Transport Phenomena.pdf

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§0.4 Concluding Comments 7 The conservation laws as applied to collisions of monatomic molecules can be obtained from the results above as follows: Eqs. 0.3-1, 0.3-2, and 0.3-4 are directly applicable; Eq. 0.3-6 is applicable if the internal energy contributions are omitted; and Eq. 0.3-8 may be used if the internal angular momentum terms are discarded. Much of this book will be concerned with setting up the conservation laws at the microscopic and macroscopic levels and applying them to problems of interest in engineering and science. The above discussion should provide a good background for this adventure. For a glimpse of the conservation laws for species mass, momentum, and energy at the microscopic and macroscopic levels, see Tables 19.2-1 and 23.5-1. §0o4 CONCLUDING COMMENTS To use the macroscopic balances intelligently, it is necessary to use information about interphase transport that comes from the equations of change. To use the equations of change, we need the transport properties, which are described by various molecular theories. Therefore, from a teaching point of view, it seems best to start at the molecular level and work upward toward the larger systems. All the discussions of theory are accompanied by examples to illustrate how the theory is applied to problem solving. Then at the end of each chapter there are problems to provide extra experience in using the ideas given in the chapter. The problems are grouped into four classes: Class A: Numerical problems, which are designed to highlight important equations in the text and to give a feeling for the orders of magnitude. Class B: Analytical problems that require doing elementary derivations using ideas mainly from the chapter. Class C: More advanced analytical problems that may bring ideas from other chapters or from other books. Class D: Problems in which intermediate mathematical skills are required. Many of the problems and illustrative examples are rather elementary in that they involve oversimplified systems or very idealized models. It is, however, necessary to start with these elementary problems in order to understand how the theory works and to develop confidence in using it. In addition, some of these elementary examples can be very useful in making order-of-magnitude estimates in complex problems. Here are a few suggestions for studying the subject of transport phenomena: • Always read the text with pencil and paper in hand; work through the details of the mathematical developments and supply any missing steps. • Whenever necessary, go back to the mathematics textbooks to brush up on calculus, differential equations, vectors, etc. This is an excellent time to review the mathematics that was learned earlier (but possibly not as carefully as it should have been). • Make it a point to give a physical interpretation of key results; that is, get in the habit of relating the physical ideas to the equations. • Always ask whether the results seem reasonable. If the results do not agree with intuition, it is important to find out which is incorrect. • Make it a habit to check the dimensions of all results. This is one very good way of locating errors in derivations. We hope that the reader will share our enthusiasm for the subject of transport phenomena. It will take some effort to learn the material, but the rewards will be worth the time and energy required.
8 Chapter 0 The Subject of <strong>Transport</strong> <strong>Phenomena</strong> QUESTIONS FOR DISCUSSION 1. What are the definitions of momentum, angular momentum, and kinetic energy for a single particle What are the dimensions of these quantities 2. What are the dimensions of velocity, angular velocity, pressure, density, force, work, and torque What are some common units used for these quantities 3. Verify that it is possible to go from Eq. 0.3-3 to Eq. 0.3-4. 4. Go through all the details needed to get Eq. 0.3-6 from Eq. 0.3-5. 5. Suppose that the origin of coordinates is shifted to a new position. What effect would that have on Eq. 0.3-7 Is the equation changed 6. Compare and contrast angular velocity and angular momentum. 7. What is meant by internal energy Potential energy 8. Is the law of conservation of mass always valid What are the limitations
Page 1 and 2: Phenomena Second Edition ,cro о Ma
Page 4 and 5: Transport Phenomena Second Edition
Page 6 and 7: Preface While momentum, heat, and m
Page 8 and 9: Contents Preface Chapter 0 The Subj
Page 10 and 11: Contents vii Ex. 8.3-3 Tangential A
Page 12 and 13: Contents ix Ex. 15.5-1 Heating of a
Page 14 and 15: Contents xi §22.7° Effects of Int
Page 16 and 17: Chapter 0 The Subject of Transport
Page 18 and 19: §0.2 Three Levels At Which Transpo
Page 20 and 21: §0.3 The Conservation Laws: An Exa
Page 24: Part One Momentum Transport
Page 27 and 28: 12 Chapter 1 Viscosity and the Mech
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58 Chapter 2 Shell Momentum Balance
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Chapter 4 Velocity Distributions wi
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178 Chapter 6 Interphase Transport
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1 182 Chapter 6 Interphase Transpor
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198 Chapter 7 Macroscopic Balances
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•< 224 Chapter 7 Macroscopic Bala
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232 Chapter 8 Polymeric Liquids onl
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234 Chapter 8 Polymeric Liquids is,
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236 Chapter 8 Polymeric Liquids Fig
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238 Chapter 8 Polymeric Liquids Upp
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240 Chapter 8 Polymeric Liquids о
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242 Chapter 8 Polymeric Liquids Tab
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244 Chapter 8 Polymeric Liquids EXA
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246 Chapter 8 Polymeric Liquids Thi
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248 Chapter 8 Polymeric Liquids EXA
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250 Chapter 8 Polymeric Liquids bet
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252 Chapter 8 Polymeric Liquids (b)
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254 Chapter 8 Polymeric Liquids Fig
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256 Chapter 8 Polymeric Liquids 10,
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258 Chapter 8 Polymeric Liquids QUE
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260 Chapter 8 Polymeric Liquids The
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262 Chapter 8 Polymeric Liquids 8C.
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Thermal Conductivity and the Mechan
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§9.1 Fourier's Law of Heat Conduct
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§9.1 Fourier's Law of Heat Conduct
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Table 9.1-4 Thermal Conductivities,
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§9.2 Temperature and Pressure Depe
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§9.3 Theory of Thermal Conductivit
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§9.3 Theory of Thermal Conductivit
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§9.4 THEORY OF THERMAL CONDUCTIVIT
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§9.6 Effective Thermal Conductivit
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§9.7 Convective Transport of Energ
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§9.8 Work Associated with Molecula
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Problems 287 9A.1 Prediction of the
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Problems 289 mated as oblate sphero
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§10.1 Shell Energy Balances; Bound
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§10.2 Heat Conduction with an Elec
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§10.2 Heat Conduction with an Elec
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§10.3 Heat Conduction with a Nucle
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§10.4 Heat Conduction with a Visco
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§10.5 Heat Conduction with a Chemi
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§10.6 Heat Conduction Through Comp
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§10.6 Heat Conduction Through Comp
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§10.7 Heat Conduction in a Cooling
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§10.7 Heat Conduction in a Cooling
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§10.8 Forced Convection 311 Forced
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§10.8 Forced Convection 313 term c
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§10.8 Forced Convection 315 Unifor
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§10.9 Free Convection 317 fluid in
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Questions for Discussion 319 The ve
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Problems 321 1 3 = V "T 2 = 61 °F
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Problems 323 Fig. 10B.4. Temperatur
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Problems 325 - T a ) Answer: P =
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Problems 327 the temperatures at th
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Problems 329 Zone II in which heat
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Problems 331 (a) Show that the diff
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Nonisothermal Systems §11.1 The en
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§11.1 The Energy Equation 335 disi
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§11.2 Special Forms of the Energy
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§11.4 Use of the Equations of Chan
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Cont. — |p=-(V-pv) 3.1-4 For p =
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§11Л Use of the Equations of Chan
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§11.5 Dimensional Analysis of the
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Problems 361 In principle, we may s
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Problems 363 for methane are: a = 2
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Problems 365 11B.6. Transpiration c
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Problems 367 examined. The wax drop
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Problems 369 (b) Choose appropriate
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Problems 371 (a) For the "true" sys
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Problems 373 The first term on the
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§12.1 Unsteady Heat Conduction in
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§12.2 Steady Heat Conduction in La
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§12.2 Steady Heat Conduction in La
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§12.3 Steady Potential Flow of Hea
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§12.4 Boundary Layer Theory for No
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Problems 395 PROBLEMS 12A.1. Unstea
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Problems 397 (d) Then solve the equ
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Problems 399 Fluid approaches with
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Problems 401 in which a 0 = k o /pC
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Problems 403 themselves at a reason
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Problems 405 (d) Obtain the lowest
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§13.1 Time-smoothed equations of c
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§13.2 The Time-Smoothed Temperatur
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§13.4 Temperature Distribution for
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§13.4 Temperature Distribution for
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§13.5 TEMPERATURE DISTRIBUTION FOR
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§13.6 Fourier Analysis of Energy T
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§13.6 Fourier Analysis of Energy T
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Sh ReSc 1/3 Vf/2 Problems 421 = 0.0
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§14.1 Definitions of Heat Transfer
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§14.2 Analytical Calculations of H
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Table 14.2-2 Asymptotic Results for
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§143 HEAT TRANSFER COEFFICIENTS FO
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§14.3 Heat Transfer Coefficients f
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