11-1
Solutions Manual for
Heat and Mass Transfer: Fundamentals & Applications
6th Edition in SI Units
Yunus A. Çengel, Afshin J. Ghajar
McGraw-Hill, 2020
Chapter 11
HEAT EXCHANGERS
PROPRIETARY AND CONFIDENTIAL
This Manual is the proprietary property of McGraw-Hill Education
and protected by copyright and other state and federal laws. By
opening and using this Manual the user agrees to the following
restrictions, and if the recipient does not agree to these
restrictions, the Manual should be promptly returned unopened
to McGraw-Hill Education: This Manual is being provided only to
authorized professors and instructors for use in preparing for the
classes using the affiliated textbook. No other use or distribution
of this Manual is permitted. This Manual may not be sold and
may not be distributed to or used by any student or other third
party. No part of this Manual may be reproduced, displayed or
distributed in any form or by any means, electronic or otherwise,
without the prior written permission of McGraw-Hill Education.
PROPRIETARY MATERIAL. © 2020 McGraw-Hill Education. Limited distribution permitted only to teachers and educators for course preparation. If
you are a student using this Manual, you are using it without permission.
, 11-2
Types of Heat Exchangers
11-1C A heat exchanger is classified as being compact if > 700 m2/m3 or (200 ft2/ft3) where is the ratio of the heat
transfer surface area to its volume which is called the area density. The area density for double-pipe heat exchanger can not
be in the order of 700. Therefore, it can not be classified as a compact heat exchanger.
11-2C Regenerative heat exchanger involves the alternate passage of the hot and cold fluid streams through the same flow
area. The static type regenerative heat exchanger is basically a porous mass which has a large heat storage capacity, such as a
ceramic wire mash. Hot and cold fluids flow through this porous mass alternately. Heat is transferred from the hot fluid to
the matrix of the regenerator during the flow of the hot fluid and from the matrix to the cold fluid. Thus the matrix serves as
a temporary heat storage medium. The dynamic type regenerator involves a rotating drum and continuous flow of the hot
and cold fluid through different portions of the drum so that any portion of the drum passes periodically through the hot
stream, storing heat and then through the cold stream, rejecting this stored heat. Again the drum serves as the medium to
transport the heat from the hot to the cold fluid stream.
11-3C In the shell and tube exchangers, baffles are commonly placed in the shell to force the shell side fluid to flow across
the shell to enhance heat transfer and to maintain uniform spacing between the tubes. Baffles disrupt the flow of fluid, and an
increased pumping power will be needed to maintain flow. On the other hand, baffles eliminate dead spots and increase heat
transfer rate.
11-4C Using six-tube passes in a shell and tube heat exchanger increases the heat transfer surface area, and the rate of heat
transfer increases. But it also increases the manufacturing costs.
11-5C Using so many tubes increases the heat transfer surface area which in turn increases the rate of heat transfer.
11-6C In counter-flow heat exchangers, the hot and the cold fluids move parallel to each other but both enter the heat
exchanger at opposite ends and flow in opposite direction. In cross-flow heat exchangers, the two fluids usually move
perpendicular to each other. The cross-flow is said to be unmixed when the plate fins force the fluid to flow through a
particular interfin spacing and prevent it from moving in the transverse direction. When the fluid is free to move in the
transverse direction, the cross-flow is said to be mixed.
PROPRIETARY MATERIAL. © 2020 McGraw-Hill Education. Limited distribution permitted only to teachers and educators for course preparation. If
you are a student using this Manual, you are using it without permission.
, 11-3
The Overall Heat Transfer Coefficient
11-7C Heat is first transferred from the hot liquid to the wall by convection, through the wall by conduction and from the
wall to the cold liquid again by convection.
11-8C When the wall thickness of the tube is small and the thermal conductivity of the tube material is high, which is usually
the case, the thermal resistance of the tube is negligible.
11-9C The heat transfer surface areas are Ai D1 L and Ao D 2 L . When the thickness of inner tube is small, it is
reasonable to assume Ai Ao As .
11-10C The effect of fouling on a heat transfer is represented by a fouling factor Rf. Its effect on the heat transfer coefficient
is accounted for by introducing a thermal resistance Rf /As. The fouling increases with increasing temperature and decreasing
velocity.
11-11C None.
11-12C When one of the convection coefficients is much smaller than the other hi << ho , and Ai A0 As . Then we have (
1/hi >> 1/ho ) and thus U i U 0 U hi .
11-13C The most common type of fouling is the precipitation of solid deposits in a fluid on the heat transfer surfaces.
Another form of fouling is corrosion and other chemical fouling. Heat exchangers may also be fouled by the growth of algae
in warm fluids. This type of fouling is called the biological fouling. Fouling represents additional resistance to heat transfer
and causes the rate of heat transfer in a heat exchanger to decrease, and the pressure drop to increase.
11-14C When the wall thickness of the tube is small and the thermal conductivity of the tube material is high, the thermal
resistance of the tube is negligible and the inner and the outer surfaces of the tube are almost identical ( Ai Ao As ). Then
the overall heat transfer coefficient of a heat exchanger can be determined to from U = (1/hi + 1/ho)-1
PROPRIETARY MATERIAL. © 2020 McGraw-Hill Education. Limited distribution permitted only to teachers and educators for course preparation. If
you are a student using this Manual, you are using it without permission.
, 11-4
11-15 Refrigerant-134a is cooled by water in a double-pipe heat exchanger. The overall heat transfer coefficient is to be
determined.
Assumptions 1 The thermal resistance of the inner tube is negligible since the tube material is highly conductive and its
thickness is negligible. 2 Both the water and refrigerant-134a flow are fully developed. 3 Properties of the water and
refrigerant-134a are constant.
Properties The properties of water at 20C are (Table A-9) Cold water
998 kg/m 3
/ 1.00410 6 m 2 /s D0
k 0.598 W/m.C Di
Pr 7.01
Analysis The hydraulic diameter for annular space is
Dh Do Di 0.025 0.01 0.015 m
Hot R-134a
The average velocity of water in the tube and the Reynolds number are
m m 0.3 kg/s
Vavg 0.729 m/s
Ac D Di
(998 kg/m 3 ) (0.025 m) (0.01 m)
2 2 2 2
o
4 4
Vavg Dh (0.729 m/s)(0.015m)
Re 10,890
1.004 10 6 m 2 / s
which is greater than 4000. Therefore flow is turbulent. Assuming fully developed flow,
hDh
Nu 0.023 Re 0.8 Pr 0.4 0.023(10,890) 0.8 (7.01) 0.4 85.0
k
and
k 0.598 W/m.C
ho Nu (85.0) = 3390 W/m 2 .C
Dh 0.015 m
Then the overall heat transfer coefficient becomes
1 1
U 1856 W/m2 .C
1 1 1 1
hi ho 4100 W/m 2 .C 3390 W/m 2 .C
Discussion This problem can also be solved using Gnielinski equation. First the friction factor is determined from the first
Petukhov equation.
f (0.790ln Re 1.64) 2 [0.790ln(10,890) 1.64]2 0.03074
hDh ( f / 8)(Re 1000) Pr (0.03074/ 8)(10,890 1000)(7.01)
Nu 86.04
k 1 12.7( f / 8) (Pr 1) 1 12.7(0.03074/ 8) 0.5 (7. 1)
0.5 2/3
k 0.598 W/m.C
ho Nu (86.04) = 3430 W/m 2 .C
Dh 0.015 m
1 1
U 1868 W/m2 .C
1 1 1 1
hi ho 4100 W/m 2 .C 3430 W/m 2 .C
The result is very close to that obtained by using the modified Colburn equation for the Nusselt number. Therefore, different
heat transfer correlations can be used to solve for the heat transfer coefficient.
PROPRIETARY MATERIAL. © 2020 McGraw-Hill Education. Limited distribution permitted only to teachers and educators for course preparation. If
you are a student using this Manual, you are using it without permission.
Solutions Manual for
Heat and Mass Transfer: Fundamentals & Applications
6th Edition in SI Units
Yunus A. Çengel, Afshin J. Ghajar
McGraw-Hill, 2020
Chapter 11
HEAT EXCHANGERS
PROPRIETARY AND CONFIDENTIAL
This Manual is the proprietary property of McGraw-Hill Education
and protected by copyright and other state and federal laws. By
opening and using this Manual the user agrees to the following
restrictions, and if the recipient does not agree to these
restrictions, the Manual should be promptly returned unopened
to McGraw-Hill Education: This Manual is being provided only to
authorized professors and instructors for use in preparing for the
classes using the affiliated textbook. No other use or distribution
of this Manual is permitted. This Manual may not be sold and
may not be distributed to or used by any student or other third
party. No part of this Manual may be reproduced, displayed or
distributed in any form or by any means, electronic or otherwise,
without the prior written permission of McGraw-Hill Education.
PROPRIETARY MATERIAL. © 2020 McGraw-Hill Education. Limited distribution permitted only to teachers and educators for course preparation. If
you are a student using this Manual, you are using it without permission.
, 11-2
Types of Heat Exchangers
11-1C A heat exchanger is classified as being compact if > 700 m2/m3 or (200 ft2/ft3) where is the ratio of the heat
transfer surface area to its volume which is called the area density. The area density for double-pipe heat exchanger can not
be in the order of 700. Therefore, it can not be classified as a compact heat exchanger.
11-2C Regenerative heat exchanger involves the alternate passage of the hot and cold fluid streams through the same flow
area. The static type regenerative heat exchanger is basically a porous mass which has a large heat storage capacity, such as a
ceramic wire mash. Hot and cold fluids flow through this porous mass alternately. Heat is transferred from the hot fluid to
the matrix of the regenerator during the flow of the hot fluid and from the matrix to the cold fluid. Thus the matrix serves as
a temporary heat storage medium. The dynamic type regenerator involves a rotating drum and continuous flow of the hot
and cold fluid through different portions of the drum so that any portion of the drum passes periodically through the hot
stream, storing heat and then through the cold stream, rejecting this stored heat. Again the drum serves as the medium to
transport the heat from the hot to the cold fluid stream.
11-3C In the shell and tube exchangers, baffles are commonly placed in the shell to force the shell side fluid to flow across
the shell to enhance heat transfer and to maintain uniform spacing between the tubes. Baffles disrupt the flow of fluid, and an
increased pumping power will be needed to maintain flow. On the other hand, baffles eliminate dead spots and increase heat
transfer rate.
11-4C Using six-tube passes in a shell and tube heat exchanger increases the heat transfer surface area, and the rate of heat
transfer increases. But it also increases the manufacturing costs.
11-5C Using so many tubes increases the heat transfer surface area which in turn increases the rate of heat transfer.
11-6C In counter-flow heat exchangers, the hot and the cold fluids move parallel to each other but both enter the heat
exchanger at opposite ends and flow in opposite direction. In cross-flow heat exchangers, the two fluids usually move
perpendicular to each other. The cross-flow is said to be unmixed when the plate fins force the fluid to flow through a
particular interfin spacing and prevent it from moving in the transverse direction. When the fluid is free to move in the
transverse direction, the cross-flow is said to be mixed.
PROPRIETARY MATERIAL. © 2020 McGraw-Hill Education. Limited distribution permitted only to teachers and educators for course preparation. If
you are a student using this Manual, you are using it without permission.
, 11-3
The Overall Heat Transfer Coefficient
11-7C Heat is first transferred from the hot liquid to the wall by convection, through the wall by conduction and from the
wall to the cold liquid again by convection.
11-8C When the wall thickness of the tube is small and the thermal conductivity of the tube material is high, which is usually
the case, the thermal resistance of the tube is negligible.
11-9C The heat transfer surface areas are Ai D1 L and Ao D 2 L . When the thickness of inner tube is small, it is
reasonable to assume Ai Ao As .
11-10C The effect of fouling on a heat transfer is represented by a fouling factor Rf. Its effect on the heat transfer coefficient
is accounted for by introducing a thermal resistance Rf /As. The fouling increases with increasing temperature and decreasing
velocity.
11-11C None.
11-12C When one of the convection coefficients is much smaller than the other hi << ho , and Ai A0 As . Then we have (
1/hi >> 1/ho ) and thus U i U 0 U hi .
11-13C The most common type of fouling is the precipitation of solid deposits in a fluid on the heat transfer surfaces.
Another form of fouling is corrosion and other chemical fouling. Heat exchangers may also be fouled by the growth of algae
in warm fluids. This type of fouling is called the biological fouling. Fouling represents additional resistance to heat transfer
and causes the rate of heat transfer in a heat exchanger to decrease, and the pressure drop to increase.
11-14C When the wall thickness of the tube is small and the thermal conductivity of the tube material is high, the thermal
resistance of the tube is negligible and the inner and the outer surfaces of the tube are almost identical ( Ai Ao As ). Then
the overall heat transfer coefficient of a heat exchanger can be determined to from U = (1/hi + 1/ho)-1
PROPRIETARY MATERIAL. © 2020 McGraw-Hill Education. Limited distribution permitted only to teachers and educators for course preparation. If
you are a student using this Manual, you are using it without permission.
, 11-4
11-15 Refrigerant-134a is cooled by water in a double-pipe heat exchanger. The overall heat transfer coefficient is to be
determined.
Assumptions 1 The thermal resistance of the inner tube is negligible since the tube material is highly conductive and its
thickness is negligible. 2 Both the water and refrigerant-134a flow are fully developed. 3 Properties of the water and
refrigerant-134a are constant.
Properties The properties of water at 20C are (Table A-9) Cold water
998 kg/m 3
/ 1.00410 6 m 2 /s D0
k 0.598 W/m.C Di
Pr 7.01
Analysis The hydraulic diameter for annular space is
Dh Do Di 0.025 0.01 0.015 m
Hot R-134a
The average velocity of water in the tube and the Reynolds number are
m m 0.3 kg/s
Vavg 0.729 m/s
Ac D Di
(998 kg/m 3 ) (0.025 m) (0.01 m)
2 2 2 2
o
4 4
Vavg Dh (0.729 m/s)(0.015m)
Re 10,890
1.004 10 6 m 2 / s
which is greater than 4000. Therefore flow is turbulent. Assuming fully developed flow,
hDh
Nu 0.023 Re 0.8 Pr 0.4 0.023(10,890) 0.8 (7.01) 0.4 85.0
k
and
k 0.598 W/m.C
ho Nu (85.0) = 3390 W/m 2 .C
Dh 0.015 m
Then the overall heat transfer coefficient becomes
1 1
U 1856 W/m2 .C
1 1 1 1
hi ho 4100 W/m 2 .C 3390 W/m 2 .C
Discussion This problem can also be solved using Gnielinski equation. First the friction factor is determined from the first
Petukhov equation.
f (0.790ln Re 1.64) 2 [0.790ln(10,890) 1.64]2 0.03074
hDh ( f / 8)(Re 1000) Pr (0.03074/ 8)(10,890 1000)(7.01)
Nu 86.04
k 1 12.7( f / 8) (Pr 1) 1 12.7(0.03074/ 8) 0.5 (7. 1)
0.5 2/3
k 0.598 W/m.C
ho Nu (86.04) = 3430 W/m 2 .C
Dh 0.015 m
1 1
U 1868 W/m2 .C
1 1 1 1
hi ho 4100 W/m 2 .C 3430 W/m 2 .C
The result is very close to that obtained by using the modified Colburn equation for the Nusselt number. Therefore, different
heat transfer correlations can be used to solve for the heat transfer coefficient.
PROPRIETARY MATERIAL. © 2020 McGraw-Hill Education. Limited distribution permitted only to teachers and educators for course preparation. If
you are a student using this Manual, you are using it without permission.
