Über die Autorin bzw. den Autor

Richard G. Griskey, PhD, PE, is Institute Professor Emeritus at the Stevens Institute of Technology in Hoboken, New Jersey.

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The subject of transport phenomena has long been thoroughly and expertly addressed on the graduate and theoretical levels. Now, Transport Phenomena and Unit Operations: A Combined Approach endeavors not only to introduce the fundamentals of the discipline to a broader, undergraduate-level audience but also to apply itself to the concerns of practicing engineers as they design, analyze, and construct industrial equipment.

Richard Griskey's innovative text combines the often separated but intimately related disciplines of transport phenomena and unit operations into one cohesive treatment. While the latter was an academic precursor to the former, undergraduate students are often exposed to one at the expense of the other. Transport Phenomena and Unit Operations bridges the gap between theory and practice, with a focus on advancing the concept of the engineer as practitioner. Chapters in this comprehensive volume include:

• Transport Processes and Coefficients
• Frictional Flow in Conduits
• Free and Forced Convective Heat Transfer
• Heat Exchangers
• Mass Transfer; Molecular Diffusion
• Equilibrium Staged Operations
• Mechanical Separations

Each chapter contains a set of comprehensive problem sets with real-world quantitative data, affording students the opportunity to test their knowledge in practical situations. Transport Phenomena and Unit Operations is an ideal text for undergraduate engineering students as well as for engineering professionals.

Aus dem Klappentext

The subject of transport phenomena has long been thoroughly and expertly addressed on the graduate and theoretical levels. Now, Transport Phenomena and Unit Operations: A Combined Approach endeavors not only to introduce the fundamentals of the discipline to a broader, undergraduate-level audience but also to apply itself to the concerns of practicing engineers as they design, analyze, and construct industrial equipment.

Richard Griskey's innovative text combines the often separated but intimately related disciplines of transport phenomena and unit operations into one cohesive treatment. While the latter was an academic precursor to the former, undergraduate students are often exposed to one at the expense of the other. Transport Phenomena and Unit Operations bridges the gap between theory and practice, with a focus on advancing the concept of the engineer as practitioner. Chapters in this comprehensive volume include:

• Transport Processes and Coefficients
• Frictional Flow in Conduits
• Free and Forced Convective Heat Transfer
• Heat Exchangers
• Mass Transfer; Molecular Diffusion
• Equilibrium Staged Operations
• Mechanical Separations

Each chapter contains a set of comprehensive problem sets with real-world quantitative data, affording students the opportunity to test their knowledge in practical situations. Transport Phenomena and Unit Operations is an ideal text for undergraduate engineering students as well as for engineering professionals.

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Transport Phenomena and Unit Operations

Wiley-Interscience

Chapter One

INTRODUCTION

The profession of chemical engineering was created to fill a pressing need. In the latter part of the nineteenth century the rapidly increasing growth complexity and size of the world's chemical industries outstripped the abilities of chemists alone to meet their ever-increasing demands. It became apparent that an engineer working closely in concert with the chemist could be the key to the problem. This engineer was destined to be a chemical engineer.

From the earliest days of the profession, chemical engineering education has been characterized by an exceptionally strong grounding in both chemistry and chemical engineering. Over the years the approach to the latter has gradually evolved; at first, the chemical engineering program was built around the concept of studying individual processes (i.e., manufacture of sulfuric acid, soap, caustic, etc.). This approach, unit processes, was a good starting point and helped to get chemical engineering off to a running start.

After some time it became apparent to chemical engineering educators that the unit processes had many operations in common (heat transfer, distillation, filtration, etc). This led to the concept of thoroughly grounding the chemical engineer in these specific operations and the introduction of the unit operations approach. Once again, this innovation served the profession well, giving its practitioners the understanding to cope with the ever-increasing complexities of the chemical and petroleum process industries.

As the educational process matured, gaining sophistication and insight, it became evident that the unit operations in themselves were mainly composed of a smaller subset of transport processes (momentum, energy, and mass transfer). This realization generated the transport phenomena approach-an approach that owes much to the classic chemical engineering text of Bird, Stewart, and Lightfoot.

There is no doubt that modern chemical engineering in indebted to the transport phenomena approach. However, at the same time there is still much that is important and useful in the unit operations approach. Finally, there is another totally different need that confronts chemical engineering education-namely, the need for today's undergraduates to have the ability to translate their formal education to engineering practice.

This text is designed to build on all of the foregoing. Its purpose is to thoroughly ground the student in basic principles (the transport processes); then to move from theoretical to semiempirical and empirical approaches (carefully and clearly indicating the rationale for these approaches); next, to synthesize an orderly approach to certain of the unit operations; and, finally, to move in the important direction of engineering practice by dealing with the analysis and design of equipment and processes.

THE PHENOMENOLOGICAL APPROACH; FLUXES, DRIVING FORCES, SYSTEMS COEFFICIENTS

In nature, the trained observer perceives that changes occur in response to imbalances or driving forces. For example, heat (energy in motion) flows from one point to another under the influence of a temperature difference. This, of course, is one of the basics of the engineering science of thermodynamics.

Likewise, we see other examples in such diverse cases as the flow of (respectively) mass, momentum, electrons, and neutrons.

Hence, simplistically we can say that a flux (see Figure 1-1) occurs when there is a driving force. Furthermore, the flux is related to a gradient by some characteristic of the system itself-the system or transport coefficient.

(1-1) Flux = Flow quantity/(Time)(Area) = (Transport coefficient)(Gradient)

The gradient for the case of temperature for one-dimensional (or directional) flow of heat is expressed as

(1-2) Temperature gradient = dT/dY

The flux equations can be derived by considering simple one-dimensional models. Consider, for example, the case of energy or heat transfer in a slab (originally at a constant temperature, [T.sub.1]) shown in Figure 1-2. Here, one of the opposite faces of the slab suddenly has its temperature increased to [T.sub.2]. The result is that heat flows from the higher to the lower temperature region. Over a period of time the temperature profile in the solid slab will change until the linear (steady-state) profile is reached (see Figure 1-2). At this point the rate of heat flow Q per unit area A will be a function of the system's transport coefficient (k, thermal conductivity) and the driving force (temperature difference) divided by distance. Hence

(1-3) Q/A = k ([T.sub.1] - [T.sub.2]) (X - O) (1-3)

If the above equation is put into differential form, the result is

(1-4) [q.sub.x] = -k dT/dx

This result applies to gases and liquids as well as solids. It is the one-dimensional form of Fourier's Law which also has y and z components

(1-5) [q.sub.Y] = -k dT/dy

(1-6) [q.sub.z] = -k dT/dz

Thus heat flux is a vector. Units of the heat flux (depending on the system chosen) are BTU/hr [ft.sup.2], calories/sec [cm.sup.2], and W/[m.sup.2].

Let us consider another situation: a liquid at rest between two plates (Figure 1-3). At a given time the bottom plate moves with a velocity V. This causes the fluid in its vicinity to also move. After a period of time with unsteady flow we attain a linear velocity profile that is associated with steady-state flow. At steady state a constant force F is needed. In this situation

(1-7) F/A = -5 O - V/Y - O

where 5 is the fluid's viscosity (i.e., transport coefficient).

Hence the F/A term is the flux of momentum (because force = d(momentum)/dt. If we use the differential form (converting F/A to a shear stress [tau]), then we obtain

(1-8) [[tau].sub.yx] = -5 d[V.sub.X]/dy

Units of [[tau].sub.yx] are poundals/[ft.sup.2], dynes/[cm.sup.2], and Newtons/[m.sup.2].

This expression is known as Newton's Law of Viscosity. Note that the shear stress is subscripted with two letters. The reason for this is that momentum transfer is not a vector (three components) but rather a tensor (nine components).

As such, momentum transport, except for special cases, differs considerably from heat transfer.

Finally, for the case of mass transfer because of concentration differences we cite Fick's First Law for a binary system:

(1-9) [J.sub.A.sub.y] = -[D.sub.AB] dCA/dy

where [J.sub.A.sub.y] is the molar flux of component A in the y direction. [D.sub.AB], the diffusivity of A in B (the other component), is the applicable transport coefficient.

As with Fourier's Law, Fick's First Law has three components and is a vector. Because of this there are many analogies between heat and mass transfer as we will see later in the text. Units of the molar flux are lb moles/hr [ft.sup.2], g mole/sec [cm.sup.2], and kg mole/sec [m.sup.2].

THE TRANSPORT COEFFICIENTS

We have seen that the transport processes (momentum, heat, and mass)...