1. Heat Transfer-Basic Modes
There are three basic modes of heat transfer. These are conduction, convection and radiation.
Your initial purpose in studying heat transfer should be to recognize where and when each
applies. This initial analysis will then lead you to choose the proper quantitative model for
further examination. We also want you to learn at this time the simple equations used to
describe each mode.
What is Heat or Thermal Energy?
Heat is often described as the motion of molecules. Molecules bounce into each
other and they transfer vibrational, rotational and translation energy. During this type of
interaction, higher energy molecules tend to give up energy to less excited molecules. We
tend to describe the overall energy of materials by temperature and particularly absolute
temperature. If we “cool” higher energy gas molecules, we take some of their energy
away. The temperature or energy will be reduced and eventually cause them to condense.
In the liquid state, they do not move as freely. There is a similar trend when we freeze
molecules to form the solid state.
Our experiences tell us that heat flows from matter of higher temperature to
lower temperature. This is sometimes called the zeroeth law of thermodynamics. So,
typically for heat transfer to occur, molecules at one position in space must have a higher
temperature than a group of nearby molecules.

2. I. Conduction
We find conduction applies when looking at heat transfer in solids or quiescent fluids. That
is, there is no bulk motion or velocity in the material. Heat transfer occurs solely from
motion at the molecular level. For example, solid metals carry heat by conduction.
The basic equation used to describe conduction is Fourier’s law:
q = - k(T)
where q = heat flux or heat flow per unit area per unit time(e.g. Btu/ft2-s)
k = thermal conductivity of the material(e.g. W/m K)
T = gradient of the temperature(K/m)
Let’s take a closer look at this equation and its physical meaning. For heat to flow, there
must be a driving force or gradient in the temperature. We see from the equation that as
the temperature gradient increases, the flow of heat increases. This makes sense from our
personal experiences. Remember also that the gradient is a vector in the direction of
greatest increase. The minus signs tells us that heat flows in the opposite direction or
towards decreasing temperature(as we expect!). We know that metals conduct heat better
than (say) glass or plastic. The material character must be represented in the equation. This
is the thermal conductivity k. Note the similarity to Newton’s Law of Viscosity and .
What methods do we use to find material properties?

3. II. Convection
The most common situation for convection is flow of a fluid past a solid surface. So, heat
transfer typically takes place from a solid phase material to an adjacent fluid(or vice versa).
For example, thermal energy in the engine block of an automobile is removed by convection
as the cooling fluid flows through the engine and back to the radiator.
Newton’s law of cooling or rate equation describes heat transfer.
q = h T
where q = heat flux
h = heat transfer coefficient, also called the film coefficient
T = temperature difference between the one phase and the other
This equation really defines the transfer coefficient. In other words, we find the value of
h that makes this true. One does not usually write Newton’s rate equation as a vector
equation. Heat flows perpendicular to the interface. T might typically be the difference
between the surface temperature of the solid and some average or bulk temperature of the
adjacent fluid.

4. III. Radiation
The third mode of heat transfer, radiation, does not utilize molecular interaction to transmit
thermal energy. Heat flows by electromagnetic radiation and can be present even in a
vacuum. Earth receives energy from the sun by this mechanism.
Radiative heat transfer becomes significant at higher temperatures. “Red hot” surfaces such
as in a furnace will transmit heat by this mechanism.
The Stefan-Botzmann equation characterizes radiative heat transfer:
q =  T4
where q = radiative heat flux
 = Stefan-Boltmann constant, x 10-8 W/m2 K4 or x 10-8 Btu/hr ft2 R4
T = temperature of the radiating surface