# Transport Phenomena: An Introduction to Advanced Topics Transport phenomena are dealing with all physical processes which cause the movement or transportation of mass, momentum and thermal energy heat. Transport properties of substances are different and they are characterized by the coefficient of viscosity for momentum , conductivity for thermal energy , and diffusivity for mass concentration. The physics of diffusion can be associated with either random molecular motions or combined effects such as molecular motion and turbulence etc.

Consider that a species for example O 2 in air with concentration C is distributed along x axis at time t. Writing the mass balance equation for this species gives: species I II I and II This is diffusion equation when the diffusivity is taken a constant. Its extension to 3D will be as follows:. The growth of the width of the dye is a diffusion-type process, which can be formulated as: Here, C is the concentration of the dye, D r is the radial diffusivity and r is radial position. Boundary condition 1: Symmetry boundary condition at the origin. Boundary condition 2: Zero concentration at infinity. The two examples given above showed that exact mathematical analytical solutions to governing equations of fluid mechanics may be too difficult.

Therefore, computational approach can be the practical method to solve equations in fluid mechanics such as the diffusion equation in complex geometries under various boundary conditions. Major steps in any CFD calculations: a Domain discretization: Create nodes and elements small control volumes in the domain of solution.

It is also called mesh generation which sometimes obeys complicated mathematical processes and calculations. It means that the governing equations which are partial differential equations PDE are written for the meshes elements produced from step a. Then we get a system of algebraic equations whose unknowns correspond to the nodes elements. Depending on the level of complexity of the problem, the software for programming and postprocesses can vary.

The package for mesh generation is usually given separately, for example, GAMBIT is one of the packages used for creating the geometry and discretizing it into various types of elements appropriate for the methods employed by the CFD packages. Anderson, J. Tannehill, R. Ferziger, M. Bird, W. Stewart, E. Average Speed The Maxwell-Boltzmann distribution is a function of the particle speed. The average speed follows from integration. Reuse and changes require a note indicating that content has been modified from the. Similar presentations. Upload Log in. My presentations Profile Feedback Log out.

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Log in. The subject of transport phenomena covers mainly three aspects: momentum transfer also known as fluid dynamics , heat transfer and mass transfer. In the field of chemical engineering, the fluid dynamics or momentum transfer occurs in industrial operations such as mixing, sedimentation, fluid flow and filtration. Heat transfer occurs in conduction and in convection transfer of heat during evaporation and drying, whereas mass transfer takes place in operations such as distillation, absorption, chemical reactions, liquid—liquid extraction, crystallization and adsorption.

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Generally a question is asked, why do we need to study these three phenomena together? There are reasons for it. Let us take a simple process where the raw materials are transported from the storage vessel to the reactor. So, the fluid flow phenomenon comes into the picture. Then, if the reaction in the reactor takes place at high temperatures generally that happens , then the raw materials have to be heated.

After the reaction, the separation processes take place with a view to isolating the product in pure form. The mass transfer operations such as distillation, absorption or crystallization may also take place. In other words, all these three transport phenomena take place.

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So, the subject of transport phenomena should be studied together on account of the following reasons: 1. The mechanisms of these three transport phenomena are closely related. Also, the governing mathematical equations are similar in nature. By analogies, we can understand one transport phenomenon from another.

For example, we can understand mass transfer or heat transfer from momentum transfer. There are many books and literature available which cover these three topics separately. But there are only a few books on the market which cover all the topics together. The subject has grown rapidly in the recent past. It is not possible to cover all the aspects of the subject in one book of this size.

So, this book covers only the introductory part to the subject. Moreover, in many universities and engineering colleges including Indian Institutes of Technology, this subject is taught at two levels, i. This book caters to the needs of the introductory level. An attempt has been made in this book to explain the phenomena of momentum transfer, heat transfer and mass transfer by flux expressions. Another approach adopted is to write shell balances for these transfer processes. The partial differential equations so obtained are solved using the boundary conditions.

The one-dimensional equations evolved are taken up in all the examples. The expressions for the conservation of momentum, heat and mass are also developed. Since it is an introductory book, care has been taken to use simple mathematical expressions and also to provide complete solutions of the problems. Students are expected to have a good knowledge of 9. Since there are many similarities in molecular transport of momentum, heat or mass, analogies among these three transport processes are also demonstrated to understand them better. This book is an outgrowth of my interactions with the students during class work and tutorials.

Simple illustrations and mathematical tools have been adopted to explain the transport phenomena in order to fulfil the needs of the students. The mechanism of momentum transfer is explained.

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## Transport Phenomena : Larry A. Glasgow :

The shell momentum balance for momentum transfer is also covered. Chapter 2 deals with the typical cases for shell momentum balance in order to obtain the velocity distribution and momentum flux for laminar flow conditions. The general equation of continuity and the equation of motion are explained in Chapter 3.

Momentum transfer in turbulent flow conditions is explained in Chapter 4. The various models like the Prandtl mixing length are also covered in this chapter. The unsteady-state flow of Newtonian fluids is explained in Chapter 5. In this chapter, convective energy transport and shell energy balances are also discussed.

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Specific problems of heat conduction in solids are highlighted in Chapter 7. These problems are solved by taking shell energy balances. The general energy equation is developed in Chapter 8. The temperature distribution in turbulent flow conditions is dealt with in Chapter 9. The unsteady-state case of heat transfer in conduction is discussed in Chapter In this chapter, convective mass transfer and shell mass balances are also covered.

Simple problems for mass transfer are discussed in Chapter 12 by taking shell mass balances for laminar flow conditions. The general equation of diffusion is explained in Chapter Mass transfer in turbulent flow condition is discussed in Chapter A specific case of diffusion for the unsteady- state condition is explained in Chapter Section D: Analogies among Momentum, Heat and Mass Transfer Chapters 16 The mechanism and governing equations for momentum, heat and mass transfer are discussed in Chapter This introductory book on transport phenomena will go a long way to cater to the needs of the students.

Constructive suggestions from readers, teachers, students and well wishers to improve this first edition of the book will be gratefully acknowledged. In gases, the molecules have more free space between them compared to the molecules in liquids. In solids, the molecules are arranged in a packed fashion.

The behaviour or the movement of the matter can be studied at the molecular level, i. The scientist studies the properties of matter at the molecular level, whereas in engineering applications we are concerned with the study of the bulk or macroscopic behaviour of solids, liquids and gases rather than their molecular behaviour. While studying engineering applications, we generally ask two questions.

## The Basics of Transport Phenomena

One, how does a particular phenomenon take place? Second, why does it take place? The same is the case when we deal with momentum transfer. When the molecule of a fluid moves, it carries some momentum with it as the mass of the molecule moves with a certain velocity in a particular direction.

Why does the molecule move? It moves because of velocity gradient in the system.

## Transport phenomena

Thus, molecules move because of velocity gradient. The heat and mass transfers will be discussed in detail in subsequent chapters. Momentum, heat and mass transfer phenomena take place by two means: Molecular transfer 2. Convective transfer Now, let us discuss these two mechanisms in detail. As shown in Figure 1. Let us also assume that there is a water pond in the vicinity. Transport Phenomena: An Introduction to Advanced Topics Transport Phenomena: An Introduction to Advanced Topics Transport Phenomena: An Introduction to Advanced Topics Transport Phenomena: An Introduction to Advanced Topics Transport Phenomena: An Introduction to Advanced Topics Transport Phenomena: An Introduction to Advanced Topics Transport Phenomena: An Introduction to Advanced Topics Transport Phenomena: An Introduction to Advanced Topics

## Related Transport Phenomena: An Introduction to Advanced Topics

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