Transport Processes Primer
Forthcoming in 2019
Table of Contents
is a concept
invented by chemical engineers
in an attempt to unify fluid mechanics,
heat transfer, and mass transfer in a stationary or moving fluid.
The procedure prescribed in texts and elsewhere involves defining
an infinitesimal or finite control volume,
and then performing an integral
or differential momentum, heat, mass, or some other balance
of a transportable entity
over the control volume to derive a governing equation.
The balance typically states that the rate of accumulation
of a certain extensive property of interest
is determined by the rates of convective and diffusive
transport across the boundaries of the control volume,
as well by the rates
of interior or surface generation or loss.
with the aforementioned approach
is that mass, momentum, energy, heat, species concentations,
and other balances appear to be
related only vaguely to Newton's second law of motion
and the fundamental principles of thermodynamics.
The main reason is that physical laws apply to
well-defined bodies or pieces of material (closed systems),
as opposed to stationary control volumes (open systems.)
Consequently, a person who introduces
fluid mechanics based
on momentum transport will be hard pressed to justify
his/her approach in the absence of hand waving.
It is possible that other physical laws can be restated
similarly in the context of open systems by allowing
mass and associated extensive properties,
such as entropy, to enter or exit
the boundaries of such systems.
the dual restatement
may appear like a band-aid
that undermines the omnipotence of the classical approach
and unnecessarily complicates the rule book of the Universe.
To ensure accuracy and scientific rigor,
the governing equations of transport phenomena
should be derived from traditional physical laws,
and the transport approach
should be validated and then employed
as a practical method of formulating
equations and obtaining solutions.
The proper method of developing transport equations
should proceed considering a fluid parcel and then
performing the following steps
Write an expression for a property of interest
attributed to a material pacel,
such as mass, momentum, internal energy,
or species concentration.
Use the Reynolds transport equation to express
the rate of change
of the parcel property
in terms of accumulation
over the parcel volume
and integrated flux
over the parcel surface.
Introduce a physical law for the rate of the change of the parcel
For example, the rate of change of mass is zero
and the rate of change of momentum is given
by Newton's second law of motion.
Regard the parcel as a control volume,
or else consider the parcel occupying at a particular instant
a control volume, to obtain an integral balance.
Apply the divergence theorem to convert boundary integrals
into volume integrals, and thereby derive governing
differential balances in the form of differential equations
written in conservative or non-conservative form.
My main goal in this
book is to review the basic concepts
of transport processes
and illustrate the origin of governing equations
by reviewing, deriving, and summarizing the equations of mass, momentum,
energy, entropy, and mass transport
for homogeneous fluids and mixtures
in the context of mechanical, chemical,
biological, biomedical, and other mainstream science and engineering.
A summary of transport equations in differential and integral
form is given in Appendix A.
features of the discourse with regard to mass transport
includes the interpretation of diffusion
in terms of monochromatic parcel kinematics,
the discussion of stresses and the equation of motion
for individual species in a mixture,
and the study of monochromatic and combined energetics.
Extensions and abstractions of the notion of open
and closed systems and transport phenomena
are discussed in Appendix B.
A summary of equations governing the motion of multi-component
mixtures is given in Appendix C.
Fundamental concepts from thermodynamics are discussed in Appendix D.
Familiarity with calculus
and fluid mechanics,
and cautioned access to Internet resources
on the subjects discussed