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CH302 Heat Transfer Operations
Question
No. Introduction to Heat Transfer
1. The essential condition for the transfer of heat from one body to another
(a) Both bodies must be in physical contact
(b) Heat content of one body must be more than that of the other
(c) One of the bodies must have a high value of thermal conductivity
(d) There must exist a temperature difference between the bodies
2. Consider system A at uniform temperature t and system B at another uniform temperature T (t > T). Let the two systems be brought into contact and be
thermally insulated from their surroundings but not from each other. Energy will flow from system A to system B because of
(a) Temperature difference
(b) Energy difference
(c) Mass difference
(d) Volumetric difference
3. Which of the following law do not govern heat transfer?
(a) First Law of Thermodynamics
(b) Second Law of Thermodynamics
(c) Zeroth Law of Thermodynamics
(d) Newton law of motion
4. The literature of heat transfer generally recognizes distinct modes of heat transfer.
How many modes are there?
a) One
b) Two
c) Three
d) Four
5. Heat transfer in liquids and gases is essentially due to_______________________
(a) Conduction
(b) Convection
(c) Radiation
(d) Conduction and convection put together
6. Conduction is a process of heat transfer from
(a) a hot body to a cold body, in a straight line, without affecting intervening
medium
(b) one particle of the body to another without the actual motion of the particles
(c) one particle of the body to another by the actual motion of the heated
particles
(d) none of the above
7. Unit of rate of heat transfer is
(a) Joule
(b) Newton
(c) Pascal
(d) Watt
8. Which statement is true regarding steady state condition?
(a) There is a variation in temperature in the course of time
(b) Heat exchange is constant
(c) It is a function of space and time coordinates
(d) Internal energy of the system changes
9. An oil cooler in a high performance engine has an outside surface area 0.12 m2
and a surface temperature of 65 degree Celsius. At any intermediate time air
moves over the surface of the cooler at a temperature of 30 degree Celsius and
gives rise to a surface coefficient equal to 45.4 W/ m2 K. Find out the heat
transfer rate?
(a) 238.43 W
(b) 190.68 W
(c) 543.67 W
(d) 675.98 W
10. The rate equation used to describe the mechanism of convection is called
Newton’s law of cooling. So rate of heat flow by convection doesn’t depend on
(a) Convective heat transfer coefficient
(b) Surface area through which heat flows
(c) Time
(d) Temperature potential difference
11. Which of the following is an example of forced convection?
(a) Chilling effect of cold wind on a warm body
(b) Flow of water in condenser tubes
(c) Cooling of billets in the atmosphere
(d) Heat exchange on cold and warm pipes
12. A radiator in a domestic heating system operates at a surface temperature of 60
degree Celsius. Calculate the heat flux at the surface of the radiator if it behaves
as a black body
(a) 697.2 W/m2
(b) 786.9 W/m2
(c) 324.7 W/m2
(d) 592.1 W/m2
13. The appropriate rate equation for convective heat transfer between a surface and
adjacent fluid prescribed by________________.
14. The radiation energy emitted by a surface depends upon _____________ of its
absolute temperature.
15. Heat transfer takes place according to ______________ law of thermodynamics.
16. The radiation energy emitted by a surface depends upon___________of its absolute
temperature.
17. Heat transfer in liquids and gases is essentially due to ___________.
18. How does heat transfer differ from thermodynamics? Is it true to say that heat transfer is essentially thermodynamics with rate equations added?
19. Write some examples to illustrate the importance of heat transfer in various fields of engineering.
20. What is the driving force for heat transfer?
21. Establish governing law of heat transfer through solid.
22. Cite an analogy that would be useful in fixing the concepts of heat conduction, convection and radiation.
23. Does any convection process involve conduction to some extent? Explain.
24. What is the difference between natural and forced convection?
25. Write the rate equations for the three modes of heat transfer. Define the symbols used and give the units for each.
26. Define thermal contact resistance.
27. Explain mechanism of heat transfer by conduction.
28. What will be your response to a person who states that heat cannot be transferred in a vacuum?
29. State by giving illustration that in practice the transfer of heat is combined effect of conduction, convection and radiation.
30. A person who sits in front of a fireplace feels warm. Through which process or
processes of heat transfer does he receives heat.
31. If cooling coils in the refrigerator are placed at the bottom in place of the top then
what will happen? Why?
32. Mention the assumptions, on which Fourier’s law of heat transfer was established.
33. Explain Newton’s law of cooling.
34. A temperature rise of 60 0C in a circular shaft of 60 mm diameter is caused by the
amount of heat generated due to friction. The thermal conductivity of the shaft material is 50 W/m 0C and heat transfer coefficient is 6.5 W/m2 0C. Determine amount of heat transferred through 2 m long shaft.
35. The outer surface of 0.4 m thick concrete wall (20 m x 6m) is kept at a
temperature of 10 0C while the inner surface is kept at 50 0C. Thermal
conductivity of the concrete is 1.2 w/m- K. Determine the thermal resistance of
the wall and heat loss through it.
36. An electronic tube has a mean surface temperature of 55 0C. Its surface area is
150 cm2. The temperature of surface is 25 0C. Calculate the heat lost from the
tube by radiation.
37. The wind velocity outside a 20 cm solid brick wall is 7m/s. The thermal
conductivity of the brick wall is 0.60 W/m-K. The inside temperature is 21 0C and
the outside one is -6.5 0C. The film coefficient between the brick and air, at a
speed of 7 m/s and a temperature of-6.5 0C, is 39.8 W/m2-K and that for the
inside a condition is 17 W/m2-K. Find the overall heat transfer coefficient and the
rate of heat transfer.
38. Consider two black parallel surfaces; assume the radiant energy from each
surface is completely absorbed by other surface. The temperature of one is 204.5 0C and of the other is 21 0C. The value of Stefan-Boltzmann constant is 5.6697 x
10-8 W/m2-K4. Find the rate of heat transfer in W/m2 and the equivalent radiation
coefficient.
Heat conduction 39. The amount of heat flow through a body by conduction is
(a) dependent upon the material of the body
(b) directly proportional to the surface area of the body
(c) directly proportional to the temperature difference on the two faces of the
body
(d) inversely proportional to the thickness of the body
(e) all of the above
40. Heat conduction in gases is due to
(a) electromagnetic waves
(b) motion of electrons
(c) mixing motion of the different layers of the gas
(d) elastic impact of molecules
41. Thermal conductivity of solid metals ______ with rise in temperature.
(a) decreases
(b) increases
(c) remains same
(d) ) unpredictable
42. Which of the following has highest thermal conductivity?
(a) boiling water (b) melting ice (c) steam
(d) solid ice
43. Cork is a good insulator because_____ (a) it is flexible and can be cast into rolls (b) ) it can be powdered
(c) it is porous (d) ) its density is low
44. Arrange thermal conductivity of materials in ascending order. Copper, steel, brick
and aluminium
(a) Copper, steel, brick, aluminium
(b) Brick, aluminium, copper, steel
(c) Brick, steel, aluminium, copper
(d) Steel, copper, brick, aluminium
45. Choose the false statement
(a) Thermal conductivity is always higher in the purest form of metal
(b) Heat treatment causes considerable variation in thermal conductivity
(c) Thermal conductivity of a damp material is considerably higher than the
thermal conductivity of the dry material and water taken individually
(d) Thermal conductivity decreases with increase in the density of the
substance
46. Thermal conductivity of non-metallic amorphous solids _____ with decrease in temperature.
(a) Decreases (b) Increases
(c) remains constant (d) unpredictable
47. Temperature distribution for a plane wall, for steady state heat flow and constant
value for thermal conductivity, is (a) logarithmic
(b) parabolic (c) linear (d) any of above
48. A composite plane wall is made up of two different materials of the same thickness and having thermal conductivities of kl and k2 respectively. The equivalent
thermal conductivity of the slab is _____. (a) k1+k2
(b) k1k2
(c) (𝑘1+ 𝑘2)
𝑘1𝑘2
(d) 𝑘1𝑘2
(𝑘1+ 𝑘2)
49. The steady state temperature distribution in a very large thin plate with uniform
surface temperatures will be
(a) Linear
(b) Parabolic
(c) Hyperbolic
(d) logarithmic
50. The heat flow equation through a sphere of inner radius r1 and outer radius r2 is
to be written in the same form as that for heat flow through a plane wall. For wall
thickness (r2 – r1) the equivalent mean radius for the spherical shell is
(a) 2
21 rr
(b) 21rr
(c) 21rr
(d)
1
2
21
logr
r
rr
e
51. Heat transfer in liquids and gases is essentially due to
(a) Conduction
(b) Convection
(c) Radiation
(d) Conduction and Convection put together
52. For steady state and constant value of thermal conductivity, the temperature
distribution associated with radial conduction through a cylinder is
(a) Linear
(b) Logarithmic
(c) Parabolic
(d) Exponential
53. The relation 02 T is referred to as
(a) Fourier’s heat conduction equation
(b) Laplace equation
(c) Poisson’s equation
(d) Lumped parameter solution for transient conduction
54. The radial heat transfer rate through hollow cylinder increases as the ratio of outer radius to inner radius
(a) decreases (b) increases
(c) constant
(d) none of the above
55. Two insulating materials (in two layers) are used to insulate a steam pipe, best result would be obtained if
(a) inferior insulation is put over pipe (first layer) and better one over it (second layer).
(b) better insulation is put over pipe (first layer) and Inferior one over it (second layer).
(c) any material as inner layer
(d) unpredictable
56. Thermal diffusivity is a
(a) dimensionless parameter (b) Mathematical formula (c) Function of temperature
(d) All of above
57. Thermal conductivity is maximum for which substance
(a) Silver
(b) Ice
(c) Aluminum
(d) Diamond
58. Materials having crystalline structure have a ____________value of thermal
conductivity than the substance in the amorphous form.
59. For an isotropic and homogeneous material, the expression
TT
12 is the
_________________equation for unsteady state heat flow with no internal heat
generation.
60. The reciprocal of thermal resistance is called__________.
61. Thermal conductivity is always_____________ in the purest form of metal.
62. Is there any relation between thermal conductivity and electrical conductivity of
metals? If yes, explain.
63. Suggest factors affecting thermal conductivity of substance.
64. Derive general heat conduction equation in cartesian coordinates for constant
thermal conductivity. And define thermal diffusivity through it. State assumptions made for it.
65. Derive general heat conduction equation in cartesian coordinates. State assumptions made for it. Also simplify it for the case of:
No internal heat generation.
One dimensional heat transfer
66. How the thermal conductivity of metals vary with temperature and pressure?
Which are the exceptions?
67. Point out and explain the various factors which affect the thermal conductivity of
a material.
68. What is thermal conductivity? How does it vary with temperature & pressure in
solids, liquids & gases?
69. Derive equation for heat transfer by combined mode through a two layer
composite wall. Also mention assumptions made for it.
70. Derive equation for heat transfer by conduction through hollow cylinder. Also
mention assumptions made for it.
71. Define thermal diffusivity and give its physical significance in heat transfer
through conduction.
72. Prove that for a hollow composite cylinder made of m hollow shells enveloping
each other the following equation will give rate of heat transfer
mm
mm
me
m
m
r
r
k
lTTq
1
1
11
log1
2
Where l is the cylinder length, T1 and Tm+1 are the inner and outer surface
temperature of composite shell. Assume k1, k2……..km are the values of thermal
conductivities of 1st, 2nd and mth shell and r1, r2…..rm+1 be the various radii of this
composite cylinder accordingly.
A hollow cylinder placed in cold atmosphere contains hot fluid. Develop an equation for prediction of heat transfer by conduction through hollow cylinder.
Also mention assumptions made for it.
73. Derive an expression for heat flow through a composite sphere taking into account
the film heat transfer coefficients on the inside and outside surface of the sphere.
74. The insulated steam pipe of 16 cm diameter is covered with 4 cm thick layer of
insulation (k=0.9 W/m-deg) and carries process steam. Determine the percentage
change in the rate of heat loss if an extra 2 cm thick layer of lagging (k=1.25
W/m-deg) is provided. Given that surrounding temperature remains constant and
the heat transfer coefficient for both the configuration is 12 W/m2-deg.
75. An insulated wall constructed of common brick 20 cm thick and plaster 2.5 cm
thick with intermediate layer of loosely packed rock-wool. The outer surfaces of
the brick and plaster are at a temperature of 600 0C and 50 0C respectively.
Calculate the thickness of insulation required in order that the heat loss per
square meter shall not exceed 600 W. The conductivities of brick, rock-wool and
plaster are 0.32, 0.045 and 0.7 W/m0 C respectively.
76. A cold storage room has walls made of 220 mm of brick on the outside, 90 mm of
plastic foam, and finally 16 mm of wood on the inside. The outside and inside air
temperatures are 25 °C and -3°C respectively. If the inside and outside heat
transfer coefficients are respectively 30 and 11 W/m2 °C, and the thermal
conductivities of brick, foam and wood are 0.99, 0.022 and 0.17 W/m°C
respectively, determine:
(i) The rate of heat removal by refrigeration if the total wall area is 85 m2
(ii) The interface temperature of the brick & foam.
77. A metal plate of 4 mm thickness (k = 95.5 W/m°C) is exposed to vapour at 100 °C
one side and cooling water at 25 °C on the opposite side. The heat transfer
coefficients on vapour side and water side are 14500 W/m2 °C and 2250 W/m2 °C
respectively. Determine: (i) The rate of heat transfer, (ii) The overall heat transfer
coefficient, and (iii) Temperature drop at each side of heat transfer.
78. A plane slab of thickness 60 cm is made of a material of thermal conductivity k =
17.5 W/m–deg. The left side of the slab absorbs a net amount of radiant energy
from a radiant source at the rate q = 530 W/m2. If the right hand face of the slab
is at a constant temperature T2 = 38 0C, set up an expression for temperature
distribution within the slab as a function of relevant space coordinates. Therefrom
work out the temperature at the mid plane of the slab and the maximum
temperature within slab. It may be presumed that the temperature distribution is
steady and there is no heat generation.
79. A wall of a furnace is made up of inside layer of silica brick 120 mm thick covered
with a layer of magnesite brick 250 mm thick. The temperatures at the inside surface of silica brick wall and outside surface of magnesite brick wall are 725 °C and 110 °C respectively. The contact thermal resistance between the two walls at
the interface is 0.0035 °C/W per unit area. If thermal conductivities of silica and magnesite bricks are 1.7 W/m °C and 5.8 W/m °C calculate: (i) The rate of heat
loss per unit area of walls, and (ii) The temperature drop at the interface.
80. A furnace wall is composed of 220 mm of fire brick, 150 mm of common brick, 50
mm of 85% magnesia and 3 mm of steel plate on the outside. If the inside surface
temperature is 1500 0C and outside surface temperature is 90 0C, estimate the
temperatures between layers and calculate the heat loss in kJ/h m2.
Assume,
k (for fire brick) = 4 kJ/m h 0C
k (for common brick) = 2.8 kJ/m h 0C
k (for 85% magnesia) = 0.24 kJ/m h 0C
k (for steel) = 240 kJ/m h 0C
81. An exterior wall of a house is made of 0.1 m layer of common brick (k = 0.7 W/m
°C) followed by 0.04 m layer of gypsum plaster (k = 0.48 W/m °C). Find heat loss through 8.7 m2 area of wall, if external and internal temperatures are 42 and 15 °C respectively. If 58.2 mm thick loosely packed rock wool insulation (k = 0.065
W/m°c) is added find effect of it on heat loss through wall in percentage.
82. A two layer wall made of metal plate of 5 mm thickness (k = 95.5 W/m 0C)
followed by insulation layer of 12 mm thickness (k = 0.55 W/m 0C) is exposed to vapour at 120 0C one side and cooling water at 25 0C on the opposite side. The heat transfer coefficients on vapour side and water side are 1050 W/m2 0C and
225 W/m2 0C respectively. Determine: (i) The rate of heat transfer, and (ii)
Temperature drop at each side of heat transfer
83. Two slabs, each 100 mm thick and made of materials with thermal conductivities
of 16 W/m-deg and 1600 W/m-deg are placed in contact which is not perfect. Due
to roughness of surfaces, only 40% of area is in contact and air fills 0.02 mm
thick gap in the remaining area. If the extreme surfaces of the arrangement are at
temperatures of 250 0C and 30 0C, determine the heat flow through the composite
system, the contact resistance and temperature drop in contact. Take thermal
conductivity of air as 0.032 W/m-deg and assume that half of the contact (of the
contact area) is due to either metal.
84. A 3 mm thick metal plate, having thermal conductivity k = 98.6 W/m-deg, is exposed to vapor at 100 0C on one side and cooling water at 30 0C on the opposite side. The heat transfer coefficients are
hi= 14200 W/m2-deg on the vapor side; h0=2325 W/ m2-deg on the water side Determine the rate of heat transfer, the overall heat transfer coefficient and drop
in temperature at each side of heat transfer.
85. A wall of a furnace is made up of inside layer of silica brick 120 mm thick covered
with a layer of magnesite brick 250 mm thick. The temperatures at the inside surface of silica brick wall and outside surface of magneside brick wall are 725 °C and 110 °C respectively. The contact thermal resistance between the two walls at
the interface is 0.0035 °C/W per unit area. If thermal conductivities of silica and magnesite bricks are 1.7 W/m °C and 5.8 W/m °C, calculate: (i) The rate of heat
loss per unit area of walls, and (ii) The temperature drop at the interface.
86. A carbon steel (K = 54 W/m 0C) rod with a cross section of an equilateral triangle (each side 5 mm) is 80 mm long. It is attached to a plane wall which is maintained
at a temperature of 400 0C, the surrounding temperature is 50 0C and convective heat transfer coefficient is 90 W/m2 0C. Compute heat dissipated by rod.
87. A 5 m long 140 mm inner diameter and 160 mm outer diameter pipe (K=240 W/m 0C) carrying saturated steam at 150 0C, is covered by a layer of lagging of
thickness of 40 mm (K= 0.8 W/m 0C). Later, an extra layer of lagging 10 mm thick (K = 1.2 W/m 0C) is added. If the surrounding temperature is 32 0C and heat transfer coefficient inside pipe is 30 W/m2 0C and outside pipe is 10 W/m2 0C, (It
is assumed that heat transfer coefficient for outside remains same for both the lagging materials) determine the percentage change in the rate of heat loss due to extra lagging layer.
88. A 10 m long insulated steam pipe (k = 250 W/m °C) with inside diameter 25 mm and outside diameter of 30 mm is to be covered with two layers of insulation, each
having thickness of 20 mm. The thermal conductivity of one material is 0.2 and the other is 1.0 W/m °C. Steam temperature is 300 °C and steam side heat
transfer coefficient is 35 W/m2 °C. Surrounding temperature is 30 °C and heat transfer coefficient is 36 W/m2 °C. Assuming that the heat transfer coefficient on outer-side is same for both insulating materials. Find out heat loss. If poor
insulation is placed next to pipe, calculate effect on heat loss.
89. A 5 m long 200 mm ID and 240 mm OD steam pipe (k = 240 W/m °C) carrying steam at 300 °C. It is covered with 40 mm thick insulation (k = 2 W/m °C). Inside
and outside heat transfer coefficient are 40 & 10 W/m2 °C respectively. Surrounding air temperature is 30 °C. Determine the quantity of heat loss and
interface temperatures.
90. The hot combustion gases at 150 0C flow through a hollow cylindrical pipe of 10
cm inner diameter and 12 cm outer diameter. The pipe is located in a space at 30 0C and the thermal conductivity of the pipe material is 200 W/m K. Neglecting
surface heat transfer coefficients, calculate the heat loss through the pipe per unit
length and the temperature at a point halfway between the inner and outer
surface. What should be the surface area normal to the direction of heat flow so
that the heat transfer through the pipe can be determined by considering material
of the pipe as a plane wall of same thickness?
91. A steam pipe ( k = 45 W/ m °C) having 70 mm inside diameter and 85 mm outside
diameter is lagged with two insulation layers; the layer in contact with the pipe is 35 mm asbestos ( k = 0.15 W/m °C) and it is covered with 25 mm thick magnesia insulation ( k = 0.075 W/m °C). The heat transfer coefficients for the inside and
outside surfaces are 220 W/m2 °C and 65 W/m2 °C respectively. If the temperature of steam is 350 °C and the ambient temperature is 30 °C, Calculate :
(1) The steady loss of heat for 50 m length of the pipe; (2) The overall heat transfer coefficients based on inside and outside surfaces
of the lagged steam main.
92. A spherical shaped vessel of 1.4 m inner diameter is 90 mm thick. Find the rate of heat leakage, if the temperature difference between the inner and outer surfaces is
220 0C. Thermal conductivity of the material of the sphere is 0.083 W/m 0C.
93. An aluminium sphere contains steam at 110 °C. The sphere (k= 185 W/m °C) has
an inner diameter of 100 mm and outer diameter of 120 mm. The sphere is located in a room where the ambient air temperature is 30 °C and the convective heat transfer coefficient between the sphere and air is 15 W/m2 °C. Determine the
heat transfer rate. To reduce the heat loss from the sphere, it is covered with a 50 mm thick layer of insulation (k= 0.20 W/m °C). Determine the heat transfer rate from the insulated
sphere. Assume that the convective resistance of the steam is negligible.
94. A sphere (inner diameter = 150 mm and outer diameter = 160 mm) having thermal
conductivity 58 W/m 0C is covered with two layers of insulation, of thickness 30 mm and 50 mm respectively and thermal conductivities 0.18 W/m 0C and 0.09
W/m 0C respectively. The temperature of inner surface of sphere is 320 0C and that of the outer surface of the insulation layers is 40 0C. Determine the quantity of heat loss per hour from sphere and interface temperatures.
95. The thermal conductivity of a material is to be determined by fabricating the material into the shape of a hollow sphere, placing an electric heater at the center
and measuring the surface temperature with thermocouples when steady state
conditions have been attained. The sphere has internal radius 3 cm, external
radius 8 cm and the corresponding temperatures are 95 0C and 85 0C when an electric input to heater is 10 watts. Determine the experimental value of thermal conductivity and the temperature at a point halfway through the wall.
Critical Thickness 96. When the thickness of insulation is less than the critical thickness of insulation,
the heat transfer from an insulated pipe will be _____________ than that from a
bare pipe.
97. It is desired to increase the heat dissipation rate over the surface of an electric
device of spherical shape of 5 mm radius exposed to convection with h = 10 W/m2
– deg by encasing it in a spherical sheath of conductivity k = 0.04 W/m2 – deg. For
maximum heat flow, the radius of sheath should be ______________.
98. Upto the critical radius of insulation
(a) Heat loss decreases with addition of insulation (b) Heat loss increases with addition of insulation (c) There occurs a decrease in heat flux
(d) Conduction heat loss is more than convection heat loss
99. Derive equation for critical radius for an insulated cylindrical body. Also mention
assumptions made for it.
100. Derive equation for critical radius for a spherical body. Also mention assumptions
made for it.
101. Explain meaning of critical radius for insulation. Develop equation for critical
radius for insulation on spherical body.
102. What is critical insulation thickness? Can you give a physical explanation of its
existence? Does a critical thickness exist for every insulated cylindrical surface?
103. What do you mean by optimum insulation thickness? What are the more important factors that should be taken into account while determining this
thickness?
104. Derive equation for critical insulation radius for a hollow cylinder.
105. A small electric heating application uses wire of 2 mm diameter with 0.8 mm thick insulation (k =0.12 W/m°C). The heat transfer coefficient (ho) on the insulated
surface is 35 W/m2 °C. Determine the critical thickness of insulation in this case and the percentage change in the heat transfer rate if the critical thickness is used. Wire is at 135°C and surrounding air is at 32°C.
106. A 5 m long steam pipe (K = 240 W/m 0C) having 200 mm ID and 240 mm OD, is carrying steam at 300 0C. It is covered with 40 mm thick insulation (K= 2 W/m 0C). Inside and outside heat transfer coefficient are 40 & 10 W/m2 0C respectively. Surrounding air temperature is 30 0C. If the insulation thickness is critical, find %
change in heat loss.
107. A cable of 10 mm outside is to be laid in an atmosphere of 25 0C (h0 = 12.5 W/m2-deg) and its surface temperature is likely to be 75 0C due to heat generated within
it. How would the heat flow from the cable be affected if it is insulated with rubber having thermal conductivity k = 0.15 W/m-deg?
108. A small electric heating application uses wire of 2 mm diameter with 0.8 mm thick
insulation (k = 0.12W/m°C). The heat transfer coefficient (ho) on the insulated surface is 35 W/m2 °C. Determine the critical thickness of insulation in this case and the percentage change in the heat transfer rate if the critical thickness is
used. Wire is at 135 °C and surrounding air is at 32°C.
109. A wire of 6.5 mm diameter at temperature of 60 °C is to be insulated by a material
having k = 0.174 W/m °C. Convection heat transfer coefficient (ho) = 8.722 W/m2 °C. The ambient temperature is 20 °C. To maximize heat loss, what is the minimum thickness of insulation is required? Find heat loss per meter length.
Extended surface (Fins) 110. On a heat transfer surface, fins are provided to _____________________.
111. On a heat transfer surface, fins are provided to
(a) Increase temperature gradient so as to enhance heat transfer
(b) Increase turbulence in flow for enhancing heat transfer
(c) Increase surface area to promote the rate of heat transfer
(d) Decrease the pressure drop of the fluid
112. Fin efficiency is defined as the ratio of the heat transferred across the fin surface
to the theoretical heat transfer across an equal area held at
(a) Temperature of fin end
(b) Constant temperature equal to that of base
(c) Average temperature of the fin
(d) None of the above
113. “Addition of insulating material does not always bring about a decrease in the
heat transfer rate for geometries with non-constant cross section area”. Comment
upon the validity of this statement.
A pipe of outside diameter 20 mm is to be insulated with asbestos which has a
thermal conductivity of 0.1 W/m-deg. The local coefficient of convective heat to
the surroundings is 5 W/m2 deg. Comment upon the utility of asbestos as the
insulating material. What should be the minimum value of thermal conductivity of
insulating material to reduce heat transfer?
114. Mention the most common types of fins and sketch them. Proceed to develop
expression for temperature distribution and total heat flow rate under steady state
conditions for an infinitely long fin.
115. A ladle is attached with a rectangular handle (fin) with insulated end (tip). Derive equation for heat transfer through it. Also mention assumptions made for it.
116. Proceed to develop expression for temperature distribution and heat dissipation
from a fin insulated at the tip. Set up the relation between fin effectiveness and fin
efficiency.
117. Derive general equation for heat flow through rectangular fin. Also mention assumptions made for it.
118. A reactor is provided rectangular fin to improve heat release rate. If the end of the
fin is insulated, how can we measure heat loss? Develop an equation for heat loss
calculation through the given fin. Also mention assumptions made for it.
119. The aluminium square fins (0.5 mm x 0.5 mm) of 12 mm length are provided on a
surface of semi conductor electronic device to carry 1 W of energy generated by electronic device. The temperature at the surface of the device should not exceed
85 °C when surrounding temperature is 40 °C. Heat transfer coefficient = 15 W/m2 °C; Thermal conductivity of aluminium = 200 W/m °C. Find number of fins required to carry out above duty. Neglect the heat loss from the end of fins.
120. Explain the dependency of thermal conductivity with temperature.
121. Explain in detail the effect of variable conductivity. Also derive the equation for the
same for the case of plane wall, tube and the sphere.
122. The wall of a cold room is composed of three layers. The outside layer is of brick
20 cm thick, the middle layer is of cork 10cm thick, and the inside layer is of
cement 5 cm thick. The temperature of the outside air is 25 0C and that inside air
is -20 0C. The film coefficient (h0) for outside air and brick is 45.4 W/m2 -0C and
the film coefficient (hi) for outside air and cement is 17 W/m2-0C.
Find: (a) The rate of heat flow under steady state conditions.
(b) The temperature on the exposed surfaces of the wall.
(c) Thermal resistance of the wall.
123. In a single experiment with a 2 cm thick sheet of pure copper having one face
maintained at 500 0C and the other at 300 0C. The measured heat flux per unit
area is 3.633MW/m2 (1 MW =106 W.) A reported value of k for this material at
1500C is 371.9 W/m-K. Determine an expression for k(T) of form k = k0(1 + bƟ)
124. A thick wall copper cylinder has an inside radius of1cm and an outside radius
of1cm.The inner and outer surface temperatures are held at 305 0C and 295 0C,
respectively. Assume k varies linearly with temp. , with k0 and b the same as in
problem -1. Determine the heat loss per length.
125. A plane wall has thickness ‘b’ and its two surfaces are maintained at temp. T1 and
T2. If the thermal conductivity of the wall material varies according to k= k0(1 +
ct + dt2),develop an expression for the steady one dimensional heat flow.
126. A steam pipe having an outside diameter of 2 cm is to be covered with two layers
of insulations; each having a thickness of 1cm.The average conductivity of one
material is five times that of the other. Assuming that the inner and outer surface
temperature of the composite insulation is fixed. Calculate by how much
percentage that heat transfer will be reduced when the better insulating material
is next to the pipe than when it is away from the pipe.
127. An electric wire 1 m diameter dissipates 500 W/m in air stream at 100 0C. If the
heat transfer coefficient is 370 W/m2-k, determine the temperature of the wire.
The temperature variation in the wire may be neglected. An insulation having k =
0.277 W/m-k is then added to the wire, thereby increasing its outer diameter to
1.5 mm. Determine the new wire temperature and explain the physical
significance of it.
128. Steel pipe 25 mm ID and 33mm OD and insulated with rock wool carries steam at
178 0C. If the surrounding air temperature is 21 0C. Calculate the rate of heat loss
from one-meter length of pipe. The thickness of insulation is 38 mm. Thermal
conductivity of steel and rock wool are 10.74 and 0.0418 cal/s-m-0C, respectively
.The inside and outside heat transfer coefficient are 1356.17 and 2.7133 cal/s-
m2-0C, respectively. Contact resistance between the pipe and insulation may be
neglected.
129. A furnace wall made up of steel 1 cm thick lined on inside with silica brick 15 cm
thick, on the outside with magnesite brick 15 cm thick. The temperature on the
inside edge of the wall is 700 0C and on the outside is 15 0C. Calculate the
quantity of the heat passed in kcal/hr-m2 and the temperature at the interface of
the steel wall and the magnesite brick. It is required to reduce the heat flow to
1000 kcal/hr-m2 by means of air gap between steel plate and magnesite brick.
Estimate the width of this gap. Thermal conductivity if kcal/hr-m-0C are 14.5,
1.4, 4.5, and 0.029 for steel, silica brick, magnesite brick and air , respectively.
130. A pin fin 2.5 mm diameter is made of copper (k = 396 W/m-k). it protrudes from a
wall maintained at 95 0C and placed in 25 0C air. The convective heat Transfer
coefficient over the fin is 10 W/m2-k. Calculate the heat loss for the two cases:
Fin length = 25 mm
Infinite fin length.
Convection 131. The _____________ physically signifies the ratio of temperature gradient at the
surface to a reference temperature gradient.
132. The characteristic dimension used in estimating the Reynolds number is the
hydraulic diameter defined as __________times the cross sectional area divided by
the wetted perimeter.
133. At prandtl number equal to _______________, the temperature distribution will be
identical to the velocity distribution.
134. For a given value of Nusselt number, the convective surface coefficient (h) is
_________________proportional to thermal conductivity (k) of the fluid and
____________proportional to the significant length (l).
135. Prandtl number essentially represents the ratio of ____________ to ______________.
136. Based on dimensional analysis Nu = C (Re)m (Pr)n
The values of constant C, m and n are evaluated______________.
137. For free convection over inclined plates, Grashoff number is multiplied by __________ where ϴ is the angle of inclination from the vertical and use vertical
plate constants.
138. ___________ number represents the ratio of kinematic viscosity to thermal diffusivity.
139. Heat transmission is directly linked with the transport of medium itself i.e. there
is actual motion of heated particles during
(a) conduction only
(b) convection only
(c) radiation only
(d) conduction as well as radiation
140. Forced convection in a liquid bath is caused by
(a) density difference brought about by temperature gradients
(b) molecular energy interaction
(c) flow of electrons in random fashion
(d) intense stirring by an external agency
141. Which dimensionless number has a significant role in forced convection?
(a) Prandtl number
(b) Reynolds number
(c) Mach number
(d) Peclet number
142. Differentiate between mechanisms of heat transfer by free and forced convection.
143. It is better to install air conditioner in the higher portion of the wall. Please explain this statement with reasons.
144. In which mode of heat transfer is the convection heat transfer coefficient usually higher, natural convection or forced convection? Why?
145. How does turbulent flow differ from laminar flow? For which flow is the heat transfer coefficient higher?
146. If cooling coils in the refrigerator are placed at the bottom in place of the top then what will happen? Why?
147. Why is the heating coil of an electric kettle placed near the bottom of the vessel?
148. Set up the relationship between local heat transfer coefficient and average heat
transfer coefficient for flow past a stationary flat plate.
149. Mention some of the areas where free and force convection mechanisms are
predominant.
150. Differentiate between mechanisms of heat transfer by free and forced convection.
Mention some of the areas where these mechanisms are predominant.
151. Give a general equation for the rate of heat transfer by convection and hence
define the coefficient of heat transfer. List the various factors on which the value of this coefficient depends.
152. An electric heater of exposed surface area 0.09 m2 and output 600 W is designed
to operate fully submerged in water. Calculate the surface temperature of the
heater when the water is at 37 0C and the surface coefficient of heat transfer is
285.3 W/m2-deg. How this value will be affected if the heater is mistakenly
operated at 37 0C in air with a surface co-efficient of 8.5 W/m2-deg?
153. Set up the relationship between local heat transfer coefficient and average heat
transfer coefficient for flow past a stationary flat plate. The temperature profile at
a particular location in a thermal boundary layer is prescribed by an expression of
the form:
2)( CyByAyT
Where A, B and C are constants. Set up an expression for the corresponding heat
transfer coefficient.
154. The temperature profile at a particular location on the surface of plate is
prescribed by the identities:
015.0
ySin
tt
tt
s
s
If thermal conductivity of air is stated to be 0.03 W/m-deg, determine the value of
convective heat transfer coefficient.
155. A 5 cm diameter steel pipe maintained at a temperature of 60 0C is kept in a large
room where the air and wall temperatures are 25 0C. If the surface emissivity of the steel is 0.7, calculate the total heat loss per unit length of pipe if convective
heat transfer coefficient is 6.5 W/m2- deg. Comment on the result.
156. Air enters a rectangular duct measuring 30 cm 40 cm with a velocity of 8.5 m/s and a temperature of 40 0C. The flowing air has a thermal conductivity 0.0242
kcal/m hr 0C, kinematic viscosity 16.9510-6 m2/s and from empirical correlation the Nusselt number has been approximated to be 425. Work out the equivalent
diameter of the flow passage, the flow Reynolds number and the convective heat flow coefficient.
157. Define the Nusselt number. How it is related to temperature gradient in the fluid
immediately in contact with the solid surface? Mention the various approaches
which have suggested for estimating the value of Nusselt number.
158. Using Dimensional analysis (Buckingham’s PI-Theorem) demonstrate that the following dimensionless parameters are possible combinations of the appropriate variables describing forced convection
Vx
, k
cp
, k
hx
Name these groups and discuss their physical significance.
159. Show by dimensional analysis (Buckingham π-theorem method) that data for
forced convection may be correlated by an equation of the form
Pr)(Re,Nu
160. hat data for forced convection may be correlated by an equation of the form
Pr)(Re,St
161. Explain in detail the mechanism of free convection. Show by dimensional analysis
(Buckingham π-theorem) that for problems in heat transfer involving free
convection only, the Nusselt number Nu =
k
hl
can be expressed as a function of
the Prandtl number Pr =
k
C pand the Grashof number Gr =
2
23
Tgl
162. List the variables that affect the forced heat transfer coefficient. Using dimensional analysis (Buckingham π-theorem), demonstrate that the following dimensionless
parameters are possible combinations of the appropriate variables describing forced convection.
PVc
h
;
Vl ; K
cP
Name these groups.
163. Experimental results for heat transfer over a thin flat plate were found to be
correlated by an expression of the form
33.05.0PrRe332.0 xxNu
Where Nux is the local value of Nusselt number at a position x measured from the
leading edge of the plate. Obtain an expression for the ratio of the average heat
transfer coefficient to the local coefficient.
164. Obtain an expression
33.05.0PrRe332.0 xxNu
for heat transfer over a thin flat
plate. Nux is the local value of Nusselt number at a position x measured from the
leading edge of the plate.
165. Show that
t for Pr > 1
t for Pr = 1
t for Pr < 1
t
respectively and Pr stands for the Prandtl number
166. Derive the relationship for the local and average skin friction coefficient for a flat
smooth plate at zero incidences. Assume the value 332.00
d
df.
167. Define the local and average skin friction coefficient for a flat smooth plate at zero
incidences. Establish the following relations for laminar boundary layer over the plate.
(i) Local skin friction coefficient
x
xcRe
664.0
(ii) Average drag coefficient
l
fcRe
328.1
Assume the value 332.00
d
df.
168. Calculate the rate of heat loss from a human body which may be considered as a
vertical cylinder 30 cm in diameter and 175 cm high in still air at 15 0C. The skin
temperature is 35 0C and emissivity at the skin surface is 0.4. Neglect sweating
and effect of clothing.
The thermo-physical properties of air at 25 0C are:
γ = 15.53 × 10-6 m2/s; k = 0.0263 W/m-deg; Pr = 0.7
Use the following correlation
33.0Pr13.0 GrNu
169. A vertical plate is under free convection with ambient still air at 20 0C. If the plate
is heated from one side and maintained at 80 0C workout the local heat transfer
coefficient at 20 cm from the lower edge. What would be the average value of
convective coefficient over the 20 cm length? Following correlation for the local
Nusselt number.
25.0
25.0
Pr)(95.0
52.0 Grpr
prNux
The thermo physical properties of air at 50 0C are:
ρ = 1.093 kg/m3 Pr = 0.698 k = 10.17 × 10-2 kJ/m hr K γ = 17.95×10-6 m2/s
170. A motor cycle cylinder consists of 10 fins; each 15 cm outside diameter (do) and
7.5 cm inside diameter (di). Calculate the rate of heat dissipation from the cylinder
fins when motor cycle is stationary.
The atmospheric air is at 20 0C and the average fin temperature is 480 0C. The
relevant thermo physical properties at the average temperature of 250 0C are:
ρ = 0.674 kg/m3 CP = 1038 J/kg K
k = 0.427 W/m K Pr = 0.677
γ = 40.61 x 10-6 m2/s
The approximate value of heat transfer coefficient may be evaluated by idealing
the fins as a single horizontal flat plate of the same area.
Use following correlations: For Horizontal flat plate:
Free convection : Laminar flow : Nu= 0.54 (Gr × Pr)1/4
Characteristic dimension = 0.9 dO.
171. A hot surface plate 40 cm × 40 cm at 100 °C is exposed to atmospheric air at 20
°C. Make calculations for the heat loss from both surface of the plate if (a) the plate is kept vertical (b) the plate is kept horizontal. The following empirical correlations have been suggested:
33.0Pr125.0 GrNu for vertical position of plate and
25.0Pr72.0 GrNu for upper surface
25.0Pr35.0 GrNu for lower surface
Where the air properties are evaluated at the mean film temperature. Thermo-physical properties of air are at 60 °C
ρ = 1.06 kg/m3
k = 0.028 W/m K Cp= 1.008 kJ/kg K
γ = 18.97 × 10-6 m2/s
172. Saturated steam at 110 0C flows inside a copper pipe (thermal conductivity 450
W/m K) having an internal diameter of 10 cm and an external diameter of 12 cm.
The heat transfer coefficient on the steam side is 12000 W/m2 K and that on the
outside surface of pipe is 18 W/m2 K. Determine the heat loss from the pipe if it is
located in space at 25 0C. How this heat loss would be affected if the pipe is lagged
with 5 cm thick insulation of thermal conductivity 0.22 W/m K.
173. Air at a temperature of 25 0C is blown across a flat plate at a mean velocity of 7.5
m/s. If the plate surface temperature is 575 0C, make calculations for the heat transferred per meter width from both sides of the plate over distance of 20 cm from the leading edge.
For heat transfer from a plate with large temperature between the plate and the fluid, the local Nusselt number is given by:
117.0
2/13/1RePr332.0
a
sx
T
TNu
Where all the properties are at the mean film temperature, Ts and Ta are the absolute temperature of the plate surface and the free stream of air in K respectively. The characteristic linear dimension is the distance from the leading
edge. The thermo physical properties of air at 300 0C are:
ρ = 0.615 kg/m3 CP = 1.0465 kJ/kg K
k = 0.1659 kJ/m hr K µ = 29.724×10-6 kg/ m s
174. A thin walled duct of 0.5 m diameter has been laid in an atmosphere of quiescent
air at 15 0C and conveys a particular gas at 205 0C. The boundary layer flow is
laminar and the convective coefficient of heat transfer is given by: 25.0
37.1
l
th W/m2-deg
Where l is the length of the duct in meters. How this value of convective coefficient compares with that computed from the following non-dimensional correlation for laminar flow natural convection for a large vertical cylinder
25.0Pr57.0 GrNu
Base your calculations on one meter length of the duct. Also estimate the convective heat loss from the duct.
The thermo physical properties of air at mean film temperature are: γ = 24.10 × 10-6 m2/s; k = 31.94 × 10-3 W/m-deg; Pr = 0.704
175. A square channel with a side 10 mm and length 1.5 m carries water with a velocity of 5 m/s. Measurements indicate that lengthwise mean temperature of water is 30 0C whilst the inner surface of channel is at 80 0C. Calculate the
convective coefficient of heat transfer from the channel wall to the water. Use the correlation:
25.0
43.08.0
Pr
PrPrRe021.0
w
Nu
Where the thermo-physical properties pertain to those at the mean bulk
temperature of water. Prw corresponds to the value of Prandtl number at the channel surface temperature and equivalent diameter is the reference dimension. The physical properties of water at 30 0C are:
ρ = 995.07 kg/m3; cp = 4174 J/kg K; k = 0.6172 W/m K; μ = 2.88 kg/m-hr; Pr = 5.42 At wall: temperature tw = 80 0C and Prw = 2.21
176. Estimate the heat transfer from a 40 W incandescent bulb at 125 0C to 25 0C in
quiescent air. Approximate the bulb as a 50 mm diameter sphere. What
percentage of the power is lost by free convection?
The appropriate correlation for the convection coefficient is
Nu = 0.60 (Gr × Pr)0.25
Where the different parameters are evaluated at the mean film temperature and
the characteristics length is the diameter of the sphere.
The thermo physical properties of air are at 75 0C:
γ = 20.55 × 10-6 m2/s
k = 0.03 W/m-deg
Pr = 0.693
177. A nuclear reactor with its core constructed of parallel vertical plates 2.25 m high
and 1.5 wide has been designed on free convection heating of liquid bismuth.
Metallurgical consideration limits the maximum surfaces temperature of the plate
to 975 0C and the lowest allowable temperature of bismuth is 325 0C. Estimate
the maximum possible heat dissipation from both sides of each plate.
The appropriate correlation for the convection coefficient is
Nu = 0.13 (Gr×Pr)1/3
The thermo physical properties of bismuth are at 650 0C:
μ = 3.12 kg/m-hr
ρ = 104 kg/m3
Cp = 150.7 J/kg-deg
k = 13.2 W/m-deg.
178. Estimate the heat transfer from a 40 W incandescent bulb at 125 0C to 25 0C in
quiescent air. Approximate the bulb as a 50 mm diameter sphere. What
percentage of the power is lost by free convection?
The appropriate correlation for the convection coefficient is
25.0Pr60.0 GrNu
Where the different parameters are evaluated at the mean film temperature and
the characteristics length is the diameter of the sphere.
The thermo physical properties of air at mean film temperature are at:
γ = 20.55 × 10-6 m2/s; k = 0.03 W/m-deg; Pr = 0.693
179. A metallic cylinder of 12.5 mm diameter and 95 mm length was heated internally
by an electrical heater, and was subjected to cross flow of air in a low speed wind
tunnel. Under a specific set of operating conditions, the following data were
recorded:
Velocity and temperature of free stream air = 10 m/s and 25.5 0C respectively
Average temperature of cylinder surface = 128.5 0C
Power dissipation by heater = 45 W
If 15% of the power dissipation is lost through the insulated end pieces of the
cylinder, determine the experimental value of the convective heat transfer
coefficient. How this value compares with the convection coefficient obtained by
using the correlation:
25.0
36.06.0
Pr
PrPrRe26.0
S
Nu
Where all properties, except PrS are evaluated at the mean bulk (free stream)
temperature of air.
k = 0.0264 W/m K; γ = 15.85 × 10-6 m2/s; and Pr = 0.706
PrS is the prandtl number of air evaluated at the average temperature of cylinder
surface; PrS = 0.691
180. A thin walled vertical duct a circular cross-section is 0.4 m in diameter. That duct
carries a gas at 470 K and the surrounding air may be considered still at 290 K.
Determine the heat transfer rate from one meter length of the duct assuming that
the boundary layer is laminar.
The general non-dimensional correlation for laminar flow, natural convection from
large vertical cylinders is:
25.0Pr56.0 GrNu
The fluid properties are to be evaluated at film temperature which is defined as
the average of the bulk fluid and wall temperature.
The heat transfer coefficient is to be prescribed by the relation: 25.0
l
TCh W/m2 K
where the length parameter (l) is in meter. Calculate the value of constant C which
would give the same heat transfer rate. At the film temperature, the thermo-
physical properties of the gas are:
ρ = 0.9315 kg/m3; cp = 1.012 kJ/kg K; μ = 22.016 × 10-6 kg/m s
k = 3.2215 × 10-2 W/m K
181. What factors affect the value of convection coefficient for water flowing inside a
circular tube? Within a condenser shell, water flows through one hundred thin
walled circular tubes (diameter = 22.5 mm and length 5 m) which have been
arranged in parallel. The mass flow rate of water is 65 kg/s and its inlet and
outlet temperatures are known to be 22 0C and 28 0C respectively. Predict the
average convection coefficient associated with water flow.
The thermo-physical properties of water at mean bulk temperature are:
ρ = 996.65 kg/m3; μ = 903.01 × 10-6 kg/m s
cp = 4.1776 kJ/kg K; k = 2.1893 kJ/m2 hr K
Use the Correlation:
40.08.0 PrRe023.0Nu
182. A hot surface plate 40 cm × 40 cm at 100 °C is exposed to atmospheric air at 20
°C. Make calculations for the heat loss from both surface of the plate if (a) the
plate is kept vertical (b) the plate is kept horizontal.
The following empirical correlations have been suggested:
33.0Pr125.0 GrNu for vertical position of plate and
25.0Pr72.0 GrNu for upper surface
25.0Pr35.0 GrNu for lower surface
where the air properties are evaluated at the mean film temperature.
Thermo-physical properties of air are at 60 °C
ρ = 1.06 kg/m3
k = 0.028 W/m K
Cp= 1.008 kJ/kg K
γ = 18.97 × 10-6 m2/s
183. Liquid mercury flows through a copper tube of 2 cm inner diameter at the rate of
1.25 kg/s. The mercury enters at 15 °C and is heated to 25 °C as it passes
through the tube. Determine the tube length which would satisfy the condition of
a constant heat flux at the wall which is at an average temperature of 40 °C. For
liquid metals, the following correlation is presumed to agree well with
experimental results:
Nu = 7 + 0.025 (Pe)0.8
where Pe is the Peclet number : Pe = Pr × Re
Thermo-physical properties of the liquid mercury are at 20 °C
ρ = 13580 kg/m3
k = 8.685 W/m K
Cp= 139.35 J/kg K
γ = 1.145 × 10-7 m2/s
Pr = 0.0249
184. Air at atmospheric pressure and 20 0C flows past a flat plate with a velocity of 4
m/s. The plate is 30 cm wide is heated uniformly throughout its entire length and
is maintained at a surface temperature of 60 0C. Make calculations for the
following parameters at 40 cm distance from the leading edge (i) thickness of
hydrodynamic and thermal boundary layers (ii) local and average friction
coefficient (iii) local and average heat transfer coefficient.
Take the following thermo-physical properties of air at the mean film temperature
of 40 0C:
= 1.18 kg/m3
CP = 1007 J/kg-deg
γ = 17 × 10-6 m2/s
k = 0.0272 W/m-deg
Thermal radiation 185. Electro-magnetic spectrum range, which is important for radiation varies from
___________ microns.
186. Thermal radiation is limited to a range of wavelength between ____________of the
spectrum of electromagnetic radiation.
187. A body which partly absorbs and partly reflects but does not allow any radiation
to pass through it ( 1 and 0 ) is called ______________.
188. The ratio of total emissive power to the absorptivity is constant for all real
surfaces with identical temperature and wavelength. This statement is referred to
as ___________.
189. The opaque body is one that _______________________________.
190. A body that allows all the incident radiation to pass through it is called _________________.
191. Thermal radiation is limited to a range of wavelength between ________of the
spectrum of electromagnetic radiation.
192. Wein’s formula of radiation gives results in reasonable agreement with experiments when ___________________ wavelengths used (Short/long).
193. Rayleigh Jean’s formula of radiation gives results in reasonable agreement with experiments when ___________________ wavelengths used (Short/long).
194. Stefan-Boltzman law applies to _______________ body. (a) black
(b) white (c) grey (d) any color
195. Kirchoff’s law applies to _______________ radiation (a) total
(b) monochromatic (c) both (a) & (b) (d) neither (a) & (b)
196. The absorptivity of a body is equal to its emissivity (a) at a particular temperature
(b) for circular bodies (c) under thermal equilibrium
(d) none of these
197. Explain the terms absorptivity, reflectivity and transmissivity of radiant energy. How are they related to each other for a black body and opaque body?
198. Enumerates some salient features of thermal radiation. Based upon the
reradiating properties of absorptivity, reflectivity and transmissivity, how would
you distinguish between the following: black body, white body, transparent body
and opaque body
Radiant energy with an intensity of 800 W/m2 strikes a flat plate normally. The
absorptivity is twice the transitivity and thrice the reflectivity. Determine the rate
of absorption, transmission and reflection of energy.
199. Define monochromatic and total emissive power. How is the later related to the
absolute temperature? Describe how the monochromatic emissive power varies
with the wavelength for emissions from a black body? At what wavelength the
black body monochromatic emissive power is maximum?
A small black body has a total emissive power of 4.5 kW/m2. Determine its
surface temperature and the wavelength of emission maximum.
200. State and prove Stefan Boltzman law relating to thermal radiation and
temperature of a radiating body. Calculate the radiant flux density from a black
body at 400 0C? If the emitted radiant energy is to be doubled, to what
temperature surface of the black body needs to be raised?
201. Making use of Planck’s law of distribution, establish the relation for the Wien’s
displacement law.
The sun emits maximum radiation at λ = 0.52 µm. Assuming the sun to be a
black body, calculate the surface temperature of the sun and the emissive ability
of the sun’s surface at that temperature. Also determine the maximum
monochromatic emissive power of the sun’s surface.
202. A polished metal pipe 5 cm outside diameter and 370 K temperature at the outer
surface is exposed to ambient conditions at 295 K temperature. The emissivity of
the surface is 0.2 and the convective coefficient of heat transfer is 11.35 W/m2-
deg. Calculate the heat transfer by radiation and natural convection per meter
length of the pipe. What would be the overall coefficient of heat transfer by the
combined mode of convection and radiation?
Heat transfer with phase change 203. In ____________ condensation, the liquid droplets fall from the plate’s surface and
there is no wetting of the surface by the condensate.
204. In case of __________boiling vaporization takes place directly from the surface.
205. In the nucleate boiling regions, the heat flux rapidly increases with excess temperature and reaches a maximum value called the ___________________.
206. The convection heat transfer coefficient in drop-wise condensation is ______________ than that in case of film condensation.
207. When vaporization takes place through a blanketing film of gas, the phenomenon is termed as ________boiling.
(a) Pool (b) Nucleate (c) Transition
(d) film
208. What is condensation and when does occurs? How does film-wise condensation
differ from drop-wise condensation? Which type has a higher heat transfer film coefficient and point out the reason thereof?
209. What is condensation and when does occurs? How does film-wise condensation differ from drop-wise condensation? Which type has a higher heat transfer film
coefficient and point out the reason thereof? In design of condensers, which of the two types of condensation is usually selected and why?
210. What is boiling? When does it occur? Discuss the various regimes of boiling
phenomenon and show the effect of ∆T on heat flux for different regimes.
Comment on critical heat flux in nucleate boiling.
211. What is boiling and when does occurs? Explain pool boiling. How does it differ from forced convection boiling?
212. How does nucleate boiling differ from film boiling?
213. Draw the boiling curve and identify the different boiling regimes. Also explain the
characteristics of each regimes
214. Explain pool boiling. How does it differ from forced convection boiling? Discuss in
detail the various regimes in boiling. When does radiation play a role in boiling
heat transfer?
Evaporation
215. In most of the evaporation operation __________ are condensed and discarded.
216. ___________ is carried out by supplying heat to a solution to vaporize solvent.
217. In case of Calendria type evaporator, the solution to be evaporated is ____________the tubes and steam flows____________the tubes in the steam chest.
218. In______________evaporator the velocity of liquid entering the tube is of the order of
2 to 6 m/s.
219. ____________ tube vertical evaporator is commonly used for handling solutions
that tend to foam.
220. The weak liquor to be fed to the evaporator is composed of non-
volatile_____________ and ____________solvent.
221. In____________ feed system, vapour and liquor flow in counter current fashion.
222. Draw schematic temperature profile of evaporator
223. Differentiate evaporation and drying.
224. How does evaporation differ from distillation?
225. State the method of feeding multiple effect evaporation system. Compare forward
feed arrangement with backward feed arrangement in case of multiple effect
evaporation system. State why the economy of single effect evaporator is less than
one and also mention the method of increasing the economy of an evaporator.
226. Classify different types of evaporators. Explain the term ‘forced circulation’ and ‘natural circulation’ in the context of evaporators. Draw neat sketch of short tube vertical evaporator and explain briefly its construction and working.
227. Draw neat sketch of falling film evaporator and explain briefly its construction and working. Compare mixed feed arrangement with parallel feed arrangement in case
of multiple effect evaporation system.
228. Draw neat sketch of batch pan evaporator and explain briefly its construction and
working. Compare forward feed arrangement with backward feed arrangement in case of multiple effect evaporation system.
229. Draw neat sketch of forced circulation evaporator and explain briefly its construction and working. Also, mention any four characteristics of solutions to be considered before selecting the evaporator.
230. Why evaporators generally operate under vacuum? Discuss various methods of
feeding in multiple effect evaporators with their relative merits and demerits.
231. What are the various types of evaporators? Draw neat sketch of Calendria type
evaporator and explain briefly its construction and working. Also, mention any four characteristics of solutions to be considered before selecting the evaporator?
232. When concentration of solution in evaporator varies with operation, what would be the behavior of boiling point of solution? Explain in detail with due example.
233. When can we use agitated thin film evaporators? How it works?
234. In which multiple effect evaporators feed flows in opposite direction of steam?
Explain its working with simple & neat figure. Also mention its advantages & disadvantages.
235. When will you select plate type evaporators? Explain construction & working of it.
236. As a chemical engineer how will you select evaporator?
Heat exchange equipments 237. Why are floating heads provided in heat Exchangers?
a) To regulate the flow
(b) To increase the pressure drop (c) To decrease the pressure drop (d) To avoid deformation of tubes due to thermal expansion.
238. An automobile radiator is_____ type of heat exchanger. (a) cross flow
(b) regenerator (c) counter flow
(d) parallel
239. Which one of the following heat exchangers gives parallel straight line pattern of temperature distribution for both cold and hot fluids?
(a) Parallel-flow with unequal heat capacities (b) Counter-flow with equal heat capacities
(c) Parallel-flow with equal heat capacities (d) Counter-flow with unequal heat capacities
240. Choose the correct statement with respect to a counter flow heat exchanger: (a) Both the fluids at inlet are in their coldest state. (b) Both the fluids at exit are in their hottest state.
(c) Both the fluids at inlet are in their hottest state. (d) One fluid is hottest and the other is coldest at inlet.
241. Baffles are provided in heat exchangers ________ (a) To reduce heat transfer rate (b) To increase heat transfer rate
(c) To remove dirt (d) To increase vibrations
242. How does heat transfer take place in regenerator type heat exchanger? (a) by generation of heat again and again (b) by indirect transfer
(c) by direct mixing of hot and cold fluids (d) by flow of hot and cold fluids alternately over a surface
243. How does heat transfer take place in regenerator type heat exchanger?
a) by generation of heat again and again (b) by indirect transfer (c) by direct mixing of hot and cold fluids
(d) by flow of hot and cold fluids alternately over a surface
244. The degree of approach, in heat exchangers, is defined as the difference between
temperatures of ________. (a) hot medium outlet and cold water outlet
(b) hot medium outlet and cold water inlet (c) cold water met and outlet (d) (d) hot medium inlet and outlet.
245. The multiple pass heat exchangers are used to _______. a) increase the rate of heat transfer
(b) reduce pressure drop (c) increase pressure drop (d) reduce fluid flow friction losses.
246. In a shell and tube heat exchanger, the corrosive liquid is normally passed through
(a) Tube side (b) Shell side (c) Either of the above
(d) None of the above
247. When can we consider heat exchanger as compact heat exchanger?
248. What is full name of ‘NTU’ in context of heat exchanger?
249. Where do we use direct contact heat exchangers in day to day life?
250. Point out the different criterion that form the basis for the classification of heat
exchanger.
251. Derive expressions for effectiveness by NTU (number of transfer units) method for
the parallel flow heat exchanger.
252. When can we consider heat exchanger as compact heat exchanger?
253. Classify heat exchangers in detail.
254. Suggest method to measure effectiveness of heat exchanger.
255. Derive equation for LMTD for counter flow heat exchanger. Also state necessary assumptions made for it.
256. Explain the concept of NTU for heat exchangers.
257. Derive expressions for effectiveness by NTU (number of transfer units) method for
the parallel flow heat exchanger.
258. Write two examples of compact heat exchangers.
259. List at least eight important parts of shell & tube heat exchanger.
260. Show temperature distribution curve for condenser & evaporator
261. Short note: compact heat exchanger
262. What do you mean by “fouling” in heat exchangers? What is the effect of it on
performance of heat exchangers?
263. What do you mean by fouling in heat exchangers? What are the effect of it on
performance of heat exchangers?
264. Write a short note on ‘plate type heat exchangers’.
265. Explain construction & working of spiral plate heat exchanger.
266. “Fouling improves performance of heat exchangers.” Are you agree with this statement? Justify.
267. Calculate the surface area required for a 1-4 pass shell & tube heat exchanger which is cooling 1 kg/s of benzene (Cp = 1.74 kJ/kg °C) from 75°C to 45°C. The
cooling water (Cp = 4.18 kJ/kg °C) at 15°C has a flow rate of 0.694 kg/s. The overall heat transfer coefficient may be taken as 0.3 kW /m2 °C.
268. Water (Cp = 4.187 kJ/kg K) is heated at the rate of 2.4 kg/s from 40 °C to 60 °C
by an oil (Cp= 1.9 kJ/kg K) at the rate of 4.3 kg/s entering at 110 °C. If hi =350 W/m2 K; ho = 300 W/m2 K, calculate the surface area required in a parallel flow
heat exchanger. Inner radius of tube is 11 mm and outer radius is 13 mm. Thermal conductivity of tube material is 50 W/m K.
269. In a counter-flow double pipe heat exchanger, water is heated from 25°C to 65°C
by oil (specific heat 1.45 kJ/kg) with mass flow rate of 0.9 kg/s. The oil is cooled
from 230°C to 160°C. If the overall heat transfer coefficient is 420 W/m2 °C,
calculate the following: the rate of heat transfer, the mass flow rate of water, and
the surface are of the heat exchanger.
270. A counter flow heat exchanger is employed to cool 0.55 kg/s (Cp = 2.45 kJ/kg °C)
of oil from 115°C to 40°C by the use of water. The inlet and outlet temperatures of
cooling water are 15°C and 75°C respectively. The overall heat transfer coefficient
is expected to be 1450 W/m2 °C. Using NTU methods, calculate the effectiveness
of heat exchanger, NTU and area required.
271. Calculate the surface area required for a cross-flow (single-pass with water mixed
and benzene unmixed) heat exchanger which is required to cool 1 kg/s of benzene
(Cp = 1.74 kJ/kg oC) from 75°C to 45°C. The cooling water (cp = 4.18 kJ/kgoC) at
15oC has a flow rate of 0.694 kg/s. The overall heat transfer coefficient may be
taken as 0.3 k W /m2 °C.
272. An oil cooler for a lubrication system has to cool 1000 kg/h of oil (cp= 2.09 kJ/kg
°C) from 80 °C to 40 °C by using a cooling water flow of 1000 kg/h at 30 °C. Give
your choice for a parallel flow or counter-flow heat exchanger, with reasons.
Calculate the surface area of the heat exchanger, if the overall heat transfer
coefficient is 24 W/m2 °C. Take Cp of water=4.18 kJ/kg °C.
273. 8000 kg/h of air at 105°C is cooled by passing it through a counter-flow heat
exchanger. Find the exit temperature of air, if water enters at 15°C and flows at a
rate of 7500 kg/h. The heat exchanger has heat transfer area equal to 20 m2 and
the overall heat transfer coefficient is 145 W /m2 °C.
Take Cp (air) = 1 kJ/kg oC and Cp (water) = 4.18 kJ/kg oC.
274. Calculate the surface area required for a 1-4 exchanger (one-shell pass and four-
tube passes) heat exchanger which is required to cool 1 kg/s of benzene (Cp =
1.74 kJ/kg °C) from 75°C to 45°C. The cooling water (Cp = 4.18 kJ/kg oC) at 15°C
has a flow rate of 0.694 kg/s. The overall heat transfer coefficient may be taken as
0.3 k W /m2 °C.
275. Calculate the surface area required for a 2- 8 heat exchanger (two-shell pass and
eight-tube passes) which is required to cool 1 kg/s of benzene (Cp = 1.74 kJ/kg oC) from 75°C to 45°C. The cooling water (cp = 4.18 kJ/kgoC) at 15oC has a flow
rate of 0.694 kg/s. The overall heat transfer coefficient may be taken as 300
W/m2 °C.
276. In a counter-flow heat exchanger, oil of specific heat of 3.6 kJ/kg flows in at the
rate of 15000 kg/h at 100 °C and is cooled by water which enters at 10 °C and
flows at the rate of 25000 kg/h. The effective heat transfer area of heat exchanger
is 10 m2 and the overall heat transfer coefficient is 500 W/m2 °C. Calculate the
outlet temperatures of oil and water.
277. Calculate the surface area required for a cross-flow (water mixed and benzene
unmixed) heat exchanger which is required to cool 1 kg/s of benzene (Cp = 1.74
kJ/kg °C) from 75 °C to 45 °C. The cooling water (Cp = 4.18 kJ/kg °C) at 15 °C
has a flow rate of 0.694 kg/s. Take benzene side heat transfer coefficient 0.3
kW/m2 °C and water side heat transfer coefficient 200 W/m2 °C.
278. A counter-flow heat exchanger of surface area 8 m2 is to be used to heat a process
liquid by using a high temperature water available from another part of the plant.
If the overall coefficient of heat transfer is 450 W/m2 K, find the exit temperatures
of the process liquid and water stream from the data given below
Hot fluid
(Water)
Cold Fluid
(Process liquid)
Inlet temperature (K) 365 300
Mass flow rate (kg/s) 1 3
Specific Heat (kJ/kg K) 4.2 2.1
279. In an open heart surgery under hypothermic conditions, the patient’s blood is
cooled before the surgery and rewarmed afterwards. The task is accomplished by
a concentric tube counter-flow heat exchanger of length 500 mm with a thin
walled inner tube of 60 mm diameter. The blood entering the heat exchanger at 20 0C and 0.05 kg/s is warmed by water at 60 0C and 0.12 kg/s. Determine the
temperature of blood at exit from the heat exchanger and the heat flow rate.
Assume the following data: cp of blood 3500 J/kg K; cp of water 4186 J/kg K;
Overall heat transfer coefficient U0 = 475 W/m2 K
280. Water is heated from 20 °C to 32 °C in a brass concentric tube heat exchanger.
Steam available at 10 kN/m2 (470 °C) is used for heating. Inside diameter of tube
is 22 mm while outside diameter is 25 mm. Steam condenses on the outer surface
of the tube. The inside and outside film coefficients of heat transfer are 800 W/m2
°C and 7500 W/m2 °C respectively. Thermal conductivity of brass tube = 116
W/m °C. Latent heat of steam = 2391 kJ/kg. Calculate the quantity of steam
required per hour per unit length of the tube.
281. In a cross-flow heat exchanger, oil of specific heat of 3.6 kJ/kg flows at the rate of
15000 kg/h at 100 0C and is cooled by water which enters at 10 0C and flows at
the rate of 25000 kg/h. The effective heat transfer area of heat exchanger is 10 m2
and the overall heat transfer coefficient is 500 W/m2 0C. Calculate the outlet
temperatures of oil and water. Consider one fluid mixed and other is unmixed.
282. Steam at atmospheric pressure enters the shell of a surface condenser in which
the water flows through a bundle of tubes of diameter 30 mm at the rate of 0.06
kg/s. The inlet and outlet temperatures of water are 20 0C and 75 0C respectively.
The condensation of steam takes place on the outside surface of the tubes. If the
overall heat transfer coefficient is 250 W/m2 0C using NTU method, calculate: (i)
The effectiveness of heat exchanger, (ii) The length of the tube and (iii) The rate of
steam condensation
283. The following data relate to a parallel flow heat exchanger in which air is heated by hot exhaust gases.
Heat transferred per hour …155450 J
Inside heat transfer coefficient …120 W/m2 0C
Outside heat transfer coefficient … 195 W/m2 0C
Inlet and outlet temperatures of hot fluid
450 0C and 250 0C respectively
Inlet and outlet temperatures of the cold fluid
…60 0C and 120 0C respectively
Inside and outside diameters of the tube
…50 mm and 60 mm respectively.
Calculate the length of the tube required for the necessary heat transfer to occur.
Neglect the tube resistance
284. Find out the length of the tube required for the following heat transfer which is
used to heat air by heating exhaust gases.
Heat transferred /hour = 167480 KJ
OD & ID of tubes = 6 cm and 5 cm
hi = 116 W/m2 K
ho = 186 W/m2 K
Tho & Thi = 150 0C and 400 0C
Tco and Tci = 100 0C and 50 0C.
Neglect the tube resistance and assume that the flow arrangement is parallel.
285. In an experiment , 2.4 Kg/s of a fluid having a specific heat 0.8 KJ/kg k enters a
counter flow heat exchanger at 300 0C and is heated to 700 0C by 2kg/s of a fluid
having a specific heat 0.96 KJ/kg-K entering the unit at 1000 0C. Show that to
heat the cooler fluid at 800 0C, all other conditions remaining unchanged, it would
require the surface area for heat transfer to be increased by 87.5%.
286. Calculate the outside tube area for a single pass condenser to handle 25000 kg/h
dry and saturated steam at 50 0C.The tubes area of 25mm OD and 22.5 mm ID
and the tube material has a thermal conductivity of 104.6 W/m-K. The average
water velocity in each tube is 2 m/s .Assume that the steam side film coefficient is
5233 W/m2-K. The inlet and outlet temp of the water are 15 0C and 25 0C,
respectively .The properties of water at mean temp. are:
Density = 998.2 kg/m3 Cp = 4.182 KJ/kg.K
Μ = 1004.5 x 10-6 NS/m2 V = 1.006 x 10-6 m2/s
K=0.598 W/m-k; The latent heat at 500C = 2374 KJ/kg
For turbulent flow inside tubes, NU =0.023 Re0.8 Pr0.3
287. In a chemical plant, 1000kg/min of the product at 700 0C (Cp = 3.6 KJ/kg -K)
area to be used to heat 1200 kg/min of the incoming fluid from 100 0C (Cp = 4.2
KJ/kg-K) If the installed heat transfer surface is 42 m2 and the overall heat
transfer coefficient is 1 KW/m2-K, compare the fluid outlet temperature with
counter flow and parallel flow arrangement.
288. Benzene is cooled from 60.6 0C to 21.1 0C in the inner pipe of a double pipe heat
Exchanger cooling water flows counter currently to the benzene, entering the
jacket at 18.3 0C and leaving at 23.9 0C. The exchanger consists of an inner pipe
of 22.2 mm (OD. and 18.9 mm ID) BWG 16 copper tubing jacketed with 38.1 mm
scheduled 40 steel pipe. The linear velocity of the benzene is 1.52 m/s. Neglecting
the resistance of the wall and scale films. And assuming L/D > 150 for both pipes,
compute the film coefficient of the benzene and water the overall coefficient based
on the outside area of the inner pipe.
Data:- At average fluid temp.
Benzene Water
Density, kg/m3 849.6 996.8
μ, kg/m-hr 1.73 3.48
k, W/m-K 0.154 0.6
Cp, cal/g-0C 0.435 1.000
