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# Solutions to Transport Phenomena 2nd Revised Edition by BSL

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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 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