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9780824719722

Momentum, Heat, and Mass Transfer Fundamentals

by ;
  • ISBN13:

    9780824719722

  • ISBN10:

    0824719727

  • Edition: 1st
  • Format: Hardcover
  • Copyright: 1999-02-23
  • Publisher: CRC Press

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Supplemental Materials

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Summary

"Presents the fundamentals of momentum, heat, and mass transfer from both a microscopic and a macroscopic perspective. Features a large number of idealized and real-world examples that we worked out in detail. "

Table of Contents

Preface v
Thumb Index vii
Essentials
1(72)
Models
1(11)
Figure 1.1-1 Modeling the weather
1(1)
Figure 1.1-2 A poor model of the weather
2(3)
Mathematical models and the real world
5(3)
Scale of the model
8(4)
The Entity Balance
12(5)
Example 1.2-1 An entity balance
14(1)
Conserved quantities
15(1)
Steady-state processes
16(1)
The Continuum Assumption
17(2)
Figure 1.3-1 Breakdown of continuum assumption
18(1)
Fluid Behavior
19(14)
Laminar and turbulent flow
19(1)
Figure 1.4.1-1 Injection of dye in pipe flow
20(1)
Newtonian fluids
21(1)
Figure 1.4.2-1 Shear between layers of fluid
21(3)
Figure 1.4.2-2 Momentum transfer between layers of fluid
24(1)
Figure 1.4.2-3 Sign convention for momentum flux between layers of fluid
24(1)
Figure 1.4.2-4 Sign convention for shear stress on surface layers of fluid
25(1)
Table 1.4.2-1 Summary of sign convention for stress/momentum flux tensor
26(1)
Figure 1.4.2-5 Migration of momentum by molecular motion
26(2)
Figure 1.4.2-6 Viscosity of common fluids
28(1)
Example 1.4.2-1 Flow of fluids between fixed parallel plates
28(1)
Complex fluids
29(1)
Figure 1.4.3-1 Complex fluids
30(1)
Figure 1.4.3-2 Mechanical analog of viscoelasticity
31(1)
Compressible vs. incompressible flows
32(1)
Averages
33(27)
General concept of average
33(1)
Example 1.5.1-1 Time-average vs distance-average speed
34(1)
Figure 1.5.1-1 Time-average speed for travel between two points
35(1)
Figure 1.5.1-2 Distance-average speed for travel between two points
36(1)
Velocity averages
37(1)
Area-averaged velocity
37(2)
Example 1.5.2-1 Area-averaged velocity for laminar pipe flow
39(1)
Figure 1.5.2-1 Velocity profile
39(2)
Time-averaged velocity
41(1)
Example 1.5.2-2 Time-averaged velocity for turbulent flow
42(1)
Example 1.5.2-3 Area-average of time-averaged velocity for turbulent pipe flow
42(2)
Temperature averages
44(2)
Example 1.5.3-1 Area-average temperature vs. bulk temperature
46(4)
Example 1.5.3-2 Bulk temperature for quadratic temperature profile, laminar pipe flow
50(2)
Concentration averages
52(2)
Example 1.5.4-1 Bulk concentration
54(3)
Arithmetic, logarithmic, and geometric means
57(2)
Example 1.5.5-1 Case examples of logarithmic mean
59(1)
Example 1.5.5-2 Approximation of logarithmic mean by arithmetic mean
59(1)
Scalars, Vectors, Tensors and Coordinate Systems
60(9)
The viscous stress tensor
60(1)
Components of the viscous stress tensor
61(1)
Figure 1.6.1-1 (a) Vectors associated by a particular viscous stress tensor with the direction of the rectangular Cartesian axes
62(1)
Figure 1.6.1-1 (b) Vector associated with the 3-direction decomposed into its components
63(1)
Types of derivatives
63(1)
Partial derivative
63(1)
Total derivative
64(1)
Substantial derivative, material derivative, derivative following the motion
64(1)
Example 1.6.2-1 Rate of change of pollen density
65(1)
Transport theorem
66(1)
Figure 1.6.3-1 Motion of continuum
67(2)
Chapter 1 Problems
69(4)
The Mass Balances
73(40)
The Macroscopic Mass Balances
73(23)
Figure 2.1-1 System for mass balances
73(1)
The macroscopic total mass balance
74(1)
Accumulation of mass
74(1)
Input and output of mass
75(2)
Simplified forms of the macroscopic total mass balance
77(1)
Example 2.1.1-1 Mass balance on a surge tank
78(1)
Figure 2.1.1-1 Surge tank
78(1)
Example 2.1.1-2 Volumetric flow rate of fluid in laminar flow in circular pipe
79(2)
Example 2.1.1-3 Air storage tank
81(1)
Example 2.1.1-4 Water manifold
82(4)
The macroscopic species mass balance
86(1)
Generation of mass of a species
87(1)
Accumulation of mass of a species
87(1)
Input and output of mass of a species
88(2)
Example 2.1.2-1 Macroscopic species mass balance with zero-order irreversible reaction
90(4)
Example 2.1.2-2 Macroscopic species mass balance with first-order irreversible reaction
94(1)
Figure 2.1.2-1 Perfectly mixed tank with reaction
94(2)
The Microscopic Mass Balances
96(9)
The microscopic total mass balance (continuity equation)
96(2)
Special cases of the continuity equation
98(1)
Continuity equation in different coordinate systems
99(1)
Table 2.2.1-1 Continuity equation (microscopic total mass balance) in rectangular, cylindrical, and spherical coordinate frames
99(1)
Example 2.2.1-1 Velocity components in two-dimensional steady incompressible flow, rectangular coordinates
99(2)
Example 2.2.1-2 Velocity components in two-dimensional steady incompressible flow, cylindrical coordinates
101(1)
Example 2.2.1-3 Compression of air
102(1)
Figure 2.2.1-1 Air compression by piston
102(1)
The microscopic species mass balance
103(2)
Diffusion
105(1)
Chapter 2 Problems
105(8)
The Energy Balances
113(56)
The Macroscopic Energy Balances
113(37)
Forms of energy
113(1)
The macroscopic total energy balance
114(1)
Rate of accumulation of energy
115(1)
Rates of input and output of energy
116(1)
Figure 3.1.2-1 Flow work
117(4)
Simplified forms of the macroscopic total energy balance
121(1)
The potential energy term
121(1)
Figure 3.1.2-2 Gravitational field of earth
122(3)
The kinetic energy term
125(2)
The enthalpy term
127(1)
Averages and the macroscopic energy equations
128(1)
Energy balance approximation-turbulent flow
128(1)
Energy balance approximation-laminar flow
129(1)
Steady-state cases of the macroscopic total energy balance
130(2)
Table 3.1.2-1 Qualitative comparison of ranges of enthalpy changes (kcal/mol) for processes involving organic compounds
132(1)
Example 3.1.2-1 Relative magnitudes of mechanical and thermal energy terms with phase change
132(1)
Figure 3.1.2-3 Mechanical energy and thermal energy terms compared for a boiler (I)
133(1)
Example 3.1.2-2 Steam production in a boiler
134(1)
Figure 3.1.2-4 Mechanical and thermal energy terms compared for a boiler (II)
134(2)
Example 3.1.2-3 Temperature rise from conversion of mechanical to thermal energy
136(1)
Figure 3.1.2-5 Water supply system
136(2)
Example 3.1.2-4 Heated tank, steady state in mass and unsteady state in energy
Figure 3.1.2-6 Heated tank
138(3)
The macroscopic mechanical energy balance
141(3)
Example 3.1.3-1 Mechanical energy and pole vaulting
144(3)
Example 3.1.3-2 Calculation of lost work in pipe
147(1)
Figure 3.1.3-1 Pipe system
147(2)
The macroscopic thermal energy balance
149(1)
The Microscopic Energy Balances
150(12)
The microscopic total energy balance
150(3)
Eulerian forms of the microscopic total energy balance
153(3)
Lagrangian forms of the microscopic total energy balance
156(1)
The microscopic mechanical energy balance
157(1)
The microscopic thermal energy balance
158(4)
Chapter 3 Problems
162(7)
The Momentum Balances
169(42)
The Macroscopic Momentum Balance
169(27)
Example 4.1-1 Momentum flux of fluid in laminar flow in circular pipe
173(1)
Types of forces
174(1)
Influence of uniform pressure over entire surface of irregular objects
175(1)
Figure 4.1.2-1 Approximation of solid by prisms
176(1)
Figure 4.1.2-2 Detail of prism
177(1)
Averages and the momentum equation
178(1)
Momentum balance approximation-turbulent flow
178(3)
Momentum balance approximation-laminar flow
181(1)
Example 4.1.3-1 Force on a nozzle
182(4)
Example 4.1.3-2 Thrust of aircraft engine
186(2)
Example 4.1.3-3 Piping support
188(4)
Example 4.1.3-4 Jet boat
192(2)
Example 4.1.3-5 Horizontal force on tank
194(2)
The Microscopic Momentum Balance
196(3)
Summary of Balance Equations and Constitutive Relationships
199(1)
Table 4.3-1 Tabulation of balance equations
199(1)
Table 4.3-2 Tabulation of common constitutive relationships
200(1)
The Momentum Equation in Non-Inertial Reference Frames
200(3)
Chapter 4 Problems
203(8)
Application of Dimensional Analysis
211(70)
Systems of Measurement
211(11)
Example 5.1-1 Weight vs. mass; g vs. gc
215(5)
Table 5.1-1a Systems of Units
220(1)
Table 5.1-1b Systems of Units
221(1)
Table 5.1-2 SI Prefixes
221(1)
Buckingham's Theorem
222(12)
Example 5.2-1 Dimensionless variables for pipe flow
223(4)
Friction factors and drag coefficients
227(2)
Shape factors
229(1)
Example 5.2.2-1 Drag force on ship hull
230(2)
Example 5.2.2-2 Deceleration of compressible fluid
232(2)
Systematic Analysis of Variables
234(11)
Example 5.3-1 Drag force on a sphere
235(1)
Example 5.3-2 Dimensionless groups for flow over a flat plate
236(2)
Example 5.3-3 Consistency of dimensionless groups across system of dimensions
238(5)
Example 5.3-4 Capillary interface height via dimensional analysis
243(2)
Dimensionless groups and differential models
245(19)
Example 5.4-1 Pipe flow of incompressible fluid with constant viscosity
249(1)
Example 5.4-2 One-dimensional energy transport
250(2)
Example 5.4-3 Mass transport in a binary mixture
252(1)
Example 5.4-4 Extrapolating model results from one category of momentum, heat, or mass transport to another
253(7)
Table 5.4-1 Dimensionless variables
260(1)
Table 5.4-2 Dedimensionalized balance equations
261(1)
Table 5.4-3 Dimensionless numbers
262(2)
Similarity, Models and Scaling
264(8)
Example 5.5-1 Drag on immersed body
266(2)
Example 5.5-2 Scale effects
268(4)
Chapter 5 Problems
272(9)
Momentum Transfer In Fluids
281(236)
Fluid Statics
281(7)
Manometers
284(1)
Example 6.1.1-1 Pressure difference using a manometer
284(1)
Figure 6.1.1-1 Measurement of pressure difference with manometer
284(1)
Example 6.1.1-2 Pressure difference between tanks
285(1)
Figure 6.1.1-2 Pressure difference between tanks
285(1)
Example 6.1.1-3 Differential manometer
286(1)
Figure 6.1.1-3 Differential manometer
286(2)
Description of Flow Fields
288(7)
Figure 6.2-1 Paths between streamlines
291(1)
Irrotational flow
292(3)
Potential Flow
295(19)
Table 6.3-1 Elementary plane flows
302(2)
Table 6.3-2 Superposition of elementary plane flows
304(3)
Example 6.3-1 Flow around a circular cylinder
307(1)
Figure 6.3-1 Flow around circular cylinder
308(1)
Example 6.3-2 Flow of an ideal fluid through a corner
309(1)
Figure 6.3-2 Flow through a corner
310(1)
Example 6.3-3 Flow around a rotating cylinder
311(3)
Laminar Flow
314(24)
Laminar flow between infinite parallel plates
315(1)
Figure 6.4.1-1 Steady flow between infinite stationary parallel plates
315(3)
Example 6.4.1-1 Steady flow between infinite parallel plates
318(1)
Figure 6.4.1-2 Flow between infinite parallel plates, top plate moving at v0
319(2)
Figure 6.4.1-3 Velocity profiles for laminar flow of Newtonian fluid between parallel plates with imposed pressure drop, top plate moving at steady velocity
321(1)
Example 6.4.1-2 Flow between infinite rotating concentric cylinders
321(1)
Laminar flow in a circular pipe
322(1)
Figure 6.4.2-1 Control volume for force balance on fluid in pipe
322(3)
Figure 6.4.2-2 Velocity profile for laminar flow of a Newtonian fluid in a pipe or duct of circular cross-section
325(1)
Figure 6.4.2-3 Shear stress profile for laminar flow of a Newtonian fluid in a pipe or duct of circular cross-section
325(1)
Example 6.4.2-1 Flow in a capillary viscometer
326(1)
Example 6.4.2-2 Flow between two concentric cylinders
327(1)
Figure 6.4.2-4 Viscometric flow between cylinders
327(3)
Example 6.4.2-3 Film flow down a wall
330(1)
Figure 6.4.2-5 Film flow down wall
331(1)
Example 6.4.2-4 Flow adjacent to a flat plate instantaneously set in motion
332(1)
Figure 6.4.2-6 Flow adjacent to flat plate instantaneously set in motion
332(6)
Turbulent Flow
338(15)
Figure 6.5-1 Local velocity in turbulent flow as a function of time
339(2)
Figure 6.5-2 Laminar and time-smoothed turbulent (1/7 power model) velocity profiles in steady pipe flow
341(1)
Time averaging the equations of change
341(6)
Example 6.5-2 Time averaging of velocity product
347(1)
The mixing length model
347(1)
Figure 6.5.2-1 Mixing length model
348(3)
Figure 6.5.2-2 Universal velocity distribution
351(1)
Example 6.5.2-1 Size of sublayer and buffer zone in turbulent flow
351(2)
The Boundary Layer Model
353(18)
Figure 6.6-1 Boundary layer development on flat plate
353(1)
Example 6.6-1 Displacement thickness
354(2)
Momentum balance - integral equations
356(1)
Figure 6.6.1-1 Element in boundary layer
356(3)
Figure 6.6.1-2 Velocity profile development in the entrance region to a pipe
359(1)
De-dimensionalization of the boundary layer equations
360(2)
Exact solution of the momentum boundary layer equations via similarity variables
362(1)
Example 6.6.3-1 Similarity variable developed from dimensional analysis
362(4)
Figure 6.6.3-1 Solution to Blasius boundary layer equation
366(1)
Example 6.6.3-2 Runge-Kutta solution of Blasius problem
366(5)
Drag Coefficients
371(67)
Figure 6.7-1 Flow around an airfoil (a) without and (b) with separation
372(3)
Drag on immersed bodies (external flow)
375(1)
Figure 6.7.1-1 Drag coefficient for smooth flat plate oriented parallel to flow stream
375(3)
Example 6.7.1-1 Drag on a flat plate
378(1)
Figure 6.7.1-2 Flow past circular cylinder
379(1)
Figure 6.7.1-3 Drag coefficient for circular cylinder
380(1)
Example 6.7.1-2 Wind force on a distillation column
380(1)
Figure 6.7.1-4 Drag coefficient for sphere
381(1)
Example 6.7.1-3 Terminal velocity of a polymer sphere in water
382(3)
Drag in conduits - pipes (internal flow)
385(1)
Table 6.7.2-1 Properties of pipe
386(9)
Figure 6.7.2-1 Momentum balance on cylindrical fluid element in horizontal pipe
395(1)
Figure 6.7.2-2 Momentum balance on cylindrical fluid element in non-horizontal pipe
396(3)
Figure 6.7.2-3 Moody friction factor chart
399(1)
Figure 6.7.2-4 Relative roughness for clean new pipes
400(2)
Example 6.7.2-1 Expansion losses
402(1)
Figure 6.7.2-5 Equivalent lengths for losses in pipes
403(2)
Example 6.7.2-2 Direction of flow between tanks at differing pressures and heights
405(1)
Example 6.7.2-3 Firction loss in a piping system
406(2)
Friction factor calculations - serial paths
408(1)
Case 1: Pressure drop unknown
409(1)
Example 6.7.2-4 Pressure loss for flow between tanks
409(2)
Case 2: Diameter unknown
411(1)
Example 6.7.2-5 Transfer line from tank to column
411(3)
Example 6.7.2-6 Minimum pipe diameter
414(2)
Case 3: Length unknown
416(1)
Example 6.7.2-7 Air supply through hose
416(1)
Case 4: Flow rate unknown
417(1)
Example 6.7.2-8 Flow rate unknown
418(4)
Figure 6.7.2-6 Friction factor vs. Karman number
422(1)
Example 6.7.2-9 Calculation of flow rate via Karman number when pressure drop is known
423(1)
Non-circular conduits
424(1)
Example 6.7.2-10 Flow in a smooth annulus
425(1)
Example 6.7.2-11 Pressure drop in a pipe annulus
426(1)
Friction factor calculations - parallel paths
427(1)
Example 6.7.2-12 Pipe network with imposed pressure drop
427(4)
Table 6.7.2-2 Convergence of Newton's Method
431(2)
Example 6.7.2-13 Flow in a parallel piping system
433(2)
Example 6.7.2-14 Input of additional fluid to an existing pipe network
435(3)
Non-Newtonian Flow
438(6)
Bingham plastics
438(1)
Figure 6.8.1-1 Tube flow of Bingham plastic
439(1)
Power-law fluids
440(3)
Example 6.8-1 Flow of polymer melt
443(1)
Flow in Porous Media
444(41)
Darcy's law
445(3)
Figure 6.9.1-1 Permeability as a function of porosity for a bed of spheres
448(4)
Table 6.9.1-1 Porosities (void fractions) for dumped packings
452(1)
Table 6.9.1-2 Porosity and permeability for typical materials
453(1)
Example 6.9.1-1 Flow of water in sandstone
454(1)
Packed beds
455(3)
Example 6.9.2-1 Pressure drop for air flowing though bed of spheres
458(2)
Example 6.9.2-2 Pressure drop for water flowing though bed of cylinders
460(2)
Filters
462(3)
Example 6.9.3-1 Production scale filter performance prediction from pilot plant data
465(2)
Example 6.9.3-2 Filter performance from data
467(2)
Example 6.9.3-3 Adapting existing filter to new product
469(3)
Flow Measurement
472(1)
Pitot tube
472(1)
Figure 6.10.1-1 Pitot tube schematic
473(1)
Figure 6.10.1-2 Flow at mouth of pitot tube
473(1)
Example 6.10.1-1 Pitot tube traverse
474(4)
Venturi meter
478(1)
Figure 6.10.2-1 Venturi schematic
478(2)
Figure 6.10.2-2 Venturi meter coefficient
480(1)
Example 6.10.2-1 Flow measurement with venturi meter
480(1)
Orifice meter and flow nozzle
481(1)
Figure 6.10.3-1 Orifice meter, flow nozzle
482(1)
Figure 6.10.3-2 Orifice coefficient
483(1)
Example 6.10.3-1 Metering of crude oil with orifice
483(2)
Chapter 6 Problems
485(32)
Heat Transfer Models
517(326)
The Nature of Heat
517(155)
Forced convection heat transfer
520(5)
Free convection heat transfer
525(3)
Table 7.1.2-1 Dimensionless Forms: Mass, Energy, and Momentum Equations for Natural and Forced Convection
528(1)
Conduction Heat Transfer Models
528(1)
Three-dimensional conduction in isotropic media
529(1)
Table 7.2.1-1 Components of Fourier Equation in Various Coordinate Systems
530(2)
Boundary conditions at solid surfaces
532(1)
Thermal conductivity
533(1)
Table 7.2.3-1 Relative Values of Thermal Conductivity
533(3)
One-dimensional steady-state conduction in rectangular coordinates
536(1)
Analytical solution
537(1)
Figure 7.2.4-1 Homogeneous solid
537(2)
Figure 7.2.4-2 Temperature profile in 1-D heat transfer by conduction, rectangular coordinates
539(1)
Interface condition between solids - series conduction
539(1)
Figure 7.2.4-3 Conduction with two solids in contact assuming no temperature drop at interface
540(1)
Figure 7.2.4-4 Temperature profile with interfacial resistance
540(1)
Figure 7.2.4-5 Contact resistance treated as an intermediate solid
541(1)
Equivalent thermal resistance - series conduction
542(1)
Figure 7.2.4-6 Development of equivalent conductance for series conduction
542(2)
Equivalent thermal resistance - parallel conduction
544(1)
Figure 7.2.4-7 Development of equivalent conductance for parallel conduction
544(1)
Figure 7.2.4-8 Equivalent circuit for parallel conduction
545(1)
Example 7.2.4-1 Series conduction through layers - constant temperature at external surfaces
546(1)
Figure 7.2.4-9 Series conduction through layers with constant temperature at external surfaces
547(2)
Example 7.2.4-2 Series conduction through layers - constant convective heat transfer coefficient at external surfaces
549(1)
Figure 7.2.4-10 Series conduction through layers with constant convective heat transfer coefficient at external surfaces
550(2)
Example 7.2.4-3 Conduction with variable thermal conductivity
552(1)
Figure 7.2.4-11 Conduction through firebrick with variable thermal conductivity
553(2)
Figure 7.2.4-12 Temperature profile
555(1)
Example 7.2.4-4 One-dimensional steady-state conduction with parallel path
555(1)
Figure 7.2.4-13 Conduction with parallel paths
555(1)
Figure 7.2.4-14 Analogous circuit
556(2)
Numerical solution
558(1)
The finite element method
558(2)
Figure 7.2.4-14 Examples of 1-D and 2-D finite elements
560(2)
Figure 7.2.4-15 Interpolation functions, Shape function
562(1)
Example 7.2.4-5 Solution by finite elements of steady-state conduction with generation
563(1)
Figure 7.2.4-16 Bar with thermal energy source
564(5)
Table 7.2.4-1 Global node numbering scheme
569(3)
Figure 7.2.4-17 Comparison of finite element and analytic solution
572(1)
Finite element method in higher dimensions
573(1)
One-dimensional steady-state conduction in cylindrical coordinates
574(1)
Figure 7.2.5-1 Conduction through the wall of a composite cylinder
574(3)
Example 7.2.5-1 Conduction in a fuel rod
577(1)
Example 7.2.5-2 Conduction through an insulated pipe
578(3)
One-dimensional steady-state conduction in spherical coordinates
581(1)
Figure 7.2.6-1 Radial conduction in spherical geometry
582(1)
Example 7.2.6-1 Conduction through shielding
583(3)
Two-dimensional steady-state conduction
586(3)
Taylor series
589(2)
Analytical solution
591(7)
Orthogonal functions
598(5)
Example 7.2.7-2 Convergence of steady-state rectangular coordinate solution
603(2)
Numerical solution
605(1)
Finite difference method
605(2)
Forward difference approximation to the first derivative
607(1)
Backward difference approximation to the first derivative
607(1)
Central difference approximation to the first derivative
608(1)
Approximation of second derivative
609(1)
Finite difference approximation to the Laplace equation
609(3)
Example 7.2.7-1 Determination of steady-state temperature distribution in a rectangular slab
612(2)
Irregular boundaries, Dirichlet boundary conditions
614(4)
Normal derivative (Neumann) boundary condition at nodal point
618(1)
Generation terms
619(2)
Example 7.2.7-2 Finite difference solution of 2-D steady-state conduction
621(8)
One-dimensional unsteady-state conduction
629(1)
Analytical methods for one-dimensional unsteady-state conduction
630(1)
Semi-infinite slab
630(1)
Figure 7.2.8-1 Semi-infinite slab with constant face temperature
630(5)
Example 7.2.8-1 Semi-infinite slab: conduction in a brick wall
635(3)
Finite slab
638(1)
Figure 7.2.8-2 Finite slab with constant face temperatures
638(8)
Figure 7.2.8-3 Unsteady-state heat transfer in a finite slab with uniform initial temperature and constant, equal surface temperatures
646(1)
Example 7.2.8-2 Finite slab model vs. semi-infinite slab model for one-dimensional unsteady-state conductive heat transfer
646(5)
Infinite cylinder and sphere
651(1)
Figure 7.2.8-4 Unsteady-state heat transfer in an infinite cylinder with uniform initial temperature and constant surface temperature
652(1)
Figure 7.2.8-5 Unsteady-state heat transfer in a sphere with uniform initial temperature and constant surface temperature
653(1)
Numerical Methods for One-Dimensional Unsteady-State Conduction
653(1)
Finite difference method
654(1)
Finite difference explicit form
654(1)
Figure 7.2.8-6 Finite difference grid for 1D unsteady-state conduction
654(2)
Example 7.2.8-3 Unsteady-state heat transfer by explicit finite differences
656(2)
Finite difference implicit form
658(4)
Example 7.2.8-4 Finite slab unsteady-state heat transfer by finite differences
662(5)
Multi-dimensional unsteady-state conduction
667(1)
Analytical solution for regular geometries
667(1)
Figure 7.2.9-1 Multidimensional unsteady-state temperature profiles for conduction in regular geometries expressed as product of one-dimensional solutions
668(1)
Numerical solution of two-dimensional unsteady-state conduction
669(1)
Finite difference method
669(1)
Figure 7.2.9-2 Alternating direction implicit method
670(1)
Finite element method
671(1)
Convection Heat Transfer Models
672(47)
The thermal boundary layer
673(2)
Figure 7.3.1-1 Solution of Equation (7.3.1-1)
675(1)
Heat transfer coefficients
675(1)
Single-phase heat transfer coefficients
676(5)
Figure 7.3.2-1 Single-phase heat transfer coefficients
681(1)
Correlations for prediction of heat transfer
681(9)
Average heat transfer coefficients
690(2)
Example 7.3.2-1 Average heat transfer coefficients for pipe flow
692(2)
Design equations for convective heat transfer
694(2)
Forced convection in laminar flow
696(3)
Table 7.3.2-1 Nusselt number limit for laminar flow in ducts with various cross-sections
699(1)
Forced convection in turbulent flow
700(2)
Example 7.3.2-2 Comparison of the Dittus-Boelter, Colburn, and Sieder-Tate equations
702(6)
Heat transfer in non-circular conduits and annular flow
708(1)
External flows, natural and forced convection
708(1)
Table 7.3.2-2 Values of b and n for Equation (7.3.2-104)
709(1)
Table 7.3.2-3 Values of a and m for use with Equation (7.3.2-105)
709(1)
Example 7.3.2-3 Heat transfer with flow normal to pipes
710(3)
Heat transfer with phase change
713(1)
Boiling - mechanism
713(2)
Figure 7.3.2-2 Boiling Curve
715(1)
Condensation - mechanism
716(1)
Boiling coefficients
716(2)
Table 7.3.2-3 Values of C for nucleate boiling model
718(1)
Condensing coefficients
718(1)
Conduction and Convection in Series
719(22)
Lumped capacitance models
721(5)
Figure 7.4.1-1 RC circuit analog of unsteady-state lumped-capacitance heat transfer
726(1)
Criteria for use of lumped capacitance models
726(1)
Figure 7.4.1-2 Steady-state conduction through solid with convection at interface
727(2)
Figure 7.4.1-3 Steady-state conduction through solid with convection at interface, small vs. large Biot number
729(1)
Figure 7.4.1-4 Unsteady-state conduction through solid with convection at interface, small vs. large Biot number
730(1)
Example 7.4.1-1 Lumped capacitance models
731(1)
Distributed capacitance models
732(2)
Figure 7.4.2-1 Mid-plane temperature for unsteady-state heat transfer in a slab of finite thickness 2L with uniform initial temperature and convective resistance at surfaces
734(1)
Figure 7.4.2-2 Temperature profile for unsteady-state heat transfer in a slab of finite thickness with uniform initial temperature and convective resistance at surfaces
735(1)
Figure 7.4.2-3 Centerline temperature for unsteady-state heat transfer in an infinite cylinder of radius r0 with uniform initial temperature and convective resistance at surfaces
736(1)
Figure 7.4.2-4 Temperature profile for unsteady-state heat transfer in an infinite cylinder of radius r0 with uniform initial temperature and convective resistance at surfaces
737(1)
Figure 7.4.2-5 Center temperature for unsteady-state heat transfer in a sphere of radius r0 with uniform initial temperature and convective resistance at surfaces
738(1)
Figure 7.4.2-6 Temperature profile for unsteady-state heat transfer in a sphere of radius r0 with uniform initial temperature and convective resistance at surfaces
739(1)
Example 7.4.2-1 Convective and conductive resistances in series
739(2)
Radiation Heat Transfer Models
741(36)
Figure 7.5-1 The electromagnetic spectrum
742(1)
Interaction of radiation and matter
742(1)
Geometric description of radiation
742(1)
Figure 7.5.1-1 Directions in space
743(1)
Intensity of radiation
743(1)
Figure 7.5.1-2 Radiation leaving A1
744(1)
Lumping of quantities used in modeling radiation
745(1)
Incident radiation
746(2)
Figure 7.5.1-3 Extreme modes of reflection
748(1)
Absorptivity
748(1)
Reflectivity
748(1)
Transmittivity
749(1)
Emitted radiation
749(1)
Blackbodies
750(1)
Blackbody radiation
751(1)
Emissivity
752(1)
Radiosity
752(1)
Radiant heat exchange between two opaque bodies with no intervening medium
753(1)
Table 7.5.2-1 History of radiation emitted
754(1)
Kirchhoffs law
755(2)
Figure 7.5.3-1 Total emissivity of some surfaces
757(1)
View factors
757(1)
Figure 7.5.4-1 Radiation between surfaces
758(1)
Reciprocity relation
759(1)
Summation rule
760(1)
Example 7.5.4-1 Integration to obtain view factor
761(3)
Table 7.5.4-1 View Factors
764(1)
Example 7.5.4-2 Use of reciprocity relation and summation rule to infer view factor for concentric spheres
764(1)
Radiant heat exchange between blackbodies
765(1)
Example 7.5.5-1 Heat transfer by radiation - blackbody
766(2)
Example 7.5.5-2 Use of view factor tables with blackbody radiation exchange
768(2)
Radiative exchange between gray bodies
770(2)
Figure 7.5.6-1 Electrical analog of net radiation from a gray surface
772(1)
Figure 7.5.6-2 Network analog of radiation exchange with gray surfaces in an enclosure
773(1)
Example 7.5.6-1 Two-gray-body exchange in enclosure
773(2)
Example 7.5.6-2 Heat transfer by radiation - gray body
775(2)
Overall Heat Transfer Coefficients
777(11)
Figure 7.6-1 Insulated pipe
777(4)
Figure 7.6-1 Overall heat transfer coefficients
781(2)
Example 7.6-1 Controlling resistance for heat transfer resistance in series - spherical container of liquid oxygen
783(2)
Example 7.6-2 Controlling resistance in replacement of section of wall of distillation column
785(2)
Example 7.6-3 Overall heat transfer coefficient with fouling
787(1)
Heat Exchangers
788(40)
Average overall temperature difference
789(7)
Countercurrent vs. concurrent operation
796(1)
Figure 7.7.2-1 T-H diagram for countercurrent flow of two streams
797(1)
Figure 7.7.2-2 T-H diagram for concurrent flow of two streams
798(1)
Figure 7.7.2-3 T-H diagram for countercurrent flow of two streams
799(1)
Figure 7.7.2-4 T-H diagram for concurrent flow of two streams
799(1)
Example 7.7.2-1 Concurrent vs. countercurrent flow in a concentric tube exchanger
800(6)
NTU method for design of heat exchangers
806(1)
Figure 7.7.3-1 T-H diagram for two streams between which sensible heat is to be exchanged in countercurrent flow
807(1)
Figure 7.7.3-2 T-H diagram for two streams between which sensible heat is to be exchanged in concurrent flow
808(1)
Figure 7.7.3-3 Pinch with concurrent operation
809(1)
Figure 7.7.3-4 Pinch with countercurrent operation
809(3)
Table 7.7.3-1a Effectiveness/NTU relationships
812(1)
Table 7.7.3-1b NTU/effectiveness relationships
812(1)
Example 7.7.3-1 Determination of effectiveness for a concurrent flow exchanger
813(4)
Example 7.7.3-2 Calculation of area using NTU and ε for a concurrent flow exchanger
817(2)
Example 7.7.3-3 Calculation of exit temperatures using NTU and ε for a heat exchanger of known area
819(3)
F-factor method for design of heat exchangers
822(3)
Figure 7.7.4-1 Correction factor to log mean temperature difference - one shell pass, 2n tube passes
825(1)
Example 7.7.4-1 Use of F Factor compared to effectiveness/NTU method
825(3)
Chapter 7 Problems
828(15)
Mass Transfer Models
843(146)
The Nature of Mass Transfer
843(2)
Diffusive Mass Transfer Models
845(37)
Velocities of components in a mixture
845(1)
Figure 8.2.1-1 Diffusion of vapor from vessel
846(1)
Figure 8.2.1-2 Evolution of concentration profile
846(2)
Figure 8.2.1-3 Velocity of molecule
848(1)
Figure 8.2.1-4 Changing velocity and displacement of single molecule via collisions
848(2)
Example 8.2.1-1 Average velocity when individual particles have the same velocity
850(1)
Figure 8.2.1-5 Identical molecules, identical velocities
850(1)
Example 8.2.1-2 Average velocity when individual particles have different velocities
851(1)
Figure 8.2.1-6 Identical molecules, differing velocities
851(2)
Example 8.2.1-3 Number average velocity, velocities in two dimensions
853(1)
Figure 8.2.1-7 Number average velocity, velocities in two dimensions
854(3)
Table 8.2.1-1 Coordinate frame motion
857(1)
Table 8.2.1-2 Mass transfer relationships
858(1)
Mechanisms of mass transfer
858(1)
Fick's law
858(2)
Table 8.2.3-1 Equivalent forms of Fick's Law referred to coordinate systems in various motions
860(1)
Figure 8.2.3-1 Flux of marbles without diffusion
861(1)
Figure 8.2.3-2 Flux of marbles with diffusion
862(1)
Figure 8.2.3-3 Fluxes compared
862(1)
Binary diffusivities
863(1)
Figure 8.2.4-1 Diffusivities in solids
864(1)
Figure 8.2.4-2 Diffusivities in liquids
864(1)
Figure 8.2.4-3 Diffusivities in gases
865(1)
Solutions of the diffusion equation
865(1)
One-dimensional equimolar counterdiffusion in rectangular coordinates
865(2)
Example 8.2.5-1 Equimolar counterdiffusion
867(1)
One-dimensional diffusion of A through stagnant B observed in rectangular coordinates
868(1)
Example 8.2.5-2 Diffusion of vapor through a stagnant gas
869(1)
Figure 8.2.5-1 Diffusion through stagnant gas layer
869(2)
One Dimensional unsteady-state diffusion in a semi-infinite slab
871(1)
Figure 8.2.5-2 Semi-infinite slab with constant face concentration
871(6)
Diffusion in porous solids
877(3)
Dispersion
880(1)
Figure 8.2.7-1 Dispersion and diffusion as a function of Peclet number
881(1)
Convective Mass Transfer Models
882(6)
The concentration boundary layer
882(1)
Figure 8.3.1-1 Concentration boundary layer
883(2)
Figure 8.3.1-2 Boundary layer
885(1)
Figure 8.3.1-3 Boundary layer solution for a flat plate
886(1)
Film theory and penetration-renewal theory
887(1)
The Mass Transfer Coefficient for a Single Phase
888(22)
Example 8.4-1 Calculation of flux from a mass transfer coefficient
892(1)
Example 8.4-2 Mass transfer using partial pressure as a driving force
893(1)
Example 8.4-3 Mass transfer using species mass density as driving force
894(1)
Design equations for single-phase mass transfer coefficients
895(1)
Flat plates
895(1)
Example 8.4.1-1 Average mass transfer coefficient from local coefficient
896(2)
Mass transfer in flow in pipes
898(1)
Mass transfer from spheres, drops, and bubbles
898(1)
Example 8.4.1-2 Comparison of mass transfer coefficient models
899(1)
Example 8.4.1-3 Mass transfer coefficient for dissolution of a sphere
900(2)
Packed beds
902(1)
Height of transfer unit models
903(4)
Dimensional analysis of mass transfer by convection
907(3)
Overall Mass Transfer Coefficients
910(11)
Figure 8.5-1 Mass transfer concentrations
911(4)
Figure 8.5-2 Interface conditions
915(1)
Example 8.5-1 Calculation of interface composition
916(3)
Incorporation of overall mass transfer coefficient into height of transfer unit model
919(1)
Example 8.5.1-1 Overall transfer units
919(2)
Relationship of Overall and Single-Phase Mass Transfer Coefficients
921(2)
Figure 8.6-1 Assumption necessary to utilize overall mass transfer coefficient
921(2)
Example 8.6-1 Controlling resistance for mass transfer
923(1)
Design of Mass Transfer Columns
923(40)
Figure 8.7-1 Typical countercurrent gas absorber
926(1)
Determination of liquid-to-gas ratio
926(1)
Figure 8.7.1-1 Gas absorption
927(3)
Calculation of tower diameter
930(2)
Figure 8.7.2-1 Norton Chemical Process Products Corporation Intalox® IMTP® Packing
932(1)
Figure 8.7.2-2 IMTP® packing pressure drop
933(1)
Table 8.7.2-1 Values of coefficient F for IMTP® packings
934(1)
Calculation of packing height
934(3)
Table 8.7.3-1 H, n integrals
937(1)
Applications
937(1)
Example 8.7.4-1 Analytical calculation of interfacial concentration
937(2)
Example 8.7.4-2 Analytical determination of number of transfer units: straight operating and equilibrium lines
939(4)
Example 8.7.4-3 Effect of change of L/G on outlet composition
943(5)
Example 8.7.4-4 Design of absorber
948(8)
Example 8.7.4-5 Economic optimization of an absorber
956(7)
Mass Transfer with Chemical Reaction
963(18)
Figure 8.8-1 Diffusion in a membrane
963(1)
Figure 8.8-2 Diffusion with instantaneous irreversible reaction in a membrane
964(1)
Example 8.8-1 Acidization of an oil well
965(2)
Figure 8.8-3 Mass transfer with slow or reversible chemical reaction
967(2)
Example 8.8-2 Mass transfer with heterogeneous reaction
969(6)
Example 8.8-3 Mass transfer with homogeneous reaction
975(6)
Chapter 8 Problems
981(8)
APPENDIX A: VECTOR AND TENSOR OPERATIONS 989(6)
A.1 Symbolic Notation
989(2)
Table A.1 Operational properties of the del operator in different coordinate frames
990(1)
A.2 Index Notation
991(4)
A.2.1 The unit tensor
992(1)
A.2.2 The alternating tensor or permutation symbol
992(3)
APPENDIX B: ERROR FUNCTION 995(2)
Table B-1 Gauss error function
995(1)
Figure B-1 Error function
996(1)
APPENDIX C: NOMENCLATURE 997(12)
Index 1009

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