Page 10 - Fundamentals of The Finite Element Method for Heat and Fluid Flow

INTRODUCTION
2
The previously-mentioned examples are only a sample of heat transfer applications to
name but a few. The solar system and the associated energy transfer are the principal
factors for existence of life on earth. It is not untrue to say that it is extremely difficult,
often impossible, to avoid some form of heat transfer in any process on earth.
The study of heat transfer provides economical and efficient solutions for critical prob-
lems encountered in many engineering items of equipment. For example, we can consider
the development of heat pipes that can transport heat at a much greater rate than copper or
silver rods of the same dimensions, even at almost isothermal conditions. The development
of present day gas turbine blades, in which the gas temperature exceeds the melting point of
the material of the blade, is possible by providing efficient cooling systems and is another
example of the success of heat transfer design methods. The design of computer chips,
which encounter heat flux of the order occurring in re-entry vehicles, especially when the
◦
surface temperature of the chips is limited to less than 100 C, is again a success story for
heat transfer analysis.
Although there are many successful heat transfer designs, further developments are still
necessary in order to increase the life span and efficiency of the many devices discussed
previously, which can lead to many more new inventions. Also, if we are to protect our
environment, it is essential to understand the many heat transfer processes involved and, if
necessary, to take appropriate action.

1.2 Heat Transfer Modes

Heat transfer is that section of engineering science that studies the energy transport between
material bodies due to a temperature difference (Bejan 1993; Holman 1989; Incropera and
Dewitt 1990; Sukhatme 1992). The three modes of heat transfer are

1. Conduction
2. Convection
3. Radiation.

The conduction mode of heat transport occurs either because of an exchange of energy
from one molecule to another, without the actual motion of the molecules, or because of
the motion of the free electrons if they are present. Therefore, this form of heat transport
depends heavily on the properties of the medium and takes place in solids, liquids and
gases if a difference in temperature exists.
Molecules present in liquids and gases have freedom of motion, and by moving from
a hot to a cold region, they carry energy with them. The transfer of heat from one region
to another, due to such macroscopic motion in a liquid or gas, added to the energy transfer
by conduction within the fluid, is called heat transfer by convection. Convection may be
free, forced or mixed. When fluid motion occurs because of a density variation caused by
temperature differences, the situation is said to be a free, or natural, convection. When
the fluid motion is caused by an external force, such as pumping or blowing, the state is