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12. Special Topics
In still other flows, multiple phases may coexist. All of the possible combinations are of importance. The solid-gas case includes such phenomena
as dust in the atmosphere, fluidized beds, and gas flow through a porous
medium. In the solid-liquid category are slurries (in which the liquid is the
continuous phase), again, porous medium flows. Gas-liquid flows include
sprays (in which the gas phase is continuous) and bubbly flows (in which
the reverse is true). Finally, there may be three-phase flows. Each of these
cases has many sub-categories.
Chemical reaction may take place in flows and again, there are many
individual cases. When the reacting species are dilute, the reaction rates may
be assumed constant (they may, however, depend on temperature) and the
reacting species are essentially passive scalars with respect to their effect on
the flow. Examples of this kind are pollutant species in the atmosphere or
the ocean. Another kind of reaction involves major species and releases a
large amount of energy. This is the case of combustion. Still another example
is that of airflow at high speeds; compressibility effects may lead to large
temperature increases and the possibility of dissociation or ionization of the
gas.
Geophysics and astrophysics also require the solution of the equations of
fluid motion. Other than plasma effects (discussed below), the new elements
in these flows are the enormous scales compared to engineering flows. In meteorology and oceanography, rotation and stratification have a great influence
on the behavior.
Finally, we mention that in plasmas (ionized fluids), electromagnetic effects play an important role. In this field, the equations of fluid motion have
to be solved along with the equations of electro-magnetism (the Maxwell
equations) and the number of phenomena and special cases is enormous.
In the remainder of this chapter, we shall describe methods for dealing
with some, but not all, of these difficulties. We should point out that each of
the topics mentioned above is an important sub-specialty of fluid mechanics
and has a large literature devoted to it; references to textbooks in each area
are given below. It is impossible to do justice to each of these topics in the
space available here.
12.2 Heat and Mass Transfer
Of the three mechanisms of heat transfer - conduction, radiation, and convection - usually presented in courses on the subject, the last is most closely
connected with fluid mechanics. The link is so strong that convective heat
transfer may be regarded as a sub-area of fluid mechanics.
Steady heat conduction is described by Laplace's equation (or equations
very similar to it) while unsteady conduction is governed by the heat equation; these equations are readily solved by methods presented in Chaps. 3, 4
and 6. A complication arises when the properties are temperature-dependent.
12. Special Topics
In still other flows, multiple phases may coexist. All of the possible combinations are of importance. The solid-gas case includes such phenomena
as dust in the atmosphere, fluidized beds, and gas flow through a porous
medium. In the solid-liquid category are slurries (in which the liquid is the
continuous phase), again, porous medium flows. Gas-liquid flows include
sprays (in which the gas phase is continuous) and bubbly flows (in which
the reverse is true). Finally, there may be three-phase flows. Each of these
cases has many sub-categories.
Chemical reaction may take place in flows and again, there are many
individual cases. When the reacting species are dilute, the reaction rates may
be assumed constant (they may, however, depend on temperature) and the
reacting species are essentially passive scalars with respect to their effect on
the flow. Examples of this kind are pollutant species in the atmosphere or
the ocean. Another kind of reaction involves major species and releases a
large amount of energy. This is the case of combustion. Still another example
is that of airflow at high speeds; compressibility effects may lead to large
temperature increases and the possibility of dissociation or ionization of the
gas.
Geophysics and astrophysics also require the solution of the equations of
fluid motion. Other than plasma effects (discussed below), the new elements
in these flows are the enormous scales compared to engineering flows. In meteorology and oceanography, rotation and stratification have a great influence
on the behavior.
Finally, we mention that in plasmas (ionized fluids), electromagnetic effects play an important role. In this field, the equations of fluid motion have
to be solved along with the equations of electro-magnetism (the Maxwell
equations) and the number of phenomena and special cases is enormous.
In the remainder of this chapter, we shall describe methods for dealing
with some, but not all, of these difficulties. We should point out that each of
the topics mentioned above is an important sub-specialty of fluid mechanics
and has a large literature devoted to it; references to textbooks in each area
are given below. It is impossible to do justice to each of these topics in the
space available here.
12.2 Heat and Mass Transfer
Of the three mechanisms of heat transfer - conduction, radiation, and convection - usually presented in courses on the subject, the last is most closely
connected with fluid mechanics. The link is so strong that convective heat
transfer may be regarded as a sub-area of fluid mechanics.
Steady heat conduction is described by Laplace's equation (or equations
very similar to it) while unsteady conduction is governed by the heat equation; these equations are readily solved by methods presented in Chaps. 3, 4
and 6. A complication arises when the properties are temperature-dependent.