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West Bengal University of technology
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B.Tech
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**Mechanical Engineering**Offline Downloads:
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1. Introduction
Energy is defined as the capacity of a substance to do work. It is a property of the substance and
it can be transferred by interaction of a system and its surroundings. The student would have
encountered these interactions during the study of Thermodynamics. However, Thermodynamics
deals with the end states of the processes and provides no information on the physical
mechanisms that caused the process to take place. Heat Transfer is an example of such a process.
A convenient definition of heat transfer is energy in transition due to temperature differences.
Heat transfer extends the Thermodynamic analysis by studying the fundamental processes and
modes of heat transfer through the development of relations used to calculate its rate.
The aim of this chapter is to console existing understanding and to familiarise the student with
the standard of notation and terminology used in this book. It will also introduce the necessary
units.
1.1 Heat Transfer Modes
The different types of heat transfer are usually referred to as ‘modes of heat transfer’. There are
three of these: conduction, convection and radiation.
x
Conduction: This occurs at molecular level when a temperature gradient exists in a medium,
which can be solid or fluid. Heat is transferred along that temperature gradient by conduction.
x
Convection: Happens in fluids in one of two mechanisms: random molecular motion which is
termed diffusion or the bulk motion of a fluid carries energy from place to place. Convection
can be either forced through for example pushing the flow along the surface or natural as that
which happens due to buoyancy forces.
x
Radiation: Occurs where heat energy is transferred by electromagnetic phenomenon, of
which the sun is a particularly important source. It happens between surfaces at different
temperatures even if there is no medium between them as long as they face each other.
In many practical problems, these three mechanisms combine to generate the total energy flow,
but it is convenient to consider them separately at this introductory stage. We need to describe
each process symbolically in an equation of reasonably simple form, which will provide the basis
for subsequent calculations. We must also identify the properties of materials, and other system
characteristics, that influence the transfer of heat.
1

1.2 System of Units
Before looking at the three distinct modes of transfer, it is appropriate to introduce some terms
and units that apply to all of them. It is worth mentioning that we will be using the SI units
throughout this book:
x
The rate of heat flow will be denoted by the symbol Q . It is measured in Watts (W) and
multiples such as (kW) and (MW).
x
It is often convenient to specify the flow of energy as the heat flow per unit area which is
also known as heat flux. This is denoted by q . Note that, q Q / A where A is the area
through which the heat flows, and that the units of heat flux are (W/m2).
x
Naturally, temperatures play a major part in the study of heat transfer. The symbol T will be
used for temperature. In SI units, temperature is measured in Kelvin or Celsius: (K) and (qC).
Sometimes the symbol t is used for temperature, but this is not appropriate in the context of
transient heat transfer, where it is convenient to use that symbol for time. Temperature
difference is denoted in Kelvin (K).
The following three subsections describe the above mentioned three modes of heat flow in more
detail. Further details of conduction, convection and radiation will be presented in Chapters 2, 3
and 4 respectively. Chapter 5 gives a brief overview of Heat Exchangers theory and application
which draws on the work from the previous Chapters.
1.3 Conduction
The conductive transfer is of immediate interest through solid materials. However, conduction
within fluids is also important as it is one of the mechanisms by which heat reaches and leaves
the surface of a solid. Moreover, the tiny voids within some solid materials contain gases that
conduct heat, albeit not very effectively unless they are replaced by liquids, an event which is not
uncommon. Provided that a fluid is still or very slowly moving, the following analysis for solids
is also applicable to conductive heat flow through a fluid.
2

Figure 1.1 shows, in schematic form, a process of conductive heat transfer and identifies the key
quantities to be considered:
Figure 1-1: One dimensional conduction
Q : the heat flow by conduction in the xdirection (W)
A : the area through which the heat flows, normal to the x-direction (m2)
3

dT
dx : the temperature gradient in the x-direction (K/m)
These quantities are related by Fourier's Law, a model proposed as early as 1822:
Q = -k A
dT
dx
or
q = -k
dT
dx 1
(1.1)
A significant feature of this equation is the negative sign. This recognises that the natural
direction for the flow of heat is from high temperature to low temperature, and hence down the
temperature gradient.
The additional quantity that appears in this relationship is k , the thermal conductivity (W/m K)
of the material through which the heat flows. This is a property of the particular heat-conducting
substance and, like other properties, depends on the state of the material, which is usually
specified by its temperature and pressure.
The dependence on temperature is of particular importance. Moreover, some materials such as
those used in building construction are capable of absorbing water, either in finite pores or at the
molecular level, and the moisture content also influences the thermal conductivity. The units of
thermal conductivity have been determined from the requirement that Fourier's law must be
dimensionally consistent.
Considering the finite slab of material shown in Figure 1.1, we see that for one-dimensional
conduction the temperature gradient is:
T - T1
dT
= 2
dx
L
2
Hence for this situation the transfer law can also be written
T -T
Q = kA 1 2
L
D =
or q = k
T1 - T2
L 3
(1.2)
k
U C
(1.3)4
Table 1.1 gives the values of thermal conductivity of some representative solid materials, for
conditions of normal temperature and pressure. Also shown are values of another property
characterising the flow of heat through materials, thermal diffusivity, which is related to the
conductivity by:
3
Where U is the density in kg / m of the material and C its specific heat capacity in J / kg K .
4

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