Transport Processes Primer

C. Pozrikidis



From the Preface

Transport phenomena or transport processes is a concept developed by chemical engineers in an effort to unify fluid mechanics, heat transfer, and mass transfer in a stationary material or moving fluid. The core procedure prescribed in texts and elsewhere involves defining a finite or infinitesimal control volume, and then performing an integral or differential momentum, heat, mass, or some other type of balance of a transportable entity to derive a governing equation.

The balance typically states that the rate of accumulation of a certain extensive property of interest, such as mass, momentum, or total energy, is determined by the rates of convective and diffusive transport across the boundaries of the control volume, as well as by appropriate rates of interior and surface loss or production. The control volume itself may be stationary or evolve in an arbitrary fashion.

One subtlety of the aforementioned approach is that mass, momentum, and energy balances are consequences of the principle of mass conservation, Newton's second law of motion, and the first law of thermodynamics. In their classical form, these natural laws apply to well-defined bodies or pieces of material (closed systems), as opposed to control volumes that allow matter to cross their boundaries (open systems).

A way out is to rewrite the natural laws so that they apply to open systems that allow solid or fluid material to enter or exit a control volume through inlets and outlets. However, the dual restatement may appear like a band-aid that undermines the omnipotence of the classical approach and unnecessarily complicates the logistics.

A further complication is that a system may be closed with regard to one property but open with regard to another. For example, a system may be closed with respect to mass but open with respect to energy. A system that is closed with regard to every possible transportable entity or transmittable field is completely isolated. The notion of open, closed, and isolated systems has been discussed in the natural sciences and under the auspices of information theory, sociology, biology, anthropology, linguistics, history, political science, and philosophy.

To ensure accuracy and scientific rigor, the governing equations of transport phenomena are best derived from the classical natural laws applied to material parcels. The transport approach may then be validated and employed as a practical method of formulating equations and obtaining solutions in science and engineering applications. The recommended procedure involves the following steps:
  1. Write an expression for a property of interest attributed to a material parcel, such as mass, momentum, total specific energy, or species mass.
  2. Use the Reynolds transport equation to express the rate of change of the parcel property in terms of accumulation over the parcel volume and associated flux integrated over the parcel surface.
  3. Introduce a physical law for the rate of change of the parcel property. 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.
  4. Regard the parcel as a control volume, or else consider the parcel occupying a control volume of interest at a particular instant to obtain an integral transport balance.
  5. Apply the divergence theorem to convert all boundary integrals into volume integrals, and discard the integral signs to derive governing differential balances in the form of differential equations written in conservative or nonconservative form.

My main goal in this book is to review the basic concepts and notions of transport processes and illustrate the origin of the governing equations by deriving and summarizing the equations of mass, momentum, energy, enthalpy, entropy, and other related transport for homogeneous fluids and mixtures of fluids in the context of mechanical, chemical, biological, biomedical, and other mainstream science and engineering.

Noteworthy features of the discourse with regard to mass transport includes the interpretation of diffusion in terms of species parcel kinematics, the discussion of Fick's and fractional diffusion laws, the introduction of partial stresses and associated equations of motion for individual species in a mixture, and the study of species and mixture energetics.

A summary of transport equations in differential and integral forms are presented and unified in Appendix A. All necessary relations from thermodynamics employed in the text are derived in Appendix B for a self-contained discourse.

Matlab programs performing numerical simulations of random walks that illustrate the nature of ordinary and fractional diffusion are listed in the text.

Errata and supplements