كتاب Momentum, Heat, and Mass Transfer Fundamentals
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 كتاب Momentum, Heat, and Mass Transfer Fundamentals

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HDF
أخوانى فى الله
أحضرت لكم كتاب
Momentum, Heat, and Mass Transfer Fundamentals
David P Kessler
Robert A. Greenkorn
Purdue University
West Lafayette, Indiana
M A R C E L
H MARCEL DEKKER , INC . NEW YORK * BASEL
D E K K E RTHUMB INDEX

كتاب Momentum, Heat, and Mass Transfer Fundamentals  M_h_a_12
و المحتوى كما يلي :


CONTENTS XI
1 ESSENTIALS 1
1.6.2 Types of derivatives 63
2 THE MASS BALANCES 73
2.1.1 The macroscopic total mass balance 74
2.1.2 The macroscopic species mass balance
2.2.1 The microscopic total mass balance (continuity equation )
2.2.2 The microscopic species mass balance
3 THE ENERGY BALANCES 113
3.1.2 The macroscopic total energy balance 114
3.1.3 The macroscopic mechanical energy balance
3.1.4 The macroscopic thermal energy balance
3.2.1 The microscopic total energy balance
3.2.2 The microscopic mechanical energy balance
3.2.3 The microscopic thermal energy balance
4 THE MOMENTUM BALANCES 169
4.1 The Macroscopic Momentum Balance
4.2 The Microscopic Momentum Balance
4.3 Summary of Balance Equations and Constitutive Relationships
5 APPLICATION OF DIMENSIONAL ANALYSIS 211
6 MOMENTUM TRANSFER IN FLUIDS
Table 6.3-1 Elementary plane flows
6.7 Drag Coefficients
Table 6.7.2-1 Properties of pipe
Figure 6.7.2-3 Moody friction factor chart
vnThumb Index a
7 HEAT TRANSFER MODELS 517
Table 7.2.1-1 Components of Fourier Equation 530
7.2.4 One-dimensional steady-state conduction in rectangular
coordinates
7.2.5 One-dimensional steady-state conduction in cylindrical
coordinates
72.6 One-dimensional steady-state conduction in spherical
coordinates
7.2.8 One-dimensional unsteady-state conduction
Semi-infinite slab
Finite slab
Infinite cylinder and sphere
7.2.9 Multi-dimensional unsteady-state conduction
7.3.2 Heat transfer coefficients
7.4 Conduction and Convection in Series
Heisler charts
7.5 Radiation Heat Transfer Models
Reciprocity relation
Summation rule
7.7.3 NTU method for design of heat exchangers
7.7.4 F-factor method for design of heat exchangers
822
8 MASS TRANSFER MODELS 843
Table 8.2.3-1 Equivalent forms of Fick’s Law
8.3 Convective Mass Transfer Models
Height of transfer unit models
8.7 Design of Mass Transfer Columns
8.8 Mass Transfer with Chemical Reaction
APPENDIX A: VECTOR AND TENSOR OPERATIONS
APPENDIX C: NOMENCLATURE
INDEX
1009TABLE OF CONTENTS
Preface
Thumb Index
1 ESSENTIALS 1
1.1 Models 1
Figure 1.1-1 Modeling the weather 1
Figure 1.1-2 A poor model of the weather
1.1.1 Mathematical models and the real world
1.1.2 Scale of the model
1.2 The Entity Balance
Example 1.2-1 An entity balance
1.2.1 Conserved quantities
1.2.2 Steady-state processes
1.3 The Continuum Assumption
Figure 1.3-1 Breakdown of continuum assumption
1.4 Fluid Behavior
1.4.1 Laminar and turbulent flow
Figure 1.4.1-1 Injection of dye in pipe flow
1.4.2 Newtonian fluids
Figure 1 ,4.2-1 Shear between layers of fluid
Figure 1.4.2-2 Momentum transfer between layers of fluid
Figure 1.4.2-3 Sign convention for momentum flux between
layers of fluid
Figure 1.4.2-4 Sign convention for shear stress on surface
layers of fluid
Table 1.4.2-1 Summary of sign convention for
stress/momentum flux tensor
Figure 1.4.2-5 Migration of momentum by molecular motion
Figure 1.4.2-6 Viscosity of common fluids
Example 1.4.2-1 Flow of fluids between fixed parallel
plates
1.4.3 Complex fluids
Figure 1.4,3-1 Complex fluids
Figure 1.4.3-2 Mechanical analog of viscoelasticity
xixu Table of Contents
1,4.4 Compressible vs. incompressible flows
1.5 Averages
1.5.1 General conce
Example /.
Figure 1.5.1-1 Time-average speed for travel between two
points
Figure 1.5.1-2 Distance-average speed for travel between two
points
1.5.2 Velocity averages
Area-averaged velocity
Example 1.5.2-1 Area-averaged velocity for laminar pipe
flow
Figure 1.5.2-1 Velocity profile
Time-averaged velocity
Example 1.5.2-2 Time-averaged velocity for turbulent
flow
Example /.5.2-3 Area-average of time-averaged velocity
for turbulent pipe flow
1.5.3 Tern perature averages
Example 1.5.3-1 Area-average temperature vs. bulk
temperature
Example 1.5.3-2 Bulk temperature for quadratic
temperature profile, laminar pipe flow
1.5.4 Concentration averages
Example 1.5.4-1 Bulk concentration
1.5.5 Arithmetic, logarithmic, and geometric means
Example 1.5.5-1 Case examples of logarithmic mean
Example 1.5.5-2 Approximation of logarithmic mean by
arithmetic mean
1.6 Scalars, Vectors, Tensors and Coordinate Systems
1.6.1 The viscous stress tensor
Components of the viscous stress tensor
Figure 1.6.1-1 (a) Vectors associated by a particular viscous
stress tensor with the direction of the rectangular Cartesian
axes
Figure 1.6.1-1 (b) Vector associated with the 3-direction
decomposed into its components
1.6.2 Types of derivatives
Partial derivative
jnt of average 33
5.1-1 Time-average vr distance-average speed
Total derivative 64
Substantial derivative, material derivative, derivative following the
motion 64
Example 1.6.2-1 Rate of change of pollen density
1.6.3 Transport theorem
66Table of Contents xm
Figure 1.6.3-1 Motion of continuum 67
Chapter 1 Problems 69
2 THE MASS BALANCES 7 3
2.1 The Macroscopic Mass Balances
Figure 2.1-1 System for mass balances
2.1.1 The macroscopic total mass balance
Accumulation of mass
Input and output of mass
Simplified forms of the macroscopic total mass balance
Example 2.1.1-l Mass balance on a surge tank
Figure 2.1.1-1 Surge tank
Example 2././-2 Volumetric flow rate offluid in laminar
flow in circular pipe
Example 2.1.1-5 Air storage tank
Example 2./.1-4 Water manifold
2.1.2 The macroscopic species mass balance
Generation of mass of a species
Accumulation of mass of a species
Input and output of mass of a species
Example 2.1.2-1 Macroscopic species mass balance with
zero-order irreversible reaction
Example 2.1.2-2 Macroscopic species mass balance with
first-order irreversible reaction
Figure 2.1.2-1 Perfectly mixed tank with reaction
2.2 The Microscopic Mass Balances
2.2.1 The microscopic total mass balance (continuity equation)
Special cases of the continuity equation
Continuity equation in different coordinate systems
Table 2.2.1-1 Continuity equation (microscopic total mass
balance) in rectangular, cylindrical, and spherical coordinate
frames
Example 2.2.1-/ Velocity components in two-dimensional
steady incompressible flow, rectangular coordinates
Example 2.2.1-2 Velocity components in two-dimensional
steady incompressible flow, cylindrical coordinates
Example 2.2./-3 Compression of air
Figure 2.2.1-1 Air compression by piston
2.2.2 The microscopic species mass balance
Diffusion
Chapter 2 Problems
3 THE ENERGY BALANCES
3.1 The Macroscopic Energy Balances
113
113xiv Table of Contents
3.1.1 Forms of energy
3.1.2 The macroscopic total energy balance
Rate of accumulation of energy
Rates of input and output of energy
Figure 3.1.2-1 Flow work
Simplified forms of the macroscopic total energy balance
The potential energy term
Figure 3.1.2-2 Gravitational field of earth
The kinetic energy term
The enthalpy term
Averages and the macroscopic energy equations
Energy balance approximation - turbulent flow
Energy balance approximation - laminar flow
Steady-state cases of the macroscopic total energy balance
Table 3.1.2-1 Qualitative comparison of ranges of enthalpy
changes (kcal/mol) for processes involving organic
compounds
Example 3.1.2-1 Relative magnitudes of mechanical and
thermal energy terms with phase change
Figure 3.1.2-3 Mechanical energy and thermal energy terms
compared for a boiler (I)
Example 3.1,2-2 Steam production in a boiler
Figure 3.1.2-4 Mechanical and thermal energy terms compared
for a boiler (II)
Example 3,1.2-3 Temperature rise from conversion of
mechanical to thermal energy
Figure 3.1.2-5 Water supply system
Example 3.1.2-4 Heated tank, steady state in mass and
unsteady state in energy
Figure 3.1.2-6 Heated tank
3.1.3 The macroscopic mechanical energy balance
Example 3.1.3-1 Mechanical energy and pole vaulting
Example 3.I.3-2 Calculation of lost work in pipe
Figure 3.1.3-1 Pipe system
3.1.4 The macroscopic thermal energy balance
3.2 The Microscopic Energy Balances
3.2.1 The microscopic total energy balance
Eulerian forms of the microscopic total energy balance
Lagrangian forms of the microscopic total energy balance
3.2.2 The microscopic mechanical energy balance
3.2.3 The microscopic thermal energy balance
Chapter 3 Problems
4 THE MOMENTUM BALANCES 169Table of Contents xv
4.1 The Macroscopic Momentum Balance 169
Example 4.I-1 Momentum flux of fluid in laminar flow in
circular pipe 173
4.1.1 Types of forces 174
4.1.2 Influence of uniform pressure over entire surface of irregular
objects 175
Figure 4.1.2-1 Approximation of solid by prisms
Figure 4.1.2-2 Detail of prism
4.1.3 Averages and the momentum equation
Momentum balance approximation - turbulent flow
Momentum balance approximation - laminar flow
Example 4,1.3-1 Force on a nozzle
Example 4.1.3-2 Thrust of aircraft engine
Example 4.1.3-3 Piping support
Example 4.1.3-4 Jet boat
Example 4.1.3-5 Horizontal force on tank
4.2 The Microscopic Momentum Balance
4.3 Summary of Balance Equations and Constitutive Relationships
Table 4.3-1 Tabulation of balance equations
Table 4.3-2 Tabulation of common constitutive relationships
4.4 The Momentum Equation in Non-Inertial Reference Frames
Chapter 4 Problems
5 APPLICATION OF DIMENSIONAL
ANALYSIS
5.1 Systems of Measurement
Example 5./-/ Weight vs. mass; g vs. gc
Table 5.1-la Systems of Units
Table 5.1-1b Systems of Units
Table 5.1-2 SI Prefixes
5.2 Buckingham's Theorem
Example 5.2-1 Dimensionless variables for pipe flow
5.2.1 Friction factors and drag coefficients
5.2.2 Shape factors
Example 5.2.2-1 Drag force on ship hull
Example 5.2.2-2 Deceleration of compressible fluid
5.3 Systematic Analysis of Variables
Example 5.3-1 Drag force on a sphere
Example 5J -2 Dimensionless groups for flow over a flat
plate
Example 5.3-3 Consistency of dimensionless groups across
system of dimensions
Example 5.3-4 Capillary interface height via dimensional
analysis
243xvi Table of Contents
5.4 Dimensionless groups and differential models
Example 5.4-1 Pipe flow of incompressible fluid with
constant viscosity
Example 5.4-2 One-dimensional energy transport
Example 5.4-3 Mass transport in a binary mixture
Example 5.4-4 Extrapolating model results from one
category of momentum, heat, or mass transport to another
Table 5.4-1 Dimensionless variables
Table 5.4-2 Dedimensionalized balance equations
Table 5.4-3 Dimensionless numbers
5.5 Similarity, Models and Scaling
Example 5.5-1 Drag on immersed body
Example 5.5-2 Scale effects
Chapter 5 Problems
6 MOMENTUM TRANSFER IN FLUIDS 281
6.1 Fluid Statics
6.1.1 Manometers
Example 6.1.1-l Pressure difference using a manometer
Figure 6.1.1-1 Measurement of pressure difference with
manometer
Example 6./. I -2 Pressure difference between tanks
Figure 6.1.1-2 Pressure difference between tanks
Example 6.1.1-3 Differential manometer
Figure 6.1.1-3 Differential manometer
6.2 Description of Flow Fields
Figure 6.2-1 Paths between streamlines
6.2.1 Irrotational flow
6.3 Potential Flow 295
Table 6.3-1 Elementary plane flows
Table 6.3-2 Superposition of elementary plane flows
Example 6.3-1 Flow around a circular cylinder
Figure 6.3-1 Flow around circular cylinder
Example 6.3-2 Flow of an ideal fluid through a corner
Figure 6.3-2 Flow through a comer
Example 6.3-3 Flow around a rotating cylinder
6.4 Laminar Flow 314
6.4.1 Laminar flow between infinite parallel plates 315
Figure 6.4.1-1 Steady flow between infinite stationary parallel
plates
Example 6.4.1-1 Steady flow between infinite parallel
plates
Figure 6.4.1-2 Flow between infinite parallel plates, top plate
moving at VQ
319Table of Contents xvn
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
Example 6.4.1-2 Flow between infinite rotating concentric
cylinders
6.4.2 Laminar flow in a circular pipe
Figure 6.4.2-1 Control volume for force balance on fluid in
pipe 322
Figure 6.4.2-2 Velocity profile for laminar flow of a
Newtonian fluid in a pipe or duct of circular cross-section
Figure 6.4.2-3 Shear stress profile for laminar flow of a
Newtonian fluid in a pipe or duct of circular cross-section
Example 6.42-1 Flow in a capillary viscometer
Example 6.42-2 Flow between two concentric cylinders
Figure 6.4.2-4 Viscometric flow between cylinders
Example 6.42-3 Film flow down a wall
Figure 6.4.2-5 Film flow down wall
Example 6.42-4 Flow adjacent to a flat plate
instantaneously set in motion
Figure 6.4.2-6 Flow adjacent to flat plate instantaneously set
in motion
6.5 Turbulent Flow
Figure 6,5-1 Local velocity in turbulent flow as a function of
time
Figure 6.5-2 Laminar and time-smoothed turbulent (1/7 power
model) velocity profiles in steady pipe flow
6.5.1 Time averaging the equations of change
Example 6.5-2 Time averaging of velocity product
6.5.2 The mixing length model
Figure 6.5.2-1 Mixing length model
Figure 6.5.2-2 Universal velocity distribution
Example 6.52-1 Size of sublayer and buffer zone in
turbulent flow
6.6 The Boundary Layer Model
Figure 6.6-\ Boundary layer development on flat plate
Example 6.6-1 Displacement thickness
6.6.1 Momentum balance - integral equations
Figure 6.6.1-1 Element in boundary layer
Figure 6.6.1-2 Velocity profile development in the entrance
region to a pipe
6.6.2 De-dimensionalization of the boundary layer equations
6.6.3 Exact solution of the momentum boundary layer equations via
similarity variables
362xvm Table of Contents
Example 6.6.3-1 Similarity variable developed from
dimensional analysis
Figure 6.63-1 Solution to Blasius boundary layer equation
Example 6.6.3-2 Runge-Kutta solution of Blasius problem
6,7 Drag Coefficients
Figure 6.7-1 Flow around an airfoil (a) without and (b) with
separation
6.7. 1 Drag on immersed bodies (external flow)
Figure 6.7.1-1 Drag coefficient for smooth flat plate oriented
parallel to flow stream
Example 6.7.I-I Drag on a flat plate
Figure 6.7.1-2 Flow past circular cylinder
Figure 6.7.1-3 Drag coefficient for circular cylinder
Example 6.7.1-2 Wind force on a distillation column
Figure 6.7.1-4 Drag coefficient for sphere
Example 6.7.1-3 Terminal velocity of a polymer sphere in
water
6.7.2 Drag in conduits - pipes (internal flow)
Table 6.7.2-1 Properties of pipe
Figure 6.7.2-1 Momentum balance on cylindrical fluid element
in horizontal pipe
Figure 6.7.2-2 Momentum balance on cylindrical fluid element
in non-horizontal pipe
Figure 6.7.2-3 Moody friction factor chart
Figure 6.7.2-4 Relative roughness for clean new pipes
Example 6.7.2-1 Expansion losses
Figure 6.7.2-5 Equivalent lengths for losses in pipes
Example 6.7.2-2 Direction of flow between tanks at
differing pressures and heights
Example 6.7.2-3 Friction loss in a piping system
Friction factor calculations - serial paths
Case 1: Pressure drop unknown
Example 6.7.2-4 Pressure loss for flow between tanks
Case 2: Diameter unknown
Example 6.7.2-5 Transfer line from tank to column
Example 6.7.2-6 Minimum pipe diameter
Case 3: Length unknown
Example 6.7.2-7 Air supply through hose
Case 4: Flow rate unknown
Example 6.7.2-8 Flow rate unknown
Figure 6.7.2-6 Friction factor vs. Karman number
Example 6.7.2-9 Calculation of flow rate via Karman
number when pressure drop is known
Non-circular conduits
424Table of Contents xix
Example 6.7.2-10 Flow in a smooth annulus
Example 6.7.2-11 Pressure drop in a pipe annulus
Friction factor calculations - parallel paths
Example 6.7.2-12 Pipe network with imposed pressure
drop
Table 6.7,2-2 Convergence of Newton’s Method
Example 6.72- /3 Flow in a parallel piping system
Example 6.7.2-14 Input of additional fluid to an existing
pipe network
6.8 Non-Newtonian Flow
6.8.1 Bingham plastics
Figure 6.8.1-1 Tube flow of Bingham plastic
6,8.2 Power-law fluids
Example 6.8-1 Flow of polymer melt
6.9 Flow in Porous Media
6.9.1 Darcy’s law
Figure 6,9.1-1 Permeability as a function of porosity for a bed
of spheres
Table 6.9.1-1 Porosities (void fractions) for dumped packings
Table 6.9.1-2 Porosity and permeability for typical
materials
Example 6.9.1- I Flow of water in sandstone
6.9.2 Packed beds
Example 6.92-1 Pressure drop for air flowing though bed
of spheres
Example 6.92-2 Pressure drop for water flowing though
bed of cylinders
6.9.3 Filters 462
Example 6.9.3-1 Production scale fdter performance
prediction from pilot plant data
Example 6.9.3-2 Filter performance from data
Example 6.9.3-3 Adapting existing filter to new product
6.10 Row Measurement
6.10.1 Pitot tube
Figure 6.10.1-1 Pitot tube schematic
Figure 6.10.1-2 Flow at mouth of pitot tube
Example 6.10.1-1 Pitot tube traverse
6.10.2 Venturi meter
Figure 6.10.2-1 Venturi schematic
Figure 6.10.2-2 Venturi meter coefficient
Example 6.10.2-1 Flow measurement with venturi meter
6.10.3 Orifice meter and flow nozzle
Figure 6.10.3-1 Orifice meter, flow nozzle
Figure 6.10.3-2 Orifice coefficient
483xx. Table of Contents
Example 6.103- / Metering of crude oil with orifice
Chapter 6 Problems
7 HEAT TRANSFER MODELS
7.1 The Nature of Heat
7.1.1 Forced convection heat transfer
7.1.2 Free convection heat transfer
Table 7.1.2-1 Dimensionless Forms: Mass, Energy, and
Momentum Equations for Natural and Forced Convection
7.2 Conduction Heat Transfer Models
7.2.1 Three-dimensional conduction in isotropic media
Table 7.2.1-1 Components of Fourier Equation in Various
Coordinate Systems
7.2.2 Boundary conditions at solid surfaces
7.2.3 Thermal conductivity
Table 7.2.3-1 Relative Values of Thermal Conductivity
7.2.4 One-dimensional steady-state conduction in rectangular
coordinates
Analytical solution
Figure 7.2.4-1 Homogeneous solid
Figure 1.2.4-2 Temperature profile in 1-D heat transfer by
conduction, rectangular coordinates
Interface condition between solids - series conduction
Figure 7.2.4-3 Conduction with two solids in contact
assuming no temperature drop at interface
Figure 7.2.4-4 Temperature profile with interfacial resistance
Figure 7.2.4-5 Contact resistance treated as an intermediate
solid
Equivalent thermal resistance - series conduction
Figure 7.2.4-6 Development of equivalent conductance for
series conduction
Equivalent thermal resistance - parallel conduction
Figure 1.2.4-1 Development of equivalent conductance for
parallel conduction
Figure 7.2.4-8 Equivalent circuit for parallel conduction
Example 7.2.4-1 Series conduction through layers -
constant temperature at external surfaces
Figure 7.2.4-9 Series conduction through layers with constant
temperature at external surfaces
Example 7.2.4-2 Series conduction through layers -
constant convective heat transfer coefficient at external
surfaces
549Table of Contents XXi
Figure 7.2.4-10 Series conduction through layers with
constant convective heat transfer coefficient at external
surfaces
Example 7.2.4-3 Conduction with variable thermal
conductivity
Figure 7.2.4-11 Conduction through firebrick with variable
thermal conductivity
Figure 7.2.4-12 Temperature profile
Example 7.2.4-4 One-dimensional steady-state conduction
with parallel path
Figure 7.2.4-13 Conduction with parallel paths
Figure 7.2.4-14 Analogous circuit
Numerical solution
The finite element method
Figure 7.2.4-14 Examples of 1-D and 2-D finite elements
Figure 7.2.4-15 Interpolation functions, Shape function
Example 7.2.4-5 Solution by finite elements of steady-state
conduction with generation
Figure 7.2,4-16 Bar with thermal energy source
Table 7.2.4-1 Global node numbering scheme
Figure 7.2,4-17 Comparison of finite element and analytic
solution
Finite element method in higher dimensions
7.2.5 One-dimensional steady-state conduction in cylindrical
coordinates
Figure 7.2.5-1 Conduction through the wall of a composite
cylinder
Example 7.2.5-1 Conduction in a fuel rod
Example 7.2.5-2 Conduction through an insulated pipe
7.2.6 One-dimensional steady-state conduction in spherical
coordinates
Figure 7,2,6-1 Radial conduction in spherical geometry
Example 7.2.6-1 Conduction through shielding
7.2.7 Two-dimensional steady-state conduction
Taylor series
Analytical solution
Orthogonal functions
Example 72.7-2 Convergence of steady-state rectangular
coordinate solution
Numerical solution
Finite difference method
Forward difference approximation to the first derivative
Backward difference approximation to the first derivative
Central difference approximation to the first derivative
608xxu Table of Contents
Approximation of second derivative
Finite difference approximation to the Laplace equation
Example 7.2.7-1 Determination of steady-state
temperature distribution in a rectangular slab
Irregular boundaries, Dirichlet boundary conditions
Normal derivative (Neumann) boundary condition at nodal point
Generation terms
Example 7.2.7 -2 Finite difference solution of 2-D steadystate conduction
7.2.8 One-dimensional unsteady-state conduction
Analytical methods for one-dimensional unsteady-state conduction
Semi-infinite slab
Figure 7.2.8-1 Semi-infinite slab with constant face
temperature
Example 7.2.8-1 Semi-infinite slab: conduction in a brick
wall
Finite slab
Figure 7.2.8-2 Finite slab with constant face temperatures
Figure 7.2.8-3 Unsteady-state heat transfer in a finite slab with
uniform initial temperature and constant, equal surface
temperatures
Example 7.2.8-2 Finite slab model vs. semi-infinite slab
model for one-dimensional unsteady-state conductive heat
transfer
Infinite cylinder and sphere
Figure 7.2.8-4 Unsteady-state heat transfer in an infinite
cylinder with uniform initial temperature and constant surface
temperature
Figure 7.2.8-5 Unsteady-state heat transfer in a sphere with
uniform initial temperature and constant surface temperature
Numerical Methods for One-Dimensional Unsteady-State
Conduction
Finite difference method
Finite difference explicit form
Figure 7.2.8-6 Finite difference grid for ID unsteady-state
conduction
Example 7.2.8-3 Unsteady-state heat transfer by explicit
finite differences
Finite difference implicit form
Example 7.2.8-4 Finite slab unsteady-state heat transfer
by finite differences
7.2.9 Multi-dimensional unsteady-state conduction
Analytical solution for regular geometries
667Table of Contents xxin
Figure 7.2.9-1 Multidimensional unsteady-state temperature
profiles for conduction in regular geometries expressed as
product of one-dimensional solutions
Numerical solution of two-dimensional unsteady-slate conduction
Finite difference method
Figure 12.9-2 Alternating direction implicit method
Finite element method
7.3 Convection Heat Transfer Models
7.3.1 The thermal boundary layer
Figure 7.3.1-1 Solution of Equation (7.3.1-1)
7.3.2 Heat transfer coefficients
Single-phase heat transfer coefficients
Figure 7.3.2-1 Single-phase heat transfer coefficients
Correlations for prediction of heat transfer
Average heat transfer coefficients
Example 7.3.2-1 Average heat transfer coefficients for
pipe flow
Design equations for convective heat transfer
Forced convection in laminar flow
Table 7.3.2-1 Nusselt number limit for laminar flow in ducts
with various cross-sections
Forced convection in turbulent flow
Example 7.3.2-2 Comparison of the Dittus-Boelter, Colburn,
and Sieder-Tate equations
Heat transfer in non-circular conduits and annular flow
External flows, natural and forced convection
Table 7.3.2-2 Values of b and n for Equation (7.3.2-104)
Table 7.3.2-3 Values of a and m for use with Equation (7.3.2-
105)
Example 7.3.2-3 Heat transfer with flow normal to pipes
Heat transfer with phase change
Boiling - mechanism
Figure 7.3.2-2 Boiling Curve
Condensation - mechanism
Boiling coefficients
Table 7.3.2-3 Values of C for nucleate boiling model
Condensing coefficients
7.4 Conduction and Convection in Series
7.4.1 Lumped capacitance models
Figure 7.4.1-1 RC circuit analog of unsteady-state lumpedcapacitance heat transfer
Criteria for use of lumped capacitance models
Figure 7.4.1-2 Steady-state conduction through solid with
convection at interface
727xxiv Table of Contents
Figure 7.4.1-3 Steady-state conduction through solid with
convection at interface, small vs. large Biot number
Figure 7.4.1-4 Unsteady-state conduction through solid with
convection at interface, small vs. large Biot number
Example 7.4.1-1 Lumped capacitance models
7.4.2 Distributed capacitance models
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
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
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
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
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
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
Example 7.4.2-1 Convective and conductive resistances
in series
7.5 Radiation Heat Transfer Models
Figure 7.5-1 The electromagnetic spectrum
7.5.1 Interaction of radiation and matter
Geometric description of radiation
Figure 7.5.1-1 Directions in space
Intensity of radiation
Figure 7.5.1-2 Radiation leaving A
Lumping of quantities used in modeling radiation
Incident radiation
Figure 7.5.1-3 Extreme modes of reflection
Absorptivity
Reflectivity
Transmittivity
Emitted radiation
Blackbodies
Blackbody radiation
Emissivity
Radiosity
752Table of Contents XXIX
Figure 8.8-2 Diffusion with instantaneous irreversible reaction
in a membrane
Example 8.8-1 Acidization of an oil well
Figure 8.8-3 Mass transfer with slow or reversible chemical
reaction
Example 8.8-2 Mass transfer with heterogeneous reaction
Example 8.8-3 Mass transfer with homogeneous reaction
Chapter 8 Problems
APPENDIX A: VECTOR AND TENSOR
OPERATIONS
A.1 Symbolic Notation
Table A.l Operational properties of the del operator in different
coordinate frames
A.2 Index Notation
A.2.1 The unit tensor
A.2.2 The alternating tensor or permutation symbol
APPENDIX B: ERROR FUNCTION
Table B-l Gauss error function
Figure B-l Error function
APPENDIX C: NOMENCLATURE 997
INDEX 1009Table of Contents xxv
7.5.2 Radiant heat exchange between two opaque bodies with no
intervening medium
Table 7.5.2-1 History of radiation emitted
7.5.3 Kirchhoffs law
Figure 7.5.3-1 Total emissivity of some surfaces
7.5.4 View factors
Figure 7.5.4-1 Radiation between surfaces
Reciprocity relation
Summation rule
Example 7.5.4-1 Integration to obtain view factor
Table 7.5.4-1 View Factors
Example 7.5.4-2 Use of reciprocity relation and
summation rule to infer view factor for concentric spheres
7.5.5 Radiant heat exchange between blackbodies
Example 7.5.5-1 Heat transfer by radiation - blackbody
Example 7.5.5-2 Use of view factor tables with blackbody
radiation exchange
7.5.6 Radiative exchange between gray bodies
Figure 7.5.6-1 Electrical analog of net radiation from a gray
surface
Figure 7.5.6-2 Network analog of radiation exchange with gray
surfaces in an enclosure
Example 7.5.6-1 Two-gray-body exchange in enclosure
Example 7.5.6-2 Heat transfer by radiation - gray body
7.6 Overall Heat Transfer Coefficients
Figure 7.6-1 Insulated pipe
Figure 7.6-1 Overall heat transfer coefficients
Example 7.6-1 Controlling resistance for heat transfer
resistances in series - spherical container of liquid oxygen
Example 7.6-2 Controlling resistance in replacement of
section of wall of distillation column
Example 7.6-3 Overall heat transfer coefficient with
fouling
7.7 Heat Exchangers
7.7.1 Average overall temperature difference
7.7.2 Countercurrent vs. concurrent operation
Figure 7.7.2-1 T-H diagram for countercurrent flow of two
streams
Figure 7.7.2-2 T-H diagram for concurrent flow of two
streams
Figure 7.7.2-3 T-H diagram for countercurrent flow of two
streams
Figure 7.7.24 T-H diagram for concurrent flow of two
streams
799xxvi Table of Contents
Example 7.7.2-1 Concurrent vs. countercurrent flow in a
concentric tube exchanger
7.7.3 NTU method for design of heat exchangers
Figure 7.7.3-1 T-H diagram for two streams between which
sensible heat is to be exchanged in countercurrent flow
Figure 7.7.3-2 T-H diagram for two streams between which
sensible heat is to be exchanged in concurrent flow
Figure 7.7.3-3 Pinch with concurrent operation
Figure 7.7.3-4 Pinch with countercurrent operation
Table 7.7.3- la Effectiveness/NTU relationships
Table 7.7.3-lb NTU/effectiveness relationships
Example 7.7.3-1 Determination of effectiveness for a
concurrent flow exchanger
Example 7.7.3-2 Calculation of area using NTU and e for a
concurrent flow exchanger
Example 7.7.3-3 Calculation of exit temperatures using
NTU and e for a heat exchanger of known area
7.7.4 F-factor method for design of heat exchangers
Figure 7.7.4-1 Correction factor to log mean temperature
difference - one shell pass, 2n tube passes
Example 7.7.4-1 Use of F Factor compared to
effectiveness/NTU method
Chapter 7 Problems 828
8 MASS TRANSFER MODELS
8.1 The Nature of Mass Transfer
8.2 Diffusive Mass Transfer Models
8.2.1 Velocities of components in a mixture
Figure 8.2.1-1 Diffusion of vapor from vessel
Figure 8.2.1-2 Evolution of concentration profile
Figure 8.2.1-3 Velocity of molecule
Figure 8.2.1-4 Changing velocity and displacement of single
molecule via collisions
Example 8.2.1-1 Average velocity when individual
particles have the same velocity
Figure 8.2.1-5 Identical molecules, identical velocities
Example 8.2.1-2 Average velocity when individual
particles have different velocities
Figure 8.2.1-6 Identical molecules, differing velocities
Example 8.2.1-3 Number average velocity, velocities in
two dimensions
Figure 8.2.1-7 Number average velocity, velocities in two
dimensions
Table 8.2.1-1 Coordinate frame motion
857Table of Contents xxv/ /
Table 8.2.1-2 Mass transfer relationships 858
8.2.2 Mechanisms of mass transfer 858
8.2.3 Fick’s law 858
Table 8.2.3-1 Equivalent forms of Fick's law referred to
coordinate systems in various motions
Figure 8.2.3-1 Flux of marbles without diffusion
Figure 8.2.3-2 Flux of marbles with diffusion
Figure 8.2.3-3 Fluxes compared
8.2.4 Binary diffusivities
Figure 8.2.4-1 Diffusivities in solids
Figure 8.2.4-2 Diffusivities in liquids
Figure 8.2.4-3 Diffusivities in gases
8.2.5 Solutions of the diffusion equation
One-dimensional equimolar counterdiffusion in rectangular
coordinates
Example 8.2.5-1 Equimolar counterdiffusion
One-dimensional diffusion of A through stagnant B observed in
rectangular coordinates
Example 8.2.5-2 Diffusion of vapor through a stagnant gas
Figure 8.2.5*1 Diffusion through stagnant gas layer
One dimensional unsteady-state diffusion in a semi-infinite slab
Figure 8.2.5-2 Semi-infinite slab with constant face
concentration
8.2.6 Diffusion in porous solids
8.2.7 Dispersion
Figure 8.2,7-1 Dispersion and diffusion as a function of Peclet
number
8.3 Convective Mass Transfer Models
8.3.1 The concentration boundary layer
Figure 8.3.1-1 Concentration boundary layer
Figure 8.3.1-2 Boundary layer
Figure 8.3.1-3 Boundary layer solution for a flat plate
8.3.2 Film theory and penetration-renewal theory
8.4 The Mass Transfer Coefficient for a Single Phase
Example 8.4-1 Calculation offlux from a mass transfer
coefficient
Example 8.4-2 Mass transfer using partial pressure as a
driving force
Example 8.4-3 Mass transfer using species mass density
as driving force
8.4,1 Design equations for single-phase mass transfer coefficients
Flat plates
Example 8.4.1-1 Average mass transfer coefficient from
local coefficient 896xxvut Table of Contents
Mass transfer in flow in pipes
Mass transfer from spheres, drops, and bubbles
Example 8.4.1-2 Comparison of mass transfer coefficient
models
Example 8.4.1-3 Mass transfer coefficient for dissolution
of a sphere
Packed beds
Height of transfer unit models
8.4.2 Dimensional analysis of mass transfer by convection
8.5 Overall Mass Transfer Coefficients
Figure 8.5-1 Mass transfer concentrations
Figure 8.5-2 Interface conditions
Example 8.5-1 Calculation of interface composition
8.5.1 Incorporation of overall mass transfer coefficient into height
of transfer unit model
Example 8.5.1-1 Overall transfer units
8.6 Relationship of Overall and Single-Phase Mass Transfer
Coefficients
Figure 8.6-1 Assumption necessary to utilize overall mass
transfer coefficient
Example 8.6-1 Controlling resistance for mass transfer
8.7 Design of Mass Transfer Columns
Figure 8.7-1 Typical countercurrent gas absorber
8.7.1 Determination of liquid-to-gas ratio
Figure 8.7.1-1 Gas absorption
8.7.2 Calculation of tower diameter
Figure 8.7.2-1 Norton Chemical Process Products Corporation
Intalox
Figure 8.7.2-2 packing pressure drop
Table 8.7.2-1 Values of coefficient F for packings
8.7.3 Calculation of packing height
Table 8.7.3-1 n integrals
8.7.4 Applications
Example 8.7.4-1 Analytical calculation of interfacial
concentration
Example 8.7.4-2 Analytical determination of number of
transfer units: straight operating and equilibrium lines
Example 8.7.4-3 Effect of change of L/G on outlet
composition
Example 8.7.4-4 Design of absorber
Example 8.7.4-5 Economic optimization of an absorber
8.8 Mass Transfer with Chemical Reaction
Figure 8.8-1 Diffusion in a membrane  


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