Environmental Engineering Reference
In-Depth Information
matter of great practical consequence because the time rate of exchange of work and heat quan-
tities determine the mechanical or thermal power that can be produced. The more power that can
be generated from a given mass of material, at a given cost, the more desirable the power system
becomes.
Depending upon the circumstances, we may want to augment or diminish the rate at which
heat flows from hot to cold environments. For example, a steam power plant boiler is designed
to facilitate the rapid heating of the circulating water by the hot combustion gases, the heat
being transferred through the wall of the metal tubes within which the water flows and outside
of which the hot gases circulate. On the other hand, when heating a building's interior space in
winter months, the loss of heat to the cold exterior environment is minimized by installing thermal
insulation in the walls.
In most cases of steady heat transfer from a hot to a cold environment, the time rate of heat
transfer
Q
may be represented by
8
Q
=
U
A
(
T
h
−
T
c
)
(3.22)
where
T
h
−
T
c
is the temperature difference between the hot and cold environments,
A
is the
surface area of material that separates the two environments and across which the heat flows, and
U
is the
heat transfer coefficient,
a property of the material separating the two environments.
9
To
attain high values of
, one should use a thin layer of a material, such as copper, that is a good
heat conductor and provide vigorous motion of the hot and cold fluids with which it is in contact.
To obtain low thermal conductances, one needs thick layers of thermally insulating material, like
foamed plastics.
Heat exchangers are passive devices that accomplish a transfer of heat, usually between two
streams of fluids, one hot and the other cold. Typically, one fluid flows inside parallel cylindrical
tubes while the other fluid flows outside of them. In a steam boiler, for example, the cold water
(or steam) flows inside the tubes while the hot combustion gases flow around them. Similarly,
in a steam power plant condenser the cold cooling water flows through the tubes while the hot
exhaust steam from the turbine passes outside the tubes, condensing on the cold surface. The use
of heat exchangers is often necessary to the functioning of a power plant, as in these examples,
but they necessarily exact penalties in the form of loss of mechanical power, increased economic
cost, and reduced thermodynamic efficiency. As an example of the latter, consider the design of
a condenser that must transfer a fixed amount of heat per unit time,
U
Q
. According to equation
(3.22), we could reduce its size (
A
), and thereby its cost, by increasing the temperature difference
(
and thereby reduce the steam cycle efficiency. Alternatively, we could increase the
heat transfer coefficient
T
h
−
T
c
)
by pumping the cooling water through the tubes at a higher speed, but
that would incur an extra pumping power loss. As a consequence, the transfer of heat at finite
rates in thermodynamic systems inevitably incurs performance penalties that cannot be reduced
to zero except by the expenditure of infinite amounts of capital. Fortunately, these performance
U
8
This expression is not a thermodynamic law, although it is in agreement with the requirement of the second
law that heat can be transferred only from a hot to a cold body, not the reverse.
9
The product
U
A
is called the thermal conductance, in analogy with the electrical conductance of an electric
circuit, which is the ratio of the electric current (analogous to the heat flux
Q
) to the voltage difference
(analogous to the temperature difference
T
h
−
T
c
).
