2-1
Solutions Manual
for
Heat and Mass Transfer: Fundamentals & Applications
5th Edition
Yunus A. Cengel & Afshin J. Ghajar
McGraw-Hill, 2015
Chapter 2
HEAT CONDUCTION EQUATION
Download Full Solution Manual for Heat and Mass Transfer Fundamentals and
Applications 5th Edition by Cengel
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to the following restrictions, and if the recipient does not agree to these restrictions, the Manual should be
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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
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reproduced, displayed or distributed in any form or by any means, electronic or otherwise, without
the prior written permission of McGraw-Hill.
,PRO PRIETARY 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.
, 2-2
Introduction
2-1C The term steady implies no change with time at any point within the medium while transient implies variation with time
or time dependence. Therefore, the temperature or heat flux remains unchanged with time during steady heat transfer through a
medium at any location although both quantities may vary from one location to another. During transient heat transfer, the
temperature and heat flux may vary with time as well as location. Heat transfer is one-dimensional if it occurs primarily in one
direction. It is two-dimensional if heat tranfer in the third dimension is negligible.
2-2C Heat transfer is a vector quantity since it has direction as well as magnitude. Therefore, we must specify both direction
and magnitude in order to describe heat transfer completely at a point. Temperature, on the other hand, is a scalar quantity.
2-3C Yes, the heat flux vector at a point P on an isothermal surface of a medium has to be perpendicular to the surface at
that point.
2-4C Isotropic materials have the same properties in all directions, and we do not need to be concerned about the variation
of properties with direction for such materials. The properties of anisotropic materials such as the fibrous or composite
materials, however, may change with direction.
2-5C In heat conduction analysis, the conversion of electrical, chemical, or nuclear energy into heat (or thermal) energy
in solids is called heat generation.
2-6C The phrase “thermal energy generation” is equivalent to “heat generation,” and they are used interchangeably. They
imply the conversion of some other form of energy into thermal energy. The phrase “energy generation,” however, is
vague since the form of energy generated is not clear.
2-7C The heat transfer process from the kitchen air to the refrigerated space is
transient in nature since the thermal conditions in the kitchen and the
refrigerator, in general, change with time. However, we would analyze this
problem as a steady heat transfer problem under the worst anticipated conditions
such as the lowest thermostat setting for the refrigerated space, and the
anticipated highest temperature in the kitchen (the so-called design conditions).
If the compressor is large enough to keep the refrigerated space at the desired
temperature setting under the presumed worst conditions, then it is large enough
to do so under all conditions by cycling on and off. Heat transfer into the
refrigerated space is three-dimensional in nature since heat will be entering
through all six sides of the refrigerator. However, heat transfer through any wall
or floor takes place in the direction normal to the surface, and thus it can be
analyzed as being one-dimensional. Therefore, this problem can be simplified
greatly by considering the heat transfer to be onedimensional at each of the four
sides as well as the top and bottom sections, and then by adding the calculated
values of heat transfer at each s urface.
PRO PRIETARY 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.
, 2-3
2-8C Heat transfer through the walls, door, and the top and bottom sections of an oven is transient in nature since the
thermal conditions in the kitchen and the oven, in general, change with time. However, we would analyze this problem as a
steady heat transfer problem under the worst anticipated conditions such as the highest temperature setting for the oven, and
the anticipated lowest temperature in the kitchen (the so called “design” conditions). If the heating element of the oven is
large enough to keep the oven at the desired temperature setting under the presumed worst conditions, then it is large
enough to do so under all conditions by cycling on and off.
Heat transfer from the oven is three-dimensional in nature since heat will be entering through all six sides of the
oven. However, heat transfer through any wall or floor takes place in the direction normal to the surface, and thus it can be
analyzed as being one-dimensional. Therefore, this problem can be simplified greatly by considering the heat transfer as
being one- dimensional at each of the four sides as well as the top and bottom sections, and then by adding the calculated
values of heat transfers at each surface.
2-9C Heat transfer to a potato in an oven can be modeled as one-dimensional since temperature differences (and thus heat
transfer) will exist in the radial direction only because of symmetry about the center point. This would be a transient heat
transfer process since the temperature at any point within the potato will change with time during cooking. Also, we would
use the spherical coordinate system to solve this problem since the entire outer surface of a spherical body can be
described by a constant value of the radius in spherical coordinates. We would place the origin at the center of the potato.
2-10C Assuming the egg to be round, heat transfer to an egg in boiling water can be modeled as one -dimensional since
temperature differences (and thus heat transfer) will primarily exist in the radial direction only because of symmetry about
the center point. This would be a transient heat transfer process since the temperature at any point within the egg will chan ge
with time during cooking. Also, we would use the spherical coordinate system to solve this problem since the entire outer
surface of a spherical body can be described by a constant value of the radius in spherical coordinates. We would place the
origin at the center of the egg.
2-11C Heat transfer to a hot dog can be modeled as two-dimensional since temperature differences (and thus heat transfer)
will exist in the radial and axial directions (but there will be symmetry about the center line and no heat transfer in the
azimuthal direction. This would be a transient heat transfer process since the temperature at any point within the hot dog
will change with time during cooking. Also, we would use the cylindrical coordinate system to solve this problem since a
cylinder is best described in cylindrical coordinates. Also, we would place the o rigin somewhere on the center line, possibly
at the center of the hot dog. Heat transfer in a very long hot dog could be considered to be one -dimensional in preliminary
calculations.
2-12C Heat transfer to a roast beef in an oven would be transient sin ce the temperature at any point within the roast will
change with time during cooking. Also, by approximating the roast as a spherical object, this heat transfer process can be
modeled as one-dimensional since temperature differences (and thus heat transfer) will primarily exist in the radial
direction because of symmetry about the center point.
2-13C Heat loss from a hot water tank in a house to the surrounding medium can be considered to be a steady heat transfer
problem. Also, it can be considered to be two-dimensional since temperature differences (and thus heat transfer) will exist
in the radial and axial directions (but there will be symmetry about the center line and no heat transfer in the azimuthal
direction.)
PRO PRIETARY 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 2
HEAT CONDUCTION EQUATION
Download Full Solution Manual for Heat and Mass Transfer Fundamentals and
Applications 5th Edition by Cengel
https://getbooksolutions.com/download/solution- manual- for- heat-and- mass-transfer- fundamentals-
and-applications-5th-edition-by-cengel
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 authorize d
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.
,PRO PRIETARY 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.
, 2-2
Introduction
2-1C The term steady implies no change with time at any point within the medium while transient implies variation with time
or time dependence. Therefore, the temperature or heat flux remains unchanged with time during steady heat transfer through a
medium at any location although both quantities may vary from one location to another. During transient heat transfer, the
temperature and heat flux may vary with time as well as location. Heat transfer is one-dimensional if it occurs primarily in one
direction. It is two-dimensional if heat tranfer in the third dimension is negligible.
2-2C Heat transfer is a vector quantity since it has direction as well as magnitude. Therefore, we must specify both direction
and magnitude in order to describe heat transfer completely at a point. Temperature, on the other hand, is a scalar quantity.
2-3C Yes, the heat flux vector at a point P on an isothermal surface of a medium has to be perpendicular to the surface at
that point.
2-4C Isotropic materials have the same properties in all directions, and we do not need to be concerned about the variation
of properties with direction for such materials. The properties of anisotropic materials such as the fibrous or composite
materials, however, may change with direction.
2-5C In heat conduction analysis, the conversion of electrical, chemical, or nuclear energy into heat (or thermal) energy
in solids is called heat generation.
2-6C The phrase “thermal energy generation” is equivalent to “heat generation,” and they are used interchangeably. They
imply the conversion of some other form of energy into thermal energy. The phrase “energy generation,” however, is
vague since the form of energy generated is not clear.
2-7C The heat transfer process from the kitchen air to the refrigerated space is
transient in nature since the thermal conditions in the kitchen and the
refrigerator, in general, change with time. However, we would analyze this
problem as a steady heat transfer problem under the worst anticipated conditions
such as the lowest thermostat setting for the refrigerated space, and the
anticipated highest temperature in the kitchen (the so-called design conditions).
If the compressor is large enough to keep the refrigerated space at the desired
temperature setting under the presumed worst conditions, then it is large enough
to do so under all conditions by cycling on and off. Heat transfer into the
refrigerated space is three-dimensional in nature since heat will be entering
through all six sides of the refrigerator. However, heat transfer through any wall
or floor takes place in the direction normal to the surface, and thus it can be
analyzed as being one-dimensional. Therefore, this problem can be simplified
greatly by considering the heat transfer to be onedimensional at each of the four
sides as well as the top and bottom sections, and then by adding the calculated
values of heat transfer at each s urface.
PRO PRIETARY 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.
, 2-3
2-8C Heat transfer through the walls, door, and the top and bottom sections of an oven is transient in nature since the
thermal conditions in the kitchen and the oven, in general, change with time. However, we would analyze this problem as a
steady heat transfer problem under the worst anticipated conditions such as the highest temperature setting for the oven, and
the anticipated lowest temperature in the kitchen (the so called “design” conditions). If the heating element of the oven is
large enough to keep the oven at the desired temperature setting under the presumed worst conditions, then it is large
enough to do so under all conditions by cycling on and off.
Heat transfer from the oven is three-dimensional in nature since heat will be entering through all six sides of the
oven. However, heat transfer through any wall or floor takes place in the direction normal to the surface, and thus it can be
analyzed as being one-dimensional. Therefore, this problem can be simplified greatly by considering the heat transfer as
being one- dimensional at each of the four sides as well as the top and bottom sections, and then by adding the calculated
values of heat transfers at each surface.
2-9C Heat transfer to a potato in an oven can be modeled as one-dimensional since temperature differences (and thus heat
transfer) will exist in the radial direction only because of symmetry about the center point. This would be a transient heat
transfer process since the temperature at any point within the potato will change with time during cooking. Also, we would
use the spherical coordinate system to solve this problem since the entire outer surface of a spherical body can be
described by a constant value of the radius in spherical coordinates. We would place the origin at the center of the potato.
2-10C Assuming the egg to be round, heat transfer to an egg in boiling water can be modeled as one -dimensional since
temperature differences (and thus heat transfer) will primarily exist in the radial direction only because of symmetry about
the center point. This would be a transient heat transfer process since the temperature at any point within the egg will chan ge
with time during cooking. Also, we would use the spherical coordinate system to solve this problem since the entire outer
surface of a spherical body can be described by a constant value of the radius in spherical coordinates. We would place the
origin at the center of the egg.
2-11C Heat transfer to a hot dog can be modeled as two-dimensional since temperature differences (and thus heat transfer)
will exist in the radial and axial directions (but there will be symmetry about the center line and no heat transfer in the
azimuthal direction. This would be a transient heat transfer process since the temperature at any point within the hot dog
will change with time during cooking. Also, we would use the cylindrical coordinate system to solve this problem since a
cylinder is best described in cylindrical coordinates. Also, we would place the o rigin somewhere on the center line, possibly
at the center of the hot dog. Heat transfer in a very long hot dog could be considered to be one -dimensional in preliminary
calculations.
2-12C Heat transfer to a roast beef in an oven would be transient sin ce the temperature at any point within the roast will
change with time during cooking. Also, by approximating the roast as a spherical object, this heat transfer process can be
modeled as one-dimensional since temperature differences (and thus heat transfer) will primarily exist in the radial
direction because of symmetry about the center point.
2-13C Heat loss from a hot water tank in a house to the surrounding medium can be considered to be a steady heat transfer
problem. Also, it can be considered to be two-dimensional since temperature differences (and thus heat transfer) will exist
in the radial and axial directions (but there will be symmetry about the center line and no heat transfer in the azimuthal
direction.)
PRO PRIETARY 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.
