Momentum, Heat, and Mass Transfer Fundamentals

by Greenkorn; Robert

• ISBN13: 9780824719722
• ISBN10: 0824719727
• Edition: 1st
• Format: Hardcover
• Copyright: 1999-02-23
• Publisher: CRC Press

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