8-1
Solutions Manual
for
Heat and Mass Transfer: Fundamentals & Applications
5th Edition
Yunus A. Cengel & Afshin J. Ghajar
McGraw-Hill, 2015
Chapter 8
INTERNAL FORCED CONVECTION
PROPRIETARY AND CONFIDENTIAL
This Manual is the proprietary property of The McGraw-Hill Companies, Inc. (“McGraw-Hill”) 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: 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.
PROPRIETARY MATERIAL. © 2015 The McGraw-Hill Companies, Inc. 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.
, 8-2
General Flow Analysis
8-1C Engine oil requires a larger pump because of its much larger density.
8-2C In fluid flow, it is convenient to work with an average or mean velocity Vavg and an average or mean temperature Tm
which remain constant in incompressible flow when the cross-sectional area of the tube is constant. The Vavg and Tm represent
the velocity and temperature, respectively, at a cross section if all the particles were at the same velocity and temperature.
8-3C The generally accepted value of the Reynolds number above which the flow in a smooth pipe is turbulent is 4000.
8-4C For flow through non-circular tubes, the Reynolds number as well as the Nusselt number and the friction factor are
4 Ac
based on the hydraulic diameter Dh defined as Dh = where Ac is the cross-sectional area of the tube and p is its
p
perimeter. The hydraulic diameter is defined such that it reduces to ordinary diameter D for circular tubes since
4 Ac 4pD
Dh = = = D.
p pD
8-5C The fluid viscosity is responsible for the development of the velocity boundary layer. For the idealized inviscid fluids
(fluids with zero viscosity), there will be no velocity boundary layer.
8-6C In the fully developed region of flow in a circular tube, the velocity profile will not change in the flow direction but the
temperature profile may.
8-7C The friction factor is highest at the tube inlet where the thickness of the boundary layer is zero, and decreases gradually
to the fully developed value. The same is true for turbulent flow.
8-8C The friction factor f remains constant along the flow direction in the fully developed region in both laminar and
turbulent flow.
8-9C In turbulent flow, the tubes with rough surfaces have much higher friction factors than the tubes with smooth surfaces.
In the case of laminar flow, the effect of surface roughness on the friction factor is negligible.
PROPRIETARY MATERIAL. © 2015 The McGraw-Hill Companies, Inc. 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.
, 8-3
8-10C The region from the tube inlet to the point at which the boundary layer merges at the centerline is called the
hydrodynamic entry region, and the length of this region is called hydrodynamic entry length. The entry length is much
longer in laminar flow than it is in turbulent flow. But at very low Reynolds numbers, Lh is very small (Lh = 1.2D at Re = 20).
8-11C The hydrodynamic and thermal entry lengths are given as Lh = 0.05 Re D and Lt = 0.05 Re Pr D for laminar flow, and
L h ≈ Lt ≈ 10 D in turbulent flow. Noting that Pr >> 1 for oils, the thermal entry length is larger than the hydrodynamic entry
length in laminar flow. In turbulent, the hydrodynamic and thermal entry lengths are independent of Re or Pr numbers, and are
comparable in magnitude.
8-12C The hydrodynamic and thermal entry lengths are given as Lh = 0.05 Re D and Lt = 0.05 Re Pr D for laminar flow, and
L h ≈ Lt ≈ 10 D in turbulent flow. Noting that Pr << 1 for liquid metals, the thermal entry length is smaller than the
hydrodynamic entry length in laminar flow. In turbulent, the hydrodynamic and thermal entry lengths are independent of Re or
Pr numbers, and are comparable in magnitude.
8-13C The region of flow over which the thermal boundary layer develops and reaches the tube center is called the thermal
entry region, and the length of this region is called the thermal entry length. The region in which the flow is both
hydrodynamically (the velocity profile is fully developed and remains unchanged) and thermally (the dimensionless
temperature profile remains unchanged) developed is called the fully developed region.
8-14C The heat flux will be higher near the inlet because the heat transfer coefficient is highest at the tube inlet where the
thickness of thermal boundary layer is zero, and decreases gradually to the fully developed value.
8-15C The heat flux will be higher near the inlet because the heat transfer coefficient is highest at the tube inlet where the
thickness of thermal boundary layer is zero, and decreases gradually to the fully developed value.
8-16C The logarithmic mean temperature difference ∆Tln is an exact representation of the average temperature difference
between the fluid and the surface for the entire tube. It truly reflects the exponential decay of the local temperature difference.
The error in using the arithmetic mean temperature increases to undesirable levels when ∆Te differs from ∆Ti by great
amounts. Therefore we should always use the logarithmic mean temperature.
8-17C When the surface temperature of tube is constant, the appropriate temperature difference for use in the Newton's law of
cooling is logarithmic mean temperature difference that can be expressed as
∆Te − ∆Ti
∆Tlm =
ln(∆Te / ∆Ti )
PROPRIETARY MATERIAL. © 2015 The McGraw-Hill Companies, Inc. 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.
, 8-4
8-18C The number of transfer units NTU is a measure of the heat transfer area and effectiveness of a heat transfer system. A
small value of NTU (NTU < 5) indicates more opportunities for heat transfer whereas a large NTU value (NTU >5) indicates
that heat transfer will not increase no matter how much we extend the length of the tube.
8-19 The average velocity and mean temperature are to be determined from the given velocity and temperature profiles.
Assumptions 1 Steady operating conditions exist. 2 Properties are constant.
Analysis The average velocity in a tube with a radius of R = D/2 is
R
∫ u(r )r dr
2
Vavg = 2
R 0
R
R 2 − 0.0125(r 2 − R 2 ) 2
∫
2
Vavg = 0.05r[1 − (r / R) ] dr = 2
2
= 0.025 m/s
R2 0 R R2 0
The mean temperature in a tube with a radius of R = D/2 is
R
∫ T (r )u(r )r dr
2
Tm = 2
Vavg R 0
R
∫
2(0.05)
Tm = 2
r[400 + 80(r / R) 2 − 30(r / R) 3 ][1 − (r / R) 2 ] dr
Vavg R 0
R
∫ [400r + 80r (r / R)
4
= 2
2
− 30r (r / R) 3 ] − [400r (r / R) 2 + 80r (r / R) 4 − 30r (r / R) 5 ] dr
R 0
=
4
R2
(105R ) = 420 K
2
Discussion Note that the average velocity is half of the maximum velocity (velocity at the center of the tube) for the given
profile. This suggests that the given velocity profile has a profile of a fully developed laminar flow or it is parabolic.
PROPRIETARY MATERIAL. © 2015 The McGraw-Hill Companies, Inc. 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
5th Edition
Yunus A. Cengel & Afshin J. Ghajar
McGraw-Hill, 2015
Chapter 8
INTERNAL FORCED CONVECTION
PROPRIETARY AND CONFIDENTIAL
This Manual is the proprietary property of The McGraw-Hill Companies, Inc. (“McGraw-Hill”) 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: 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.
PROPRIETARY MATERIAL. © 2015 The McGraw-Hill Companies, Inc. 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.
, 8-2
General Flow Analysis
8-1C Engine oil requires a larger pump because of its much larger density.
8-2C In fluid flow, it is convenient to work with an average or mean velocity Vavg and an average or mean temperature Tm
which remain constant in incompressible flow when the cross-sectional area of the tube is constant. The Vavg and Tm represent
the velocity and temperature, respectively, at a cross section if all the particles were at the same velocity and temperature.
8-3C The generally accepted value of the Reynolds number above which the flow in a smooth pipe is turbulent is 4000.
8-4C For flow through non-circular tubes, the Reynolds number as well as the Nusselt number and the friction factor are
4 Ac
based on the hydraulic diameter Dh defined as Dh = where Ac is the cross-sectional area of the tube and p is its
p
perimeter. The hydraulic diameter is defined such that it reduces to ordinary diameter D for circular tubes since
4 Ac 4pD
Dh = = = D.
p pD
8-5C The fluid viscosity is responsible for the development of the velocity boundary layer. For the idealized inviscid fluids
(fluids with zero viscosity), there will be no velocity boundary layer.
8-6C In the fully developed region of flow in a circular tube, the velocity profile will not change in the flow direction but the
temperature profile may.
8-7C The friction factor is highest at the tube inlet where the thickness of the boundary layer is zero, and decreases gradually
to the fully developed value. The same is true for turbulent flow.
8-8C The friction factor f remains constant along the flow direction in the fully developed region in both laminar and
turbulent flow.
8-9C In turbulent flow, the tubes with rough surfaces have much higher friction factors than the tubes with smooth surfaces.
In the case of laminar flow, the effect of surface roughness on the friction factor is negligible.
PROPRIETARY MATERIAL. © 2015 The McGraw-Hill Companies, Inc. 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.
, 8-3
8-10C The region from the tube inlet to the point at which the boundary layer merges at the centerline is called the
hydrodynamic entry region, and the length of this region is called hydrodynamic entry length. The entry length is much
longer in laminar flow than it is in turbulent flow. But at very low Reynolds numbers, Lh is very small (Lh = 1.2D at Re = 20).
8-11C The hydrodynamic and thermal entry lengths are given as Lh = 0.05 Re D and Lt = 0.05 Re Pr D for laminar flow, and
L h ≈ Lt ≈ 10 D in turbulent flow. Noting that Pr >> 1 for oils, the thermal entry length is larger than the hydrodynamic entry
length in laminar flow. In turbulent, the hydrodynamic and thermal entry lengths are independent of Re or Pr numbers, and are
comparable in magnitude.
8-12C The hydrodynamic and thermal entry lengths are given as Lh = 0.05 Re D and Lt = 0.05 Re Pr D for laminar flow, and
L h ≈ Lt ≈ 10 D in turbulent flow. Noting that Pr << 1 for liquid metals, the thermal entry length is smaller than the
hydrodynamic entry length in laminar flow. In turbulent, the hydrodynamic and thermal entry lengths are independent of Re or
Pr numbers, and are comparable in magnitude.
8-13C The region of flow over which the thermal boundary layer develops and reaches the tube center is called the thermal
entry region, and the length of this region is called the thermal entry length. The region in which the flow is both
hydrodynamically (the velocity profile is fully developed and remains unchanged) and thermally (the dimensionless
temperature profile remains unchanged) developed is called the fully developed region.
8-14C The heat flux will be higher near the inlet because the heat transfer coefficient is highest at the tube inlet where the
thickness of thermal boundary layer is zero, and decreases gradually to the fully developed value.
8-15C The heat flux will be higher near the inlet because the heat transfer coefficient is highest at the tube inlet where the
thickness of thermal boundary layer is zero, and decreases gradually to the fully developed value.
8-16C The logarithmic mean temperature difference ∆Tln is an exact representation of the average temperature difference
between the fluid and the surface for the entire tube. It truly reflects the exponential decay of the local temperature difference.
The error in using the arithmetic mean temperature increases to undesirable levels when ∆Te differs from ∆Ti by great
amounts. Therefore we should always use the logarithmic mean temperature.
8-17C When the surface temperature of tube is constant, the appropriate temperature difference for use in the Newton's law of
cooling is logarithmic mean temperature difference that can be expressed as
∆Te − ∆Ti
∆Tlm =
ln(∆Te / ∆Ti )
PROPRIETARY MATERIAL. © 2015 The McGraw-Hill Companies, Inc. 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.
, 8-4
8-18C The number of transfer units NTU is a measure of the heat transfer area and effectiveness of a heat transfer system. A
small value of NTU (NTU < 5) indicates more opportunities for heat transfer whereas a large NTU value (NTU >5) indicates
that heat transfer will not increase no matter how much we extend the length of the tube.
8-19 The average velocity and mean temperature are to be determined from the given velocity and temperature profiles.
Assumptions 1 Steady operating conditions exist. 2 Properties are constant.
Analysis The average velocity in a tube with a radius of R = D/2 is
R
∫ u(r )r dr
2
Vavg = 2
R 0
R
R 2 − 0.0125(r 2 − R 2 ) 2
∫
2
Vavg = 0.05r[1 − (r / R) ] dr = 2
2
= 0.025 m/s
R2 0 R R2 0
The mean temperature in a tube with a radius of R = D/2 is
R
∫ T (r )u(r )r dr
2
Tm = 2
Vavg R 0
R
∫
2(0.05)
Tm = 2
r[400 + 80(r / R) 2 − 30(r / R) 3 ][1 − (r / R) 2 ] dr
Vavg R 0
R
∫ [400r + 80r (r / R)
4
= 2
2
− 30r (r / R) 3 ] − [400r (r / R) 2 + 80r (r / R) 4 − 30r (r / R) 5 ] dr
R 0
=
4
R2
(105R ) = 420 K
2
Discussion Note that the average velocity is half of the maximum velocity (velocity at the center of the tube) for the given
profile. This suggests that the given velocity profile has a profile of a fully developed laminar flow or it is parabolic.
PROPRIETARY MATERIAL. © 2015 The McGraw-Hill Companies, Inc. 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.
