Note to Students and Instructors on the Power Point
The presentation is intended to be used along with the text. It
helps minimize the instructor from writing out all the equations.
Many equations need to be further elaborated by the instructor.
In this chapter, we
• Define heat transfer
• Show the relationship between thermodynamics and heat transfer
• Define the three modes of heat transfer – conduction, convection,
• Give a brief introduction to each mode of heat transfer
• Briefly describe a few cases where heat transfer plays an important
• Suggest a methodology for the solution of heat transfer problems
• Define some of the significant terms used in the book.
Heat transfer is energy transfer resulting only from temperature
1.1 Relationship between
thermodynamics and heat
First law of thermodynamics
is a statement of
conservation of energy and
deals with equilibrium
states. Consider a spherical
copper ball initially at a
suddenly immersed in water
as shown in the figure.
Applying the first law of thermodynamics we find that the final
temperature of the ball and water is 36.7 oC. But the first law will not
give the time required to go from the initial state to the final state.
In the study of heat transfer we attempt to the additional questions of
the temperature distribution and the heat transfer rate as functions of
1.2 Modes of Heat Transfer
Heat transfer is a surface phenomenon – heat transfer occurs from (or
to) a surface.
Three modes of heat transfer are generally recognized.
Conduction: Heat transfer in a solid or a stationary fluid
Convection: Heat transfer in a in motion. Two modes of convection:
In forced convection fluid motion occurs due to an external force and
the motion continues with or without heat transfer
In natural convection fluid motion is caused solely by temperature
Both conduction and convection require a material medium.
Radiation does not require a material medium.
In conduction and convection one can determine the heat transfer rate
from an elemental area by knowing the conditions of the material in
the immediate vicinity of the area.
In radiation one needs to know the entire field that the area sees.
The heat transport in conduction and convection is much, much
slower than in radiation.
Conduction heat transfer is heat transfer in solids and fluids without
Conductive heat transfer generally occurs in solids though it may
occur in fluids without macroscopic motion or with rigid body
The basis for analysis of conduction is the first law of
thermodynamics in conjuction with Fourier’s Law of Conduction.
Fourier’s law: conductive heat flux at a point in a given direction is
proportional to the magnitude of the temperature gradient in that
direction and is positive in the direction of decreasing temperature.
In steady state, no part of the
solid stores energy, and the
heat transfer rate across every
cross section perpendicular to
the x-direction is uniform. As
the cross sectional area is
uniform, the heat flux is also
uniform, Integrating Eq. (1.3.2)
kdT q dx
'' 1 2
x x x x
q q dA kA
'' 1 2
Thermal conductivity k is a property of the material and is always
positive. It varies from about 0.0262 W/m K for air to about 2300
W/m K for carbon (type IIa diamond), i.e., by a factor of 100 000.
The negative sign in Fourier’s law satisfies the second law of
thermodynamics. For heat transfer to be positive in the x-direction
the temperature gradient in that direction should be negative i.e.,
heat transfer occurs in the direction of decreasing temperature.
When there is a temperature gradient in a fluid in bulk motion
heat transfer occurs by two mechanisms.
Molecular motion – conduction
Bulk motion of fluid packets
Total heat transfer is the sum of the two.
Convective heat transfer coefficient is defined by Eq. (1.4.1.)
c c s f
q h T T
The convective heat transfer coefficient is always positive.
With uniform surface temperature Ts and Tf if the heat flux is local
we obtain the local heat transfer coefficient.
If the heat flux is the average over an area we get the average heat
The choice of the reference temperature Tf is arbitrary. With each
correlation the choice of the reference temperature for defining the
convective heat transfer coefficient should be stated.
However, by convention the reference temperature for external
flows such of an semi-infinite fluid flow over a flat plate, cylinder,
sphere and so on, the reference temperature is the temperature of the
fluid far away from the surface, known as the free stream
temperature usually denoted by T. In internal flows the reference
temperature is usually the bulk temperature Tb. A detailed definition
of the bulk temperature is given under internal flows.
Convection is subdivided into forced and natural convection.
In forced convection the fluid flow continues whether there is heat
transfer or not. In natural convection the fluid flow is caused solely
be temperature differences due to heat transfer, in the presence of a
Some representative values of the convective heat transfer
coefficients in each mode is given in Table 1.4.1.
In natural heat transfer, radiative heat transfer may form significant
part of the total heat transfer.
All materials emit energy by radiation in the form electro-magnetic
waves or photons.
The maximum radiative heat flux that can be emitted by a solid
surface at a defined surface temperature, the black body emissive
power is given by the Stefan-Boltzmann law,
A surface that emits the maximum energy flux is an ideal radiator,
also known as a black surface. The emitted energy flux of any real
surface is less than the maximum.
Consider the radiative heat transfer
from a convex surface completely
enclosed by a second much larger
surface as shown in Figure 1.5.1.
The two surfaces are separated by
medium that does not participate in
No part of the inner surface can see
any other part of itself – no part is
concave. In this case the heat
radiative transfer rate is given by:
Analogous to the convective heat transfer coefficient we may define
a radiative heat transfer coefficient employing Eq. (1.5.3) for this
From Eq. (1.5.4) it is clear that the radiative heat transfer
coefficient is a function of the temperatures of the two surfaces and
the emissivity of the inner surface. However, in many cases the
variation of the coefficient with temperatures is such that an
average value can be used.
1.6 Surface heat transfer coefficient
In many cases of natural convection the radiative heat transfer rate is
a significant part of the total heat rate. In such cases a surface heat
transfer coefficient – the ratio of the total heat flux to a chactraristic
In such cases the surface heat transfer coefficient is given by:
h = hc + hr
Pure substance: Contains only one type of molecules.
Uniform: The value of a parameter does not vary spatially.
Homogeneous mixture: Contains more than one phase of a pure
substance so mixed that every volumetric element contains the same
proportion of molecules of different substances or phases. Examples:
Air or steam and water droplets.
In a uniform state, the properties of a homogeneous substance the
thermodynamic (density, internal energy…) and transport properties
viscosity, thermal conductivity…) are spatially independent.
Isotropic substance: Properties are direction independent.
One-dimensional: Variable of interest varies with only one spatial
1.9 Terminology (continued)
Steady State: Variable of interest does not change with time.
Transient or dynamic state: Variable is time dependent.
Control Mass (also system, closed system): focus is on an
Control Volume (open system): A region in space. Can be moving,
deformable or rigid.
Uncertainty: Indicates that a value of a variable cannot be treated as
Causes of uncertainty:
Uncertainties in the values measured with instruments.
Actual measurement in an environment that is not identical to where
original measurements were made.
Lack of repeatability in the measured values. Two ways of indicating
1. Express the value of a variable as x y
2. Express the value of x as % 100 /
x z z y x
1.10 Methodology in the solution of heat transfer problems
Balance of mass
Control Mass: Mass remains constant.
Rate of change of mass within the CV + net rate of mass flow
rate out = 0
Balance of linear momentum: In a specified direction
Rate of change of momentum = sum of all the forces on the mass
Rate of change of linear momentum of the mass in the CV + net
rate of momentum flow out = sum of all the forces on the
material in the CV
Balance of Energy (First Law of Thermodynamics)
Assumption: changes in kinetic and potential energies are negligible.
Rate of change of internal energy of the mass = net rate of heat
transfer to the mass – net rate of work transfer from the mass +
rate of internal energy generation.
Rate of change of internal energy of the mass in the CV + net rate
of enthalpy flow out of the CV = Net rate of heat transfer to the
CV – net rate of work transfer from the CV + rate of internal
energy generation in the CV.
1.12 Some suggestions for solving problems
1. Read the problem statement carefully and translate them into
2. Transfer all the information in the problem statement to the
3. List all assumptions. Some assumptions may need to be
made while solving the problems.
4. Find and list all the required properties.
5. Conceptualize the solution by writing all the steps.
6. Apply your analysis in symbolic form. Substitute the
numerical values at the end.
7. Present your solution in a neat and orderly manner.
8. For some problems defend every step of the solution.
9. The purpose of solving problems is to ensure a good
understanding of the material and the analysis.