The Newman Lectures on Transport Phenomena

John Newman, Vincent Battaglia

• Publisher: Jenny Stanford Publishing
• Year: 2020
• ISBN:
  9781351609623
• Edition: 1
• Topic: Biological Sciences
• Subtopic: Biotechnology
• Index: Biological Sciences

Prof. Newmanis considered one of the great chemical engineers of his time. His reputation derives from his mastery of all phases of the subject matter, his clarity of thought, and his ability to reduce complex problems to their essential core elements. He is a member of the National Academy of Engineering, Washington, DC, USA, and has won numerous national awards including every award offered by the Electrochemical Society, USA. His motto, as known by his colleagues, is "do it right the first time." He has been teaching undergraduate and graduate core subject courses at the University of California, Berkeley (UC Berkeley), USA, since joining the faculty in 1966. His method is to write out, in long form, everything he expects to convey to his class on a subject on any given day. He has maintained and updated his lecture notes from notepad to computer throughout his career. This book is an exact reproduction of those notes.

This book demonstrates how to solve the classic problems of fluid mechanics, starting with the Navier–Stokes equation. It explains when it is appropriate to simplify a problem by neglecting certain terms through proper dimensional analysis. It covers concepts such as microscopic interpretation of fluxes, multicomponent diffusion, entropy production, nonnewtonian fluids, natural convection, turbulent flow, and hydrodynamic stability. It amply arms any serious problem solver with the tools to address any problem.

SECTION B:
LAMINAR FLOW SOLUTIONS

Chapter 13

Introduction

In Chapters 13 through 30, we shall study laminar flow solutions for problems arising in fluid mechanics and mass transfer. The preceding chapters provide a complicated set of nonlinear partial differential equations, which presumably describe such processes but which are quite difficult to solve. Simplifying assumptions are usually necessary.

In these notes, we shall, for the most part, assume that all fluid properties are constant. Thus, for an incompressible Newtonian fluid, the stress relation 2.3 may be written as

(13.1)

and the equations of continuity 2.1 and motion 2.2 become

(13.2)

(13.3)

(Note that ∇ · (∇v)* = 0 for an incompressible fluid.)

Furthermore, for an incompressible fluid with no free surfaces, it is frequently convenient to combine the pressure term and the gravitational term_

(13.4)

This is permissible (for an incompressible fluid) as long as g can be expressed as -∇Φ), the gradient of a gravitational potential. Then the equation of motion becomes

(13.5)

For a fluid of constant viscosity and density, variations of pressure are only of dynamical significance, serving to accelerate or decelerate the fluid but not to cause the fluid properties to vary. The hydrostatic pressure gradient ρg does not contribute significantly to the accelerating force, and Eq. 13.4 can be regarded as subtracting the hydrostatic pressure from the total or thermodynamic pressure p to leave the “dynamic pressure” P.

For over a century, fluid mechanists have diligently sought solutions to Eqs. 13.2 and 13.3 or Eqs. 13.2 and 13.5.

We shall frequently assume that mass transfer processes are described by the equation of convective diffusion:

(13.6)

Here c_i represents the concentration of the diffusing species and D is a diffusion coefficient, assumed to be constant. This equation can describe diffusion in a binary mixture under certain conditions. If we substitute Eq. 6.5 into Eq. 6.3 and assume that ρ and D_AB are constants and that there are no reactions in the bulk of the solution (r_A= 0), then we obtain

Division by the molar mass gives

which is the same as Eq. 13.6. Under certain conditions, Eq. 13.6 can describe transport in multicomponent systems (see Problem 8.4).

For heat transfer in a pure fluid of constant density and thermal conductivity, Eqs. 4.3 and 4.4 yield

If Ĉ_v can be taken to be constant and if viscous dissipation can be neglected, this equation is of the same form as the equation of convective diffusion 13.6, and the thermal diffusivity is k/ρĈ_v.^† Consequently, we shall not treat heat-transfer problems separately from mass-transfer problems. The presence of an interfacial velocity ...

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Table of Contents
• Introduction
• Section A: Basic Transport Relations
• Section B: Laminar Flow Solutions
• Section C: Transport in Turbulent Flow
• Appendix A: Vectors and Tensors
• Appendix B: Similarity Transformations
• Index