Transport Processes Primer

# Transport Processes Primer

#### C. Pozrikidis

Forthcoming in 2019

Transport phenomena or transport processes 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.

One concern 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. However, 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
1. Write an expression for a property of interest attributed to a material pacel, such as mass, momentum, internal energy, or species concentration.
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 integrated flux over the parcel surface.
3. Introduce a physical law for the rate of the 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 at a particular instant a control volume, to obtain an integral balance.
5. 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 and notions 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 of fluids 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.

Noteworthy 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 are assumed.