Heat & Mass Transfer 5th Edition – Chapter 7 External Forced Convection | Detailed Worked Solutions & Step-By-Step Explanations | 2025/2026 Study Guide

7-1


Solutions Manual
for
Heat and Mass Transfer: Fundamentals & Applications
5th Edition
Yunus A. Cengel & Afshin J. Ghajar
McGraw-Hill, 2015




Chapter 7
EXTERNAL FORCED CONVECTION
(Last updated August 1, 2015)




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, 7-2
Drag Force and Heat Transfer in External Flow


7-1C The velocity of the fluid relative to the immersed solid body sufficiently far away from a body is called the free-stream
velocity, V. The upstream (or approach) velocity V is the velocity of the approaching fluid far ahead of the body. These two
velocities are equal if the flow is uniform and the body is small relative to the scale of the free-stream flow.




7-2C 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.




7-3C 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.




7-4C When the drag force FD, the upstream velocity V, 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.




7-5C 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.




7-6C The part of drag that is due directly to wall shear stress w is called the skin friction drag FD, 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 drag FD, pressure. For slender bodies such as airfoils, the friction drag is usually more significant.




7-7C 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”).




7-8C 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.




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, 7-3
7-9C 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.




7-10C 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.




Flow over Flat Plates


7-11C 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.




7-12C The friction and the heat transfer coefficients change with position in laminar flow over a flat plate.




7-13C 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.




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, 7-4
7-14 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 1 The flow is steady and incompressible. 2 The critical Reynolds number is Recr = 5105. 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 25C are  = 1.184 kg/m3 and  = 1.562×10–5 m2/s (Table
A-15).
Analysis The distance from the leading edge of the plate where the flow becomes turbulent is the distance xcr where the
Reynolds number becomes equal to the critical Reynolds number,
Vx cr
Re cr  
 V
 Re cr (1.562 10 5 m 2 /s)(5 10 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    0.006903 m  0.69 cm
Re1x/ 2 Re1cr/ 2 (5 10 5 )

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.




7-15 Water 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 1 The flow is steady and incompressible. 2 The critical Reynolds number is Recr = 5105. 3 The surface of the
plate is smooth.
Properties The density and dynamic viscosity of water at 1 atm and 25C are  = 997 kg/m3 and  = 0.891×10–3 kg/ms
(Table A-9).
Analysis The distance from the leading edge of the plate where the flow becomes turbulent is the distance xcr where the
Reynolds number becomes equal to the critical Reynolds number,
Vx cr V
Re cr  

 Re cr (0.89110 3 kg/m  s)(5 10 5 )
x cr    0.056 m  5.6 cm xcr
V (997 kg/m 3 )(8 m/s)

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(0.056 m)
 cr    cr    0.00040 m  0.4 mm
Re1x/ 2 Re1cr/ 2 (5 10 5 )

Therefore, the flow becomes turbulent after about 5 cm from the leading edge of the plate, and the thickness of the boundary
layer at that location is 0.4 mm.
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.




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preparation. If you are a student using this Manual, you are using it without permission.