8-1
Solutions Manual
for
Heat and Mass Transfer: Fundamentals & Applications
Fourth Edition
Yunus A. Cengel & Afshin J. Ghajar
McGraw-Hill, 2011
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. © 2011 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 The generally accepted value of the Reynolds number above which the flow in a smooth pipe is turbulent is 4000.
8-3C 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 D h = 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 4πD
Dh = = = D.
p πD
8-4C 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.
8-5C 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.
8-6C 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.
8-7C The friction factor f remains constant along the flow direction in the fully developed region in both laminar and
turbulent flow.
8-8C 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.
PROPRIETARY MATERIAL. © 2011 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
8-9C 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.
8-10C 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.
8-11C 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.
8-12C 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.
8-13C 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 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.
8-17C 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).
PROPRIETARY MATERIAL. © 2011 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 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 )
8-19 Air flows inside a duct and it is cooled by water outside. The exit temperature of air and the rate of heat transfer are to
be determined.
Assumptions 1 Steady operating conditions exist. 2 The surface
temperature of the duct is constant. 3 The thermal resistance of the duct 10°C
is negligible.
Properties The properties of air at the anticipated average temperature of
30°C are (Table A-15)
Air
ρ = 1.164 kg/m 3 50°C D = 18 cm
7 m/s
c p = 1007 J/kg.°C
L = 12 m
Analysis The mass flow rate of water is
⎛ πD 2 ⎞ 2
m& = ρAcVavg = ρ ⎜⎜ ⎟Vavg = (1.164 kg/m 3 ) π (0.18 m) (7 m/s) = 0.2073 kg/s
⎟
⎝ 4 ⎠ 4
As = πDL = π (0.18 m)(12 m) = 6.786 m 2
The exit temperature of air is determined from
( 65)( 6.786)
−
− hAs /( m& c p ) ( 0.2073)(1007 )
Te = Ts − (Ts − Ti )e = 10 − (10 − 50)e = 14.84 °C
The logarithmic mean temperature difference and the rate of heat transfer are
Te − Ti 14.84 − 50
∆Tlm = = = 16.65°C
⎛ T − Te ⎞ ⎛ 10 − 14.84 ⎞
ln⎜⎜ s ⎟
⎟
ln⎜ ⎟
⎝ Ts − Ti ⎠ ⎝ 10 − 50 ⎠
Q& = hAs ∆Tlm = (65 W/m 2 .°C)(6.786 m 2 )(16.65°C) = 7343 W = 7.34 kW
PROPRIETARY MATERIAL. © 2011 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
Fourth Edition
Yunus A. Cengel & Afshin J. Ghajar
McGraw-Hill, 2011
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. © 2011 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 The generally accepted value of the Reynolds number above which the flow in a smooth pipe is turbulent is 4000.
8-3C 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 D h = 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 4πD
Dh = = = D.
p πD
8-4C 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.
8-5C 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.
8-6C 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.
8-7C The friction factor f remains constant along the flow direction in the fully developed region in both laminar and
turbulent flow.
8-8C 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.
PROPRIETARY MATERIAL. © 2011 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
8-9C 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.
8-10C 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.
8-11C 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.
8-12C 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.
8-13C 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 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.
8-17C 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).
PROPRIETARY MATERIAL. © 2011 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 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 )
8-19 Air flows inside a duct and it is cooled by water outside. The exit temperature of air and the rate of heat transfer are to
be determined.
Assumptions 1 Steady operating conditions exist. 2 The surface
temperature of the duct is constant. 3 The thermal resistance of the duct 10°C
is negligible.
Properties The properties of air at the anticipated average temperature of
30°C are (Table A-15)
Air
ρ = 1.164 kg/m 3 50°C D = 18 cm
7 m/s
c p = 1007 J/kg.°C
L = 12 m
Analysis The mass flow rate of water is
⎛ πD 2 ⎞ 2
m& = ρAcVavg = ρ ⎜⎜ ⎟Vavg = (1.164 kg/m 3 ) π (0.18 m) (7 m/s) = 0.2073 kg/s
⎟
⎝ 4 ⎠ 4
As = πDL = π (0.18 m)(12 m) = 6.786 m 2
The exit temperature of air is determined from
( 65)( 6.786)
−
− hAs /( m& c p ) ( 0.2073)(1007 )
Te = Ts − (Ts − Ti )e = 10 − (10 − 50)e = 14.84 °C
The logarithmic mean temperature difference and the rate of heat transfer are
Te − Ti 14.84 − 50
∆Tlm = = = 16.65°C
⎛ T − Te ⎞ ⎛ 10 − 14.84 ⎞
ln⎜⎜ s ⎟
⎟
ln⎜ ⎟
⎝ Ts − Ti ⎠ ⎝ 10 − 50 ⎠
Q& = hAs ∆Tlm = (65 W/m 2 .°C)(6.786 m 2 )(16.65°C) = 7343 W = 7.34 kW
PROPRIETARY MATERIAL. © 2011 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.
