow heat exchanger (both fluids unmixed) at 5 0C and flows at the
rate of 4500 kg/h to cool 4000 kg/h of air that is initially at 35 0C. Assuming overall heat
transfer coefficient as 150 W/ m2 K, calculate the exit temperature of water for an exchanger
surface area of 25 m2.
**
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Code No: V3114
R07
Set No: 3
7. a) What are the different regimes of pool boiling?. Explain where and why does radiation
play a significant role in heat transfer during boiling.
b) A vertical square plate, of 40 x 40 cm, is exposed to steam at atmospheric pressure. The
plate temperature is 980C. Calculate the heat transfer and the mass of steam condensed per
day.
8. a) Explain Plank’s distribution law.
b) Two parallel plates 0.5 x 1.0 m are spaced 0.5 m apart. One plate is maintained at 10000C
and the other at 5000C. The emissivities of the plates are 0.2 and 0.5, respectively. The
plates are located in a very large room, the walls of which are maintained at 300C. The plates
exchange heat with each other and with the room, but only the plate surfaces facing each
other are to be considered in the analysis. Find the net heat transfer to each plate and to the
room.
**
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R07
Set No: 4
Code No: V3114
III B.Tech. I Semester Supplementary Examinations, December - 2013
HEAT TRANSFER
(Common to Mechanical Engineering and Automobile Engineering)
Time: 3 Hours
Max Marks: 80
Answer any FIVE Questions
All Questions carry equal marks
**
1. a) Define thermal conductivity. Name some good conductors of heat; some poor conductors.
b) Derive, starting from fundamentals, general conduction equation in Cartesian coordinates
and deduce it to one dimensional steady state condition with no internal heat generation.
2.
a) A thick walled tube of stainless steel with 2.5 cm inner diameter and 4.5 cm outer
diameter is covered with a 3 cm layer of asbestos insulation. If the inside wall temperature
of the pipe is maintained at 5000C, calculate the heat loss per meter of length. Also calculate
the tube-insulation interface temperature.
b) A thick walled copper cylinder has an inside radius of 1 cm and an outside radius of 2 cm.
The inner and outer surfaces are held at 310 0C and 2900C respectively. Assume k varies
with temperature as k (W/mK) = 371.9 [ 1 - 9.25 × 10-5( T - 150 ) ]. Determine the heat loss
per unit length.
3.
a) What are the different charts used to solve transient conduction problems and what is their
significance?
b) Derive an expression for temperature distribution in systems with negligible internal
resistance.
c) An aluminum sphere weighing 5 kg and initially a temperature of 350 0C is suddenly
immersed in a fluid at 500C. The heat transfer coefficient is 60 W/m2 0C. Estimate the time
required to cool the sphere to 1000C. Take for aluminum = 2700 kg/m3, c = 900 J/kgK and
k = 200 W/mK.
4.
a) What is the significance of dimensional analysis? Derive expressions for Reynolds, Pradtl
and Nusselt numbers using dimensional analysis.
b) Air at 2 bar and 2000C is heated as it flows through a tube with a diameter of 2 cm at a
velocity of 10 m/s. Calculate the heat transfer per unit length of tube if a constant heat flux
condition is maintained at the wall and the wall temperature is 250C above the air
temperature, all along the length of the tube. How much would the bulk temperature
increase over a 3-m length of the tube?
5.
a) Write a brief note on Continuity, Momentum and Energy Equations.
b) Calculate the heat-transfer rate per unit length for flow at a speed of 6 m/s over a 0.025
mm diameter cylinder maintained at 600C. Perform the calculation for i) air at 200C and 1
atm and ii) water at 200C.
6.
a) Define effectiveness of heat exchangers and obtain an expression for it in case of a
parallel flow heat exchanger.
b) Hot oil with a capacity rate of 2500 W/K flows through a double pipe heat exchange. It
enters at 3500 C and leaves at 3000 C. Cold fluid enters at 300C and leaves at 2000 C. If the
overall heat transfer coefficient is 800 W/m2 K, determine the heat exchanger area required
for (i) parallel flow and (ii) counter flow. Give your conclusion based on the values you get.
**
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Code No: V3114
R07
Set No: 4
7. a) What is meant by sub cooled and saturated boiling? Explain.
b) Saturated steam at 1.03 bar pressure condenses on the outside of a 30 cm diameter tube
whose surface is maintained at 95 0C. The tube is 15 m long. Calculate the heat transfer
coefficient and the amount of steam condensed per hour.
8. a) What is a radiation shield and how does it reduces radiation heat transfer rate?
b) Define i) Emissive power & Emissivity ii) Black body & Opaque body
c) The net radiation from the surface of two parallel plates maintained at temperatures T 1
and T2 is to be reduced by 75 times. Calculate the number of screens to be placed between
these two surfaces to achieve this reduction in heat exchange, assuming the emissivity of the
screens as 0.05 and that of the surfaces as 0.8.
**
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