7-1
Solutions Manual for
Heat and Mass Transfer: Fundamentals & Applications
6th Edition in SI Units
Yunus A. Çengel, Afshin J. Ghajar
McGraw-Hill, 2020
Chapter 7
EXTERNAL FORCED CONVECTION
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
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authorized professors and instructors for use in preparing for the
classes using the affiliated textbook. No other use or distribution
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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.
, 7-2
Drag Force and Heat Transfer in External Flow
7-1C The force a flowing fluid exerts on a body in the flow direction is called drag. Drag is caused by friction between the
fluid and the solid surface, and the pressure difference between the front and back of the body. We try to minimize drag in
order to reduce fuel consumption in vehicles, improve safety and durability of structures subjected to high winds, and to
reduce noise and vibration.
7-2C The force a flowing fluid exerts on a body in the normal direction to flow that tend to move the body in that direction is
called lift. It is caused by the components of the pressure and wall shear forces in the normal direction to flow. The wall shear
also contributes to lift (unless the body is very slim), but its contribution is usually small.
7-3C When the drag force FD, the upstream velocityV, and the fluid density are measured during flow over a body, the drag
coefficient can be determined from
FD
CD
1
2
V 2 A
where A is ordinarily the frontal area (the area projected on a plane normal to the direction of flow) of the body.
7-4C The frontal area of a body is the area seen by a person when looking from upstream. The frontal area is appropriate to
use in drag and lift calculations for blunt bodies such as cars, cylinders, and spheres.
7-5C The part of drag that is due directly to wall shear stress w is called the skin friction dragFD, friction since it is caused by
frictional effects, and the part that is due directly to pressure P and depends strongly on the shape of the body is called the
pressure dragFD, pressure. For slender bodies such as airfoils, the friction drag is usually more significant.
7-6C A body is said to be streamlined if a conscious effort is made to align its shape with the anticipated streamlines in the
flow. Otherwise, a body tends to block the flow, and is said to be blunt. A tennis ball is a blunt body (unless the velocity is
very low and we have “creeping flow”).
7-7C As a result of streamlining, (a) friction drag increases, (b) pressure drag decreases, and (c) total drag decreases at high
Reynolds numbers (the general case), but increases at very low Reynolds numbers since the friction drag dominates at low
Reynolds numbers.
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.
, 7-3
7-8C The friction drag coefficient is independent of surface roughness in laminar flow, but is a strong function of surface
roughness in turbulent flow due to surface roughness elements protruding further into the highly viscous laminar sublayer.
7-9C At sufficiently high velocities, the fluid stream detaches itself from the surface of the body. This is called separation. It
is caused by a fluid flowing over a curved surface at a high velocity (or technically, by adverse pressure gradient). Separation
increases the drag coefficient drastically.
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.
, 7-4
Flow over Flat Plates
7-10C The friction coefficient represents the resistance to fluid flow over a flat plate. It is proportional to the drag force
acting on the plate. The drag coefficient for a flat surface is equivalent to the mean friction coefficient.
7-11C The friction and the heat transfer coefficients change with position in laminar flow over a flat plate.
7-12C The average friction and heat transfer coefficients in flow over a flat plate are determined by integrating the local
friction and heat transfer coefficients over the entire plate, and then dividing them by the length of the plate.
7-13 Air is flowing over a long flat plate with a specified velocity. The distance from the leading edge of the plate where the
flow becomes turbulent, and the thickness of the boundary layer at that location are to be determined.
Assumptions 1The flow is steady and incompressible. 2 The critical Reynolds number is Recr = 5105. 3 Air is an ideal gas.
4 The surface of the plate is smooth.
Properties The density and kinematic viscosity of air at 1 atm and 25C are = 1.184 kg/m3 and = 1.562×10–5 m2/s (Table
A-15).
AnalysisThe distance from the leading edge of the plate where the flow becomes turbulent is the distance xcrwhere the
Reynolds number becomes equal to the critical Reynolds number,
Vx cr
Re cr
V
5
Re cr (1.562 10 m /s)(5 10 )
2 5
x cr 0.976 m
V 8 m/s
xcr
The thickness of the boundary layer at that location is obtained by substituting
this value of x into the laminar boundary layer thickness relation,
5x 5 x cr 5(0.976 m)
x cr 0.006903m 0.69 cm
Re 1x/ 2 Re 1cr/ 2 (5 105 )
Discussion When the flow becomes turbulent, the boundary layer thickness starts to increase, and the value of its thickness
can be determined from the boundary layer thickness relation for turbulent flow.
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 7
EXTERNAL FORCED CONVECTION
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.
, 7-2
Drag Force and Heat Transfer in External Flow
7-1C The force a flowing fluid exerts on a body in the flow direction is called drag. Drag is caused by friction between the
fluid and the solid surface, and the pressure difference between the front and back of the body. We try to minimize drag in
order to reduce fuel consumption in vehicles, improve safety and durability of structures subjected to high winds, and to
reduce noise and vibration.
7-2C The force a flowing fluid exerts on a body in the normal direction to flow that tend to move the body in that direction is
called lift. It is caused by the components of the pressure and wall shear forces in the normal direction to flow. The wall shear
also contributes to lift (unless the body is very slim), but its contribution is usually small.
7-3C When the drag force FD, the upstream velocityV, and the fluid density are measured during flow over a body, the drag
coefficient can be determined from
FD
CD
1
2
V 2 A
where A is ordinarily the frontal area (the area projected on a plane normal to the direction of flow) of the body.
7-4C The frontal area of a body is the area seen by a person when looking from upstream. The frontal area is appropriate to
use in drag and lift calculations for blunt bodies such as cars, cylinders, and spheres.
7-5C The part of drag that is due directly to wall shear stress w is called the skin friction dragFD, friction since it is caused by
frictional effects, and the part that is due directly to pressure P and depends strongly on the shape of the body is called the
pressure dragFD, pressure. For slender bodies such as airfoils, the friction drag is usually more significant.
7-6C A body is said to be streamlined if a conscious effort is made to align its shape with the anticipated streamlines in the
flow. Otherwise, a body tends to block the flow, and is said to be blunt. A tennis ball is a blunt body (unless the velocity is
very low and we have “creeping flow”).
7-7C As a result of streamlining, (a) friction drag increases, (b) pressure drag decreases, and (c) total drag decreases at high
Reynolds numbers (the general case), but increases at very low Reynolds numbers since the friction drag dominates at low
Reynolds numbers.
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.
, 7-3
7-8C The friction drag coefficient is independent of surface roughness in laminar flow, but is a strong function of surface
roughness in turbulent flow due to surface roughness elements protruding further into the highly viscous laminar sublayer.
7-9C At sufficiently high velocities, the fluid stream detaches itself from the surface of the body. This is called separation. It
is caused by a fluid flowing over a curved surface at a high velocity (or technically, by adverse pressure gradient). Separation
increases the drag coefficient drastically.
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.
, 7-4
Flow over Flat Plates
7-10C The friction coefficient represents the resistance to fluid flow over a flat plate. It is proportional to the drag force
acting on the plate. The drag coefficient for a flat surface is equivalent to the mean friction coefficient.
7-11C The friction and the heat transfer coefficients change with position in laminar flow over a flat plate.
7-12C The average friction and heat transfer coefficients in flow over a flat plate are determined by integrating the local
friction and heat transfer coefficients over the entire plate, and then dividing them by the length of the plate.
7-13 Air is flowing over a long flat plate with a specified velocity. The distance from the leading edge of the plate where the
flow becomes turbulent, and the thickness of the boundary layer at that location are to be determined.
Assumptions 1The flow is steady and incompressible. 2 The critical Reynolds number is Recr = 5105. 3 Air is an ideal gas.
4 The surface of the plate is smooth.
Properties The density and kinematic viscosity of air at 1 atm and 25C are = 1.184 kg/m3 and = 1.562×10–5 m2/s (Table
A-15).
AnalysisThe distance from the leading edge of the plate where the flow becomes turbulent is the distance xcrwhere the
Reynolds number becomes equal to the critical Reynolds number,
Vx cr
Re cr
V
5
Re cr (1.562 10 m /s)(5 10 )
2 5
x cr 0.976 m
V 8 m/s
xcr
The thickness of the boundary layer at that location is obtained by substituting
this value of x into the laminar boundary layer thickness relation,
5x 5 x cr 5(0.976 m)
x cr 0.006903m 0.69 cm
Re 1x/ 2 Re 1cr/ 2 (5 105 )
Discussion When the flow becomes turbulent, the boundary layer thickness starts to increase, and the value of its thickness
can be determined from the boundary layer thickness relation for turbulent flow.
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.
