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| Appendix A: Vector and Tensor Notation | ||||||||
|---|---|---|---|---|---|---|---|---|
| Section A.1 | Section A.2 | Section A.3 | Section A.4 | Section A.5 | Section A.6 | Section A.7 | ||
| Exercise 1 | Exercise 1 | Exercise 7 | Exercise 1 | Exercise 1 | Exercise 7 | Exercise 1 | Exercise 1 | Exercise 1 |
| Exercise 2 | Exercise 2 | Exercise 2 | Exercise 2 | Exercise 8 | Exercise 2 | Exercise 2 | Exercise 2 | |
| Exercise 3 | Exercise 3 | Exercise 3 | Exercise 3 | Exercise 9 | Exercise 3 | Exercise 3 | ||
| Exercise 4 | Exercise 4 | Exercise 4 | Exercise 4 | Exercise 10 | Exercise 4 | Exercise 4 | ||
| Exercise 5 | Exercise 5 | Exercise 5 | Exercise 5 | Exercise 5 | ||||
| Exercise 6 | Exercise 6 | Exercise 6 | ||||||
| Chapter 1: Viscosity and the Mechanisms of Momentum Transport | |
|---|---|
| Problem 1A.1: Estimation of dense-gas viscosity | Problem 1A.2: Estimation of the viscosity of methyl fluoride |
| Problem 1A.3: Computation of the viscosities of gases at low density | Problem 1A.4: Gas-mixture viscosities at low density |
| Problem 1A.5: Viscosities of chlorine-air mixtures at low density | Problem 1A.6: Estimation of liquid viscosity |
| Problem 1A.7: Molecular velocity and mean free path | Problem 1B.1: Velocity profiles and the stress components |
| Problem 1B.2: A fluid in a state of rigid rotation | Problem 1B.3: Viscosity of suspensions |
| Problem 1C.1: Some consequences of the Maxwell-Boltzmann distribution | Problem 1C.2: The wall collision frequency |
| Problem 1C.3: Pressure of an ideal gas | Problem 1D.1: Uniform rotation of a fluid |
| Problem 1D.2: Force on a surface of arbitrary orientation | |
| Chapter 2: Shell Momentum Balances and Velocity Distributions in Laminar Flow | |
|---|---|
| Problem 2A.1: Thickness of a falling film | Problem 2A.2: Determination of capillary radius by flow measurement |
| Problem 2A.3: Volume flow rate through an annulus | Problem 2A.4: Loss of catalyst particles in stack gas |
| Problem 2B.1: Different choice of coordinates for the falling film problem | Problem 2B.2: Alternate procedure for solving flow problems |
| Problem 2B.3: Laminar flow in a narrow slit | Problem 2B.4: Laminar slit flow with a moving wall ("plane Couette flow") |
| Problem 2B.5: Interrelation of slit and annulus formulas | Problem 2B.6: Flow of a film on the outside of a circular tube |
| Problem 2B.7: Annular flow with inner cylinder moving axially | Problem 2B.8: Analysis of a capillary flowmeter |
| Problem 2B.9: Low-density phenomena in compressible tube flow | Problem 2B.10: Incompressible flow in a slightly tapered tube |
| Problem 2B.11: The cone-and-plate viscometer | Problem 2B.12: Flow of a fluid in a network of tubes |
| Problem 2C.1: Performance of an electric dust collector | Problem 2C.2: Residence time distribution in tube flow |
| Problem 2C.3: Velocity distribution in a tube | Problem 2C.4: Falling-cylinder viscometer |
| Problem 2C.5: Falling film on a conical surface | Problem 2C.6: Rotating cone pump |
| Problem 2C.7: A simple rate-of-climb indicator | Problem 2D.1: Rolling-ball viscometer |
| Problem 2D.2: Drainage of liquids | |
| Chapter 3: The Equations of Change for Isothermal Systems | |
|---|---|
| Problem 3A.1: Torque required to turn a friction bearing | Problem 3A.2: Friction loss in bearings |
| Problem 3A.3: Effect of altitude on air pressure | Problem 3A.4: Viscosity determination with a rotating-cylinder viscometer |
| Problem 3A.5: Fabrication of a parabolic mirror | Problem 3A.6: Scale-up of an agitated tank |
| Problem 3A.7: Air entrainment in a draining tank | Problem 3B.1: Flow between coaxial cylinders and concentric spheres |
| Problem 3B.2: Laminar flow in a triangular duct | Problem 3B.3: Laminar flow in a square duct |
| Problem 3B.4: Creeping flow between two concentric spheres | Problem 3B.5: Parallel-disk viscometer |
| Problem 3B.6: Circulating axial flow in an annulus | Problem 3B.7: Momentum fluxes for creeping flow into a slot |
| Problem 3B.8: Velocity distribution for creeping flow toward a slot | Problem 3B.9: Slow transverse flow around a cylinder |
| Problem 3B.10: Radial flow between parallel disks | Problem 3B.11: Radial flow between two coaxial cylinders |
| Problem 3B.12: Pressure distribution in incompressible fluids | Problem 3B.13: Flow of a fluid through a sudden contraction |
| Problem 3B.14: Torricelli's equation for efflux from a tank | Problem 3B.15: Shape of free surface in tangential annular flow |
| Problem 3B.16: Flow in a slit with uniform cross flow | Problem 3C.1: Parallel-disk compression viscometer |
| Problem 3C.2: Normal stresses at solid surfaces for compressible fluids | Problem 3C.3: Deformation of a fluid line |
| Problem 3C.4: Alternative methods of solving the Couette viscometer problem by use of angular momentum concepts | Problem 3C.5: Two-phase interfacial boundary conditions |
| Problem 3D.1: Derivation of the equations of change by integral theorems | Problem 3D.2: The equation of change for vorticity |
| Problem 3D.3: Alternate form of the equation of motion | |
| Chapter 4: Velocity Distributions with More Than One Independent Variable | |
|---|---|
| Problem 4A.1: Time for attainment of steady state in tube flow | Problem 4A.2: Velocity near a moving sphere |
| Problem 4A.3: Construction of streamlines for the potential around a cylinder | Problem 4A.4: Comparison of exact and approximate profiles for flow along a flat plate |
| Problem 4A.5: Numerical demonstration of the von Kármán momentum balance | Problem 4A.6: Use of boundary-layer formulas |
| Problem 4A.7: Entrance flow in conduits | Problem 4B.1: Flow of a fluid with a suddenly applied constant wall stress |
| Problem 4B.2: Flow near a wall suddenly set in motion (approximate solution) | Problem 4B.3: Creeping flow around a spherical bubble |
| Problem 4B.4: Use of the vorticity equation | Problem 4B.5: Steady potential flow around a stationary sphere |
| Problem 4B.6: Potential flow near a stagnation point | Problem 4B.7: Vortex flow |
| Problem 4B.8: The flow field about a line source | Problem 4B.9: Checking solutions to unsteady flow problems |
| Problem 4C.1: Laminar entrance flow in a slit | Problem 4C.2: Torsional oscillatory viscometer |
| Problem 4C.3: Darcy's equation for flow through porous media | Problem 4C.4: Radial flow through a porous medium |
| Problem 4D.1: Flow near an oscillating wall | Problem 4D.2: Start-up of laminar flow in a circular tube |
| Problem 4D.3: Flows in the disk-and-tube system | Problem 4D.4: Unsteady annular flows |
| Problem 4D.5: Stream functions for three-dimensional flow | |
| Chapter 5: Velocity Distributions in Turbulent Flow | |
|---|---|
| Problem 5A.1: Pressure drop needed for laminar-turbulent transition | Problem 5A.2: Velocity distribution in turbulent pipe flow |
| Problem 5B.1: Average flow velocity in turbulent tube flow | Problem 5B.2: Mass flow rate in a turbulent circular jet |
| Problem 5B.3: The eddy viscosity expression in the viscous sublayer | Problem 5C.1: Two-dimensional turbulent jet |
| Problem 5C.2: Axial turbulent flow in an annulus | Problem 5C.3: Instability in a simple mechanical system |
| Problem 5D.1: Derivation of the equation of change for the Reynolds stresses | Problem 5D.2: Kinetic energy of turbulence |
| Chapter 6: Interphase Transport in Isothermal Systems | |
|---|---|
| Problem 6A.1: Pressure drop required for a pipe with fittings | Problem 6A.2: Pressure difference required for flow in pipe with elevation change |
| Problem 6A.3: Flow rate for a given pressure drop | Problem 6A.4: Motion of a sphere in a liquid |
| Problem 6A.5: Sphere diameter for a given terminal velocity | Problem 6A.6: Estimation of void fraction of a packed column |
| Problem 6A.7: Estimation of pressure drops in annular flow | Problem 6A.8: Force on a water tower in a gale |
| Problem 6A.9: Flow of gas through a packed column | Problem 6A.10: Determination of pipe diameter |
| Problem 6B.1: Effect of error in friction factor calculations | Problem 6B.2: Friction factor for flow along a flat plate |
| Problem 6B.3: Friction factor for laminar flow in a slit | Problem 6B.4: Friction factor for a rotating disk |
| Problem 6B.5: Turbulent flow in horizontal pipes | Problem 6B.6: Inadequacy of mean hydraulic radius for laminar flow |
| Problem 6B.7: Falling sphere in Newton's drag-law region | Problem 6B.8: Design of an experiment to verify the f vs. Re chart for spheres |
| Problem 6B.9: Friction factor for flow past an infinite cylinder | Problem 6C.1: Two-dimensional particle trajectories |
| Problem 6C.2: Wall effects for a sphere falling in a cylinder | Problem 6C.3: Power input to an agitated tank |
| Problem 6D.1: Friction factor for a bubble in a clean liquid | |
| Chapter 7: Macroscopic Balances for Isothermal Flow Systems | |
|---|---|
| Problem 7A.1: Pressure rise in a sudden enlargement | Problem 7A.2: Pumping a hydrochloric acid solution |
| Problem 7A.3: Compressible gas flow in a cylindrical pipe | Problem 7A.4: Incompressible flow in an annulus |
| Problem 7A.5: Force on a U-bend | Problem 7A.6: Flow-rate calculation |
| Problem 7A.7: Evaluation of various velocity averages from Pitot tube data | Problem 7B.1: Velocity averages from the 1/7 power law |
| Problem 7B.2: Relation between force and viscous loss for flow in conduits of variable cross section | Problem 7B.3: Flow through a sudden enlargement |
| Problem 7B.4: Flow between two tanks | Problem 7B.5: Revised design of an air duct |
| Problem 7B.6: Multiple discharge into a common conduit | Problem 7B.7: Inventory variations in a gas reservoir |
| Problem 7B.8: Change in liquid height with time | Problem 7B.9: Draining of a cylindrical tank with exit pipe |
| Problem 7B.10: Efflux time for draining a conical tank | Problem 7B.11: Disintegration of wood chips |
| Problem 7B.12: Criterion for vapor-free flow in a pipeline | Problem 7C.1: End corrections in tube viscometers |
| Problem 7D.1: Derivation of the macroscopic balances from the equations of change | |
| Chapter 8: Polymeric Liquids | |
|---|---|
| Problem 8A.1: Flow of a polyisoprene solution in a pipe | Problem 8A.2: Pumping of a polyethylene oxide solution |
| Problem 8B.1: Flow of a polymeric film | Problem 8B.2: Power law flow in a narrow slit |
| Problem 8B.3: Non-Newtonian flow in an annulus | Problem 8B.4: Flow of a polymeric liquid in a tapered tube |
| Problem 8B.5: Slit flow of a Bingham fluid | Problem 8B.6: Derivation of the Buckingham-Reiner equation |
| Problem 8B.7: The complex-viscosity components for the Jeffreys fluid | Problem 8B.8: Stress relaxation after cessation of shear flow |
| Problem 8B.9: Draining of a tank with an exit pipe | Problem 8B.10: The Giesekus model |
| Problem 8C.1: The cone-and-plate viscometer | Problem 8C.2: Squeezing flow between parallel disks |
| Problem 8C.3: Verification of Giesekus viscosity function | Problem 8C.4: Tube Flow for the Oldroyd 6-Constant Model |
| Problem 8C.5: Chain Models with Rigid-Rod Connectors | |
| Appendix A: Vector and Tensor Notation | ||||||||
|---|---|---|---|---|---|---|---|---|
| Section A.1 | Section A.2 | Section A.3 | Section A.4 | Section A.5 | Section A.6 | Section A.7 | ||
| Exercise 1 | Exercise 1 | Exercise 7 | Exercise 1 | Exercise 1 | Exercise 7 | Exercise 1 | Exercise 1 | Exercise 1 |
| Exercise 2 | Exercise 2 | Exercise 2 | Exercise 2 | Exercise 8 | Exercise 2 | Exercise 2 | Exercise 2 | |
| Exercise 3 | Exercise 3 | Exercise 3 | Exercise 3 | Exercise 9 | Exercise 3 | Exercise 3 | ||
| Exercise 4 | Exercise 4 | Exercise 4 | Exercise 4 | Exercise 10 | Exercise 4 | Exercise 4 | ||
| Exercise 5 | Exercise 5 | Exercise 5 | Exercise 5 | Exercise 5 | ||||
| Exercise 6 | Exercise 6 | Exercise 6 | ||||||
| Chapter 9: Thermal Conductivity and the Mechanisms of Energy Transport | |
|---|---|
| Problem 9A.1: Prediction of thermal conductivities of gases at low density | Problem 9A.2: Computation of the Prandtl numbers for gases at low density |
| Problem 9A.3: Estimation of the thermal conductivity of a dense gas | Problem 9A.4: Prediction of the thermal conductivity of a gas mixture |
| Problem 9A.5: Estimation of the thermal conductivity of a pure liquid | Problem 9A.6: Calculation of the Lorenz number |
| Problem 9A.7: Corroboration of the Wiedemann-Franz-Lorenz law | Problem 9A.8: Thermal conductivity and Prandtl number of a polyatomic gas |
| Problem 9A.9: Thermal conductivity of gaseous chlorine | Problem 9A.10: Thermal conductivity of chlorine-air mixtures |
| Problem 9A.11: Thermal conductivity of quartz sand | Problem 9A.12: Calculation of molecular diameters from transport properties |
| Problem 9C.1: Enskog theory for dense gases | |
| Chapter 10: Shell Energy Balances and Temperature Distributions in Solids and Laminar Flow | |
|---|---|
| Problem 10A.1: Heat loss from an insulated pipe | Problem 10A.2: Heat loss from a rectangular fin |
| Problem 10A.3: Maximum temperature in a lubricant | Problem 10A.4: Current-carrying capacity of a wire |
| Problem 10A.5: Free convection velocity | Problem 10A.6: Insulating power of a wall |
| Problem 10A.7: Viscous heating in a ball-point pen | Problem 10B.1: Heat conduction from a sphere to a stagnant fluid |
| Problem 10B.2: Viscous heating in slit flow | Problem 10B.3: Heat conduction in a nuclear fuel rod assembly |
| Problem 10B.4: Heat conduction in an annulus | Problem 10B.5: Viscous heat generation in a polymer melt |
| Problem 10B.6: Insulation thickness for a furnace wall | Problem 10B.7: Forced-convection heat transfer in flow between parallel plates |
| Problem 10B.8: Electrical heating of a pipe | Problem 10B.9: Plug flow with forced-convection heat transfer |
| Problem 10B.10: Free convection in an annulus of finite height | Problem 10B.11: Free convection with temperature-dependent viscosity |
| Problem 10B.12: Heat conduction with temperature-dependent thermal conductivity | Problem 10B.13: Flow reactor with exponentially temperature-dependent source |
| Problem 10B.14: Evaporation loss from an oxygen tank | Problem 10B.15: Radial temperature gradients in an annular chemical reactor |
| Problem 10B.14: Evaporation loss from an oxygen tank | Problem 10B.15: Radial temperature gradients in an annular chemical reactor |
| Problem 10B.16: Temperature distribution in a hot-wire anemometer | Problem 10B.17: Non-Newtonian flow with forced-convection heat transfer |
| Problem 10B.18: Reactor temperature profiles with axial heat flux | Problem 10C.1: Heating of an electric wire with temperature-dependent electrical and thermal conductivity |
| Problem 10C.2: Viscous heating with temperature-dependent viscosity and thermal conductivity | Problem 10C.3: Viscous heating in a cone-and-plate viscometer |
| Problem 10D.1: Heat loss from a circular fin | Problem 10D.2: Duct flow with constant wall heat flux and arbitrary velocity distribution |
| Chapter 11: The Equations of Change for Nonisothermal Systems | |
|---|---|
| Problem 11A.1: Temperature in a friction bearing | Problem 11A.2: Viscosity variation and velocity gradients in a nonisothermal film |
| Problem 11A.3: Transpiration cooling | Problem 11A.4: Free-convection heat loss from a vertical surface |
| Problem 11A.5: Velocity, temperature, and pressure changes in a shock wave | Problem 11A.6: Adiabatic frictionless compression of an ideal gas |
| Problem 11A.7: Effect of free convection on the insulating value of a horizontal air space | Problem 11B.1: Adiabatic frictionless processes in an ideal gas |
| Problem 11B.2: Viscous heating in laminar tube flow (asymptotic solutions) | Problem 11B.3: Velocity distribution in a nonisothermal film |
| Problem 11B.4: Heat conduction in a spherical shell | Problem 11B.5: Axial heat conduction in a wire |
| Problem 11B.6: Transpiration cooling in a planar system | Problem 11B.7: Reduction of evaporation losses by transpiration |
| Problem 11B.8: Temperature distribution in an embedded sphere | Problem 11B.9: Heat flow in a solid bounded by two conical surfaces |
| Problem 11B.10: Freezing of a spherical drop | Problem 11B.11: Temperature rise in a spherical catalyst pellet |
| Problem 11B.12: Stability of an exothermic reaction system | Problem 11B.13: Laminar annular flow with constant wall heat flux |
| Problem 11B.14: Unsteady-state heating of a sphere | Problem 11B.15: Dimensionless variables for free convection |
| Problem 11C.1: The speed of propagation of sound waves | Problem 11C.2: Free convection in a slot |
| Problem 11C.3: Tangential annular flow of a highly viscous liquid | Problem 11C.4: Heat conduction with variable thermal conductivity |
| Problem 11C.5: Effective thermal conductivity of a solid with spherical inclusions | Problem 11C.6: Interfacial boundary conditions |
| Problem 11C.7: Effect of surface-tension gradients on a falling film | Problem 11D.1: Equation of change for entropy |
| Problem 11D.2: Viscous heating in laminar tube flow | Problem 11D.3: Derivation of the energy equation using integral theorems |
| Chapter 12: Temperature Distributions with More than One Independent Variable | |
|---|---|
| Problem 12A.1: Unsteady-state heat conduction in an iron sphere | Problem 12A.2: Comparison of the two slab solutions for short times |
| Problem 12A.3: Bonding with a thermosetting adhesive | Problem 12A.4: Quenching of a steel billet |
| Problem 12A.5: Measurement of thermal diffusivity from amplitude of temperature oscillations | Problem 12A.6: Forced convection from a sphere in creeping flow |
| Problem 12B.1: Measurement of thermal diffusivity in an unsteady-state experiment | Problem 12B.2: Two-dimensional forced convection with a line heat source |
| Problem 12B.3: Heating of a wall (constant wall heat flux) | Problem 12B.4: Heat transfer from a wall to a falling film (short contact time limit) |
| Problem 12B.5: Temperature in a slab with heat production | Problem 12B.6: Forced convection in slow flow across a cylinder |
| Problem 12B.7: Timetable for roasting turkey | Problem 12B.8: Use of asymptotic boundary layer solution |
| Problem 12B.9: Non-Newtonian heat transfer with constant wall heat flux (asymptotic solution for small axial distances) | Problem 12C.1: Product solutions for unsteady heat conduction in solids |
| Problem 12C.2: Heating of a semi-infinite slab with variable thermal conductivity | Problem 12C.3: Heat conduction with phase change (the Neumann-Stefan problem) |
| Problem 12C.4: Viscous heating in oscillatory flow | Problem 12C.5: Solar heat penetration |
| Problem 12C.6: Heat transfer in a falling non-Newtonian film | Problem 12D.1: Unsteady-state heating of a slab (Laplace transform method) |
| Problem 12D.2: The Graetz-Nusselt problem | Problem 12D.3: The Graetz-Nusselt problem (asymptotic solution for large z) |
| Problem 12D.4: The Graetz-Nusselt problem (asymptotic solution for small z) | Problem 12D.5: The Graetz problem for flow between parallel plates |
| Problem 12D.6: The constant wall heat flux problem for parallel plates | Problem 12D.7: Asymptotic solution for small z for laminar tube flow with constant heat flux |
| Problem 12D.8: Forced conduction heat transfer from a flat plate (thermal boundary layer extends beyond the momentum boundary layer) | |
| Chapter 13: Temperature Distributions in Turbulent Flow | |
|---|---|
| Problem 13B.1: Wall heat flux for turbulent flow in tubes (approximate) | Problem 13B.2: Wall heat flux for turbulent flow in tubes |
| Problem 13C.1: Wall heat flux for turbulent flow between two parallel plates | Problem 13D.1: The temperature profile for turbulent flow in tubes |
| Chapter 14: Interphase Transport in Nonisothermal Systems | |
|---|---|
| Problem 14A.1: Average heat transfer coefficients | Problem 14A.2: Heat transfer in laminar tube flow |
| Problem 14A.3: Effect of flow rate on exit temperature from a heat exchanger | Problem 14A.4: Local heat transfer coefficient for turbulent forced convection in a tube |
| Problem 14A.5: Heat transfer from condensing vapors | Problem 14A.6: Forced-convection heat transfer from an isolated sphere |
| Problem 14A.7: Free convection heat transfer from an isolated sphere | Problem 14A.8: Heat loss by free convection from a horizontal pipe immersed in a liquid |
| Problem 14A.9: The ice-fisherman on Lake Mendota | Problem 14B.1: Limiting local Nusselt number for plug flow with constant heat flux |
| Problem 14B.2: Local overall heat transfer coefficient | Problem 14B.3: The hot-wire anemometer |
| Problem 14B.4: Dimensional analysis | Problem 14B.5: Relation between hloc and hln |
| Problem 14B.6: Heat loss by free convection from a pipe | Problem 14C.1: The Nusselt expression for film condensation heat transfer coefficients |
| Problem 14C.2: Heat transfer correlations for agitated tanks | Problem 14D.1: Heat transfer from an oblate ellipsoid of revolution |
| Chapter 15: Macroscopic Balances for Nonisothermal Systems | |
|---|---|
| Problem 15A.1: Heat transfer in double-pipe heat exchangers | Problem 15A.2: Adiabatic flow of natural gas in a pipeline |
| Problem 15A.3: Mixing of two ideal-gas streams | Problem 15A.4: Flow through a Venturi tube |
| Problem 15A.5: Free batch expansion of a compressible fluid | Problem 15A.6: Heating of air in a tube |
| Problem 15A.7: Operation of a simple double-pipe heat exchanger | Problem 15B.1: Performance of a double-pipe heat exchanger with variable overall heat transfer coefficient |
| Problem 15B.2: Pressure drop in turbulent flow in a slightly converging tube | Problem 15B.3: Steady flow of ideal gases in ducts of constant cross section |
| Problem 15B.4: The Mach number in the mixing of two fluid streams | Problem 15B.5: Limiting discharge rates for Venturi meters |
| Problem 15B.6: Flow of a compressible fluid through a convergent-divergent nozzle | Problem 15B.7: Transient thermal behavior of a chromatographic device |
| Problem 15B.8: Continuous heating of a slurry in an agitated tank | Problem 15C.1: Parallel-counterflow heat exchangers |
| Problem 15C.2: Discharge of air from a large tank | Problem 15C.3: Stagnation temperature |
| Problem 15D.1: The macroscopic entropy balance | Problem 15D.2: Derivation of the macroscopic energy balance |
| Problem 15D.3: Operation of a heat-exchange device | Problem 15D.4: Discharge of a gas from a moving tank |
| Problem 15D.5: The classical Bernoulli equation | |
| Chapter 16: Energy Transport by Radiation | |
|---|---|
| Problem 16A.1: Approximation of a black body by a hole in a sphere | Problem 16A.2: Efficiency of a solar engine |
| Problem 16A.3: Radiant heating requirement | Problem 16A.4: Steady-state temperature of a roof |
| Problem 16A.5: Radiation errors in temperature measurements | Problem 16A.6: Surface temperatures on the Earth's moon |
| Problem 16B.1: Reference temperature for effective emissivity | Problem 16B.2: Radiation across an annular gap |
| Problem 16B.3: Multiple radiation shields | Problem 16B.4: Radiation and conduction through absorbing media |
| Problem 16B.5: Cooling of a black body in vacuo | Problem 16B.6: Heat loss from an insulated pipe |
| Problem 16C.1: Integration of the view-factor integral for a pair of disks | Problem 16D.1: Heat loss from a wire carrying an electric current |
| Appendix A: Vector and Tensor Notation | ||||||||
|---|---|---|---|---|---|---|---|---|
| Section A.1 | Section A.2 | Section A.3 | Section A.4 | Section A.5 | Section A.6 | Section A.7 | ||
| Exercise 1 | Exercise 1 | Exercise 7 | Exercise 1 | Exercise 1 | Exercise 7 | Exercise 1 | Exercise 1 | Exercise 1 |
| Exercise 2 | Exercise 2 | Exercise 2 | Exercise 2 | Exercise 8 | Exercise 2 | Exercise 2 | Exercise 2 | |
| Exercise 3 | Exercise 3 | Exercise 3 | Exercise 3 | Exercise 9 | Exercise 3 | Exercise 3 | ||
| Exercise 4 | Exercise 4 | Exercise 4 | Exercise 4 | Exercise 10 | Exercise 4 | Exercise 4 | ||
| Exercise 5 | Exercise 5 | Exercise 5 | Exercise 5 | Exercise 5 | ||||
| Exercise 6 | Exercise 6 | Exercise 6 | ||||||
| Chapter 17: Diffusivity and the Mechanisms of Mass Transport | |
|---|---|
| Problem 17A.1: Prediction of a low-density binary diffusivity | Problem 17A.2: Extrapolation of binary diffusivity to a very high temperature |
| Problem 17A.3: Self-diffusion in liquid mercury | Problem 17A.4: Schmidt numbers for binary gas mixtures at low density |
| Problem 17A.5: Estimation of diffusivity for a binary mixture at high density | Problem 17A.6: Diffusivity and Schmidt number for chlorine-air mixtures |
| Problem 17A.7: The Schmidt number for self-diffusion | Problem 17A.8: Correction of high-density diffusivity for temperature |
| Problem 17A.9: Prediction of critical cDAB values | Problem 17A.10: Estimation of liquid diffusivities |
| Problem 17B.1: Interrelation of composition variables in mixtures | Problem 17B.2: Relations among fluxes in multicomponent systems |
| Problem 17B.3: Relations between fluxes in binary systems | Problem 17B.4: Equivalence of various forms of Fick's law for binary mixtures |
| Problem 17C.1: Mass flux with respect to volume average velocity | Problem 17C.2: Mass flux with respect to the solvent velocity |
| Problem 17C.3: Determination of Lennard-Jones potential parameters from diffusivity data of a binary gas mixture | |
| Chapter 18: Concentration Distributions in Solids and in Laminar Flow | |
|---|---|
| Problem 18A.1: Evaporation Rate | Problem 18A.2: Sublimation of small iodine spheres in still air |
| Problem 18A.3: Estimating the error in calculating the absorption rate | Problem 18A.4: Chlorine absorption in a falling film |
| Problem 18A.5: Measurement of diffusivity by the point-source method | Problem 18A.6: Determination of diffusivity for ether-air system |
| Problem 18A.7: Mass flux from a circulating bubble | Problem 18B.1: Diffusion through a stagnant film---alternate derivation |
| Problem 18B.2: Error in neglecting the convection term in evaporation | Problem 18B.3: Effect of mass transfer rate on the concentration profiles |
| Problem 18B.4: Absorption with chemical reaction | Problem 18B.5: Absorption of chlorine by cyclohexene |
| Problem 18B.6: Two-bulb experiment for measuring gas diffusivity---quasi-steady-state analysis | Problem 18B.7: Diffusion from a suspended droplet |
| Problem 18B.8: Method for separating helium from natural gas | Problem 18B.9: Rate of leaching |
| Problem 18B.10: Constant-evaporating mixtures | Problem 18B.11: Diffusion with fast second-order reaction |
| Problem 18B.12: A sectioned-cell experiment for measuring gas-phase diffusivity | Problem 18B.13: Tarnishing of metal surfaces |
| Problem 18B.14: Effectiveness factors for thin disks | Problem 18B.15: Diffusion and heterogeneous reaction in a slender cylindrical tube with a closed end |
| Problem 18B.16: Effect of temperature and pressure on evaporation rate | Problem 18B.17: Reaction rates in large and small particles |
| Problem 18B.18: Evaporation rate for small mole fraction of the volatile liquid | Problem 18B.19: Oxygen uptake by a bacterial aggregate |
| Problem 18C.1: Diffusion from a point source in a moving stream | Problem 18C.2: Diffusion and reaction in a partially impregnated catalyst |
| Problem 18C.3: Absorption rate in a falling film | Problem 18C.4: Estimation of the required length of an isothermal reactor |
| Problem 18C.5: Steady-state evaporation | Problem 18D.1: Effectiveness factors for long cylinders |
| Problem 18D.2: Gas absorption in a falling film with chemical reaction | |
| Chapter 19: Equations of Change for Multicomponent Systems | |
|---|---|
| Problem 19A.1: Dehumidification of air | Problem 19B.1: Steady-state evaporation |
| Problem 19B.2: Gas absorption with chemical reaction | Problem 19B.3: Concentration-dependent diffusivity |
| Problem 19B.4: Oxidation of silicon | Problem 19B.5: The Maxwell-Stefan equations for multicomponent gas mixtures |
| Problem 19B.6: Diffusion and chemical reaction in a liquid | Problem 19B.7: Various forms of the species continuity equation |
| Problem 19C.1: Alternate form of the binary diffusion equation | Problem 19D.1: Derivation of the equation of continuity |
| Problem 19D.2: Derivation of the equation of change for temperature for a multicomponent system | Problem 19D.3: Gas separation by atmolysis or "sweep diffusion" |
| Problem 19D.4: Steady-state diffusion from a rotating disk | |
| Chapter 20: Concentration Distributions with More than One Independent Variable | |
|---|---|
| Problem 20A.1: Measurement of diffusivity by unsteady-state evaporation | Problem 20A.2: Absorption of oxygen from a growing bubble |
| Problem 20A.3: Rate of evaporation of n-octane | Problem 20A.4: Effect of bubble size on interfacial composition |
| Problem 20A.5: Absorption with rapid second-order reaction | Problem 20A.6: Rapid forced-convection mass transfer into a laminar boundary layer |
| Problem 20A.7: Slow forced-convection mass tranfer into a laminar boundary layer | Problem 20B.1: Extension of the Arnold problem to account for interphase transfer of both species |
| Problem 20B.2: Extension of the Arnold problem to nonisothermal diffusion | Problem 20B.3: Stoichiometric boundary condition for rapid irreversible reaction |
| Problem 20B.4: Taylor dispersion in slit flow | Problem 20B.5: Diffusion from an instantaneous point source |
| Problem 20B.6: Unsteady diffusion with first-order chemical reaction | Problem 20B.7: Simultaneous momentum, heat, and mass transfer: alternate boundary conditions |
| Problem 20B.8: Absorption from a pulsating bubble | Problem 20B.9: Verification of the solution of the Taylor-dispersion equation |
| Problem 20C.1: Order-of-magnitude analysis of gas absorption from a growing bubble | Problem 20C.2: Effect of surface curvature on absorption from a growing bubble |
| Problem 20C.3: Absorption with chemical reaction in a semi-infinite medium | Problem 20C.4: Design of fluid control circuits |
| Problem 20C.5: Dissociation of a gas caused by a temperature gradient | Problem 20D.1: Two-bulb experiment for measuring gas diffusivities-analytical solution |
| Problem 20D.2: Unsteady-state interphase diffusion | Problem 20D.3: Critical size of an autocatalytic system |
| Problem 20D.4: Dispersion of a broad pulse in steady, laminar axial flow in a tube | Problem 20D.5: Velocity divergence in interfacially embedded coordinates |
| Chapter 21: Concentration Distributions in Turbulent Flow | |
|---|---|
| Problem 21A.1: Determination of eddy diffusivity | Problem 21A.2: Heat and mass transfer analogy |
| Problem 21B.1: Wall mass flux for turbulent flow with no chemical reactions | Problem 21B.2: Alternate expressions for the turbulent mass flux |
| Problem 21B.3: An asymptotic expression for the turbulent mass flux | Problem 21B.4: Deposition of silver from a turbulent stream |
| Problem 21B.5: Mixing-length expression for the velocity profile | |
| Chapter 22: Interphase Transport in Nonisothermal Mixtures | |
|---|---|
| Problem 22A.1: Prediction of mass transfer coefficients in closed channels | Problem 22A.2: Calculation of gas composition from psychrometric data |
| Problem 22A.3: Calculating the inlet air temperature for drying in a fixed bed | Problem 22A.4: Rate of drying of granular solids in a fixed bed |
| Problem 22B.1: Evaporation of a freely falling drop | Problem 22B.2: Effect of radiation on psychrometric measurements |
| Problem 22B.3: Film theory with variable transport properties | Problem 22B.4: An evaporative ice maker |
| Problem 22B.5: Oxygen stripping | Problem 22B.6: Controlling diffusional resistance |
| Problem 22B.7: Determination of diffusivity | Problem 22B.8: Marangoni effects in condensation of vapors |
| Problem 22B.9: Film model for spheres | Problem 22B.10: Film model for cylinders |
| Problem 22C.1: Calculation of ultrafiltration rates | |
| Chapter 23: Macroscopic Balances for Multicomponent Systems | |
|---|---|
| Problem 23A.1: Expansion of a gas mixture: very slow reaction rate | Problem 23A.2: Height of a packed-tower absorber |
| Problem 23B.1: Effective average driving forces in a gas absorber | Problem 23B.2: Expansion of a gas mixture: very fast reaction rate |
| Problem 23B.3: Startup of a chemical reactor | Problem 23B.4: Irreversible first-order reaction in a continuous reactor |
| Problem 23B.5: Mass and enthalpy balances in an adiabatic splitter | Problem 23B.6: Flow distribution in an ideal cascade |
| Problem 23B.7: Isotope separation and the value function | Problem 23C.1: Irreversible second-order reaction in an agitated tank |
| Problem 23C.2: Protein purification | Problem 23C.3: Physical significance of the zeroth and first moments |
| Problem 23C.4: Analogy between the unsteady operation of an adsorption column and a cross-flow heat exchanger | Problem 23D.1: Unsteady-state operation of a packed column |
| Problem 23D.2: Additivity of the lower moments | Problem 23D.3: Start-up of a chemical reactor |
| Problem 23D.4: Transient behavior of N reactors in series | |
| Chapter 24: Other Mechanisms for Mass Transport | |
|---|---|
| Problem 24A.1: Thermal diffusion | Problem 24A.2: Ultracentrifugation of proteins |
| Problem 24A.3: Ionic diffusivities | Problem 24B.1: The dimensions of the Lorentz force |
| Problem 24B.2: Junction potentials | Problem 24B.3: Donnan exclusion |
| Problem 24B.4: Osmotic pressure | Problem 24B.5: Permeability of a perfectly selective filtration membrane |
| Problem 24B.6: Model insensitivity | Problem 24C.1: Expressions for the mass flux |
| Problem 24C.2: Differential centrifugation | Problem 24C.3: Transport characteristics of sodium chloride |
| Problem 24C.4: Departures from electroneutrality | Problem 24C.5: Dielectrophoretic driving forces |
| Problem 24C.6: Effects of small inclusions in a dielectric medium | Problem 24C.7: Frictionally induced selective filtration |
| Problem 24C.8: Thermodynamically induced selective filtration | Problem 24C.9: Facilitated transport |
| Problem 24D.1: Entropy flux and entropy production | |
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