(295a) The Fundamental Concepts of Transport and Reaction

       A secure knowledge of the elementary but fundamental concepts of chemical engineering, both valid and invalid, that evolved in the course of somewhat over a century, should be in the mental library of all graduating students and practicing engineers. The allowable word count for this abstract permits only for a few illustrative examples in a representative set of topics in a single context. Fluid mechanics, heat transfer, and chemical conversions in steady flow through a round tube are my choices in that respect. A more complete list of concepts will be included in the extended abstract for the CDROM for the meeting, and an expanded set of topics and venues is planned for an eventual publication.

            Elementary concepts are here defined as those that are so concise that they can be memorized without drill. The identification and exposure of concepts that were once accepted as valid but that are now known to be false or inferior is as important as a list of the legitimate survivors, so examples of the false ones are also listed and examined. Two characteristics of chemical engineering that contribute to its vitality are its breadth in the sense of fluids, and its reliance on universalities. However, these very characteristics encourage the application of concepts beyond their limits of validity. It is more difficult to persuade students and practicing engineers to discard false concepts than to accept new ones. Therefore book writers should be careful to avoid the introduction of false concepts, and teachers and industrial mentors should assume the responsibility of identifying those that have found their way into textbooks and into accepted practices, respectively, and also of pointing out the limitations and errors introduced by idealizations and approximations. The designation of concepts that originated with one our idols as false or out-dated is painful, but science and technology can progress only by doing so.

     I am incapable of identifying all false or over-extended concepts, and if I were, such a list and discussion would further exceed the limitations of this format. I hope that my illustrative listings inspire others to search out and identify those in their own domain of expertise. A single listing is utilized for both the true and false concepts because it is often difficult to draw a firm line between them.  

            As a very important disclaimer before examining specific examples, the elementary concepts listed here provide at best a skeletal structure. They are not a substitute for the full accounts to be found in textbooks and handbooks or in the minds of experienced practitioners.

Overall

            An Eulerian frame of reference. The use of one or more spatial coordinates rather than a temporal one could be said to be the defining concept of chemical engineering. Its adoption is a natural consequence of the discovery that heat transfer and chemical conversions are carried out most effectively and efficiently in steady flow through a round tube. Its ubiquity tends to overshadow its importance. Physicists and chemists, who live in a Lagrangian universe are helpless when faced with diffusion in a flowing system.

Fluid mechanics

            Fully developed flow. This concept was a necessary precursor for the derivation of Poiseuille's law for the pressure drop in a round tube or parallel-plate channel as well as for the various empirical expressions for turbulent flow in a round tube. Although a good approximation for a long tube and thereby very useful in a practical sense, it should not be forgotten that all real tubular flows encompass a regime of development. This concept implies invariant physical properties, including density.

            The parallel-plate channel. This is a hypothetical geometry and thereby an example of a "false" concept in a realistic sense. It can, however, be interpreted as an asymptote for a wide rectangular channel. Also, it shares some characteristics, such as a parabolic velocity distribution, with a round tube. This concept is over-used because of its simplicity, namely one-dimensionality and the absence of curvature.

            The friction factor. This quantity is not a "fudge  factor" but simply a convenient, defined combination of real (measurable) quantities. For example, an exact theoretical expression exists for the friction factor in fully developed laminar flow.

            Prandtl's law of the wall. Although this concept has a speculative origin, it appears to be exact in an asymptotic sense.

            Prandt's law of the center. Just as for its counterpart, this speculative concept  appears to be exact in an asymptotic sense.

            Millikan's law of the region of overlap. This concept, just as its counterparts (and components) appears to have validity in an asymptote sense.

            Time-averaging. Space-averaging by Reynolds, from which time-averaging evolved, is my choice as the greatest contribution of all time to the modeling of turbulent flow. The concept meets the standard of succinctness even though its detailed implementation does not.

            Direct numerical simulation. When this concept was first proposed and implemented it was expected to make all other modeling of turbulent flows obsolete but its promise remains unfulfilled because of unresolved computational limitations.

            The eddy viscosity. This concept of Boussinesq has recently been shown to be a valid one, whereas most subsequent models for transport by turbulence are not.

Heat and mass transfer

            The heat transfer coefficient. The recognition by Newton that the rate of convective heat transfer is proportional to the area and the difference in temperature led to the replacement of four variables with one and is thereby the cornerstone of all predictive and correlative equations for convection.

            Rayleigh's method of dimensional analysis. All prior and subsequent methodologies and interpretations are false or redundant. Students struggle to master this concept but their efforts are more than repaid by the understanding it confers.

            Correlation in terms of products of powers of dimensionless groups. Although initiated by no less than Nusselt himself in the very  investigation that defined the dimensionless group named in his honor, this my candidate for the most pernicious concept in the history of heat transfer.  

            Fully developed convection. This concept was elevated to viability by Seban and Shimazaki, who revealed its dependence on the thermal boundary condition.

            The turbulent Prandtl number. The representation of the turbulent shear stress and the turbulent heat flux density as fractions of the total shear stress and heat flux density, respectively, reveals  that this concept does not evoke empiricism.

            Analogies between heat and momentum transfer. Although the similarities of the partial differential equations of conservation are the source of this concept, every one of the classical implementations, and in particular the Colburn equation, is invalid functionally and highly inaccurate numerically.

            The analogy between heat and mass transfer. This concept has been proven to be false by Hanratty and his collaborators but it persists in many textbooks. 

            The effective thickness. The concept of representation of the rate of convection by an effective thickness for conduction, as devised by Langmuir in 1912 in the context of the estimating the heat loss from the filament of a light bulb, provides a first-order correction for the effect of curvature in relationships such as the Lévêque equation in which it is neglected.

Chemical conversions

Plug flow. This concept is the most pernicious one in all of chemical engineering. It occurs physically only when a semi-solid is pushed through a tube with a plunger. Plug flow is not approached as the Reynolds number increases – the velocity goes to zero at the wall, and the profile is more nearly parabolic than flat. The length of the reactor required for a specified conversion may be up to twice that so-predicted and the error in the concentration of secondary products such as pollutants may be unbounded. Perhaps most serious of all, it precludes the consideration of external heat exchange.

Perfect radial mixing. This concept produces the same solutions as plug flow but is physically conceivable as an asymptote for Pr_T → 0 and Sc_T→ 0 and thereby an upper bound for the conversion. The other shortcomings remain.

Fully developed flow with no radial mixing. The solutions produced by means of this  idealization constitute lower bounds for the conversion, and are thereby complementary to  those for perfect radial mixing.

Rate mechanisms in terms of concentrations. This concept, which all undergraduates in chemical engineering must recognize as incompatible with thermodynamic considerations, particularly for gases, is deeply imbedded in all the textbooks of reaction engineering, but that does not relieve the faculty of their responsibility to say so, or the journals to refuse to propagate its usage.

Global models for combustion. This important class of reactions has long been known to proceed only by means of free-radical mechanisms. Furthermore, most of the critical free-radical mechanisms have been identified and quantified. This concept should  be abandoned.

A pseudo stationary state for the concentrations of free radicals. This concept of J. A. Christiansen is one of the greatest in the history of chemistry in that it explained the previously puzzling observations of fractional and bilinear mechanisms. However, it is inapplicable for combustion because of the infrequency of the collisions between the molecules and free radicals.