Note: Book Chapters that correspond to the listed course outcome(s) are provided in square brackets [].

Transport Phenomena refers to the study of the motion and balance of momentum, heat, and mass in engineering problems. These three modes of transport are studied concurrently for several reasons: they have similar molecular origins, they yield similar governing equations/principles, they often occur simultaneously, and they require similar mathematical/conceptual tools.

In this section we define and introduce several conceptual tools necessary for studying transport, and answer several pertinent engineering questions:

What are my options in visualizing/conceptualizing the movement of momentum, heat, mass?

- Discuss the relationship between Thermodynamics and Transport Processes
- Summarize the critical aspects of continuum mechanics
- Explain the continuum hypothesis and the origin of its breakdown [Ch 1.1, 1.2]
- Define and give examples of (fluid) property fields [Ch 1.3]

- Differentiate between an Eulerian and Lagrangian description
- Explain the difference between an Eulerian and Lagrangian viewpoints [Ch 3.2]
- Identify and differentiate between streaklines, streamlines, and pathlines [Ch 3.3, 3.4]
- Mathematically derive streaklines, streamlines, and pathlines from an Eulerian velocity field
- Define systems and control volumes and identify when each is a useful frame of reference [Ch 3.5]

By what underlying mechanisms does this transport take place? [Ch 3.1]

- Explain and give examples of the three primary modes of heat transfer [Ch 15.1-15.4]
- Describe the primary modes of mass transfer [Ch 24.1-24.3]
- Identify the underlying forces and conceptual hurdles in
momentum transport
- Name and explain the origin of forces acting on fluids in a control volume [Ch 2.1-2.4]
- Define laminar, turbulent, and transition flow regimes [Ch 12.1]
- Distinguish between external and internal flows
- Explain the meaning of fully-developed flow and calculate the entrance region length necessary for a pipe flow

What global understanding of the problem can be achieved through simple reasoning?

- Apply dimensional analysis to generalize problem descriptions
- Perform simple dimensional analysis, using the Buckingham Pi method [Ch 11.1-11.4]
- Calculate the Reynolds Number and use it to predict flow regimes

Much of Transport Phenomena deals with the *exchange* of
momentum, mass, or heat between two (or many) objects. Often, the
most mathematically simple way to consider how and how fast
exchanges take place is to look at *driving forces* and
*resistances*.

In momentum transport, we are interested in driving forces that arise from differences in pressure and/or velocity.

- Solve problems in fluid hydrostatics
- Derive the pressure field equation [2.1]
- Calculate the pressure distribution in a fluid or system of fluids that is at rest [2.2]
- Use Archimedes' principle to calculate buoyant forces on (partially) immersed objects [2.3-2.4]

- Use friction factors and/or drag coefficients to calculate
viscous (and pressure) forces in fluids [12.2, 13.2-13.4]
- Distinguish between lift, drag, skin friction, and form drag
- Calculate friction factors from correlations and read friction factors off of charts
- Use drag coefficient correlations and/or charts to calculate drag on submersed objects (external flows)
- Estimate frictional energy losses in pipes and pipe networks

In heat and mass transport, our driving forces arise from differences in concentration and temperature.

- Perform convection and convection/radiation problems
- Perform convective heat transfer calculations [15.3, 19.1, 19.2]
- Perform convective mass transfer calculations [24.3, 28.1, 28.2]
- Perform radiative heat transfer calculations [15.4, 23.1, 23.2, (23.7)]
- Calculate the thermal resistance and magnitude of heat flow in combined convective/radiative systems [15.5]

The mathematical analysis of the diffusion of heat, mass, or
momentum is incorporated into *constitutive laws* that
relate this diffusion to easily measurable quantities (like
temperature, velocity (pressure), and concentration).

- Use a resistor analogy to solve for heat flows [15.5, 17.1]
- Calculate the thermal resistance and magnitude of conductive heat flow/flux through a planar wall
- Calculate the thermal resistance and magnitude of conductive heat flow/flux through multiple planar walls
- Calculate the thermal resistance and magnitude of conductive heat flow/flux through a cylindrical shell
- Calculate the thermal resistance and magnitude of conductive heat flow/flux through a spherical shell
- Calculate the resistance and magnitude of heat flow in systems in which multiple modes of heat transfer are present
- Extend the resistor analogy to non-one-dimensional problems using shape factors [Ch 17.4]
- Determine the heat flow through these solids from their temperature profiles
- Use film theory and other correlations to obtain h [19.5]

- Explain and calculate viscous stresses [7.1, 7.2, 7.4]
- Calculate viscous stresses/forces from velocity distributions
- Identify Newtonian and non-Newtonian behavior from stress versus strain curves

- Solve diffusive mass flows problems
- Explain the difference between the total flux and the diffusive flux [24.1]
- Calculate the magnitude of diffusive mass flow/flux through a planar film in equimolar counter-diffusion [25.4]
- Calculate the magnitude of diffusive mass flow/flux through a
planar
*stagnant*film [26.1] - Calculate the magnitude of diffusive mass flow/flux for systems with non-zero bulk flow
- Calculate the magnitude of diffusive mass flow/flux through a cylindrical and spherical shells
- Use film theory and other correlations to obtain kc [28.6]
- Use the two-resistance model to perform fluid-fluid mass transfer calculations [29.1-29.3]
- Calculate mass/molar flows/fluxes from concentration profiles

A *microscopic* or *continuum* description of
transport requires that we examine "diffusion" of our conserved
quantities at the molecular level.

- Estimate transport properties from molecular calculations
- Explain the molecular origins of fluid viscosity and shear stresses.
- Estimate fluid viscosities [7.3]
- Explain the molecular origins of thermal and mass diffusion/conduction [15.2, 24.2]
- Estimate thermal and mass diffusivities/conductivities [15.2, 24.2]

Scaling up to solving problems using process equipment requires both continuum and macroscopic knowledge of transport, and is industrially quite significant.

- Analyze heat transfer equipment
- Distinguish between exchanger types [22.1]
- Solve the "thermodynamic" problem [22.2]
- Visualize the changing driving forces in co-current versus counter-current exchangers [22.2]
- Calculate the "average" driving force from the heat flow and resistance [22.2]
- Calculate the heat duty of an exchanger from the "average" driving force and total resistance [22.2]
- Calculate the heat flow in an exchanger from the exchanger's effectiveness [22.4]

- Analyze mass transfer equipment [31.5, 31.6]
- Calculate the mass exchanged in a well-mixed contactor or the time necessary to achieve a particular exchange
- Calculate the "average" driving force in a continuous contactor
- Calculate the mass exchange in a continuous contactor and/or the size of the column

Because Transport deals with *rates* it is often the case
that we must consider non-steady (or transient) operation (when the
rates do not exactly cancel). In this section, we examine
*scalar* transport (heat and mass transfer) where some
non-steady problems can be simplified significantly.

- Explain the utility of the Biot number [18.1]
- Identify "regimes" of transient response based on the value of the Biot number
- Use the "lumped" equation to solve "1D" transient heat transfer problems [18.1]
- Use the "lumped" equation to solve "1D" transient mass transfer problems [27.1]
- Use Gurney-Lurie charts to solve heat and mass transfer problems [18.2, 27.4]
- Use the semi-infinite approximation to solve both transient heat and mass problems for "short" times [18.1, 27.2]

Shell or integral (macroscopic) balances are often relatively simple to solve, both conceptually and mechanically, as only limited data is necessary. At the same time, many problems require only the level of detail that may be extracted from these types of balances and thus they represent powerful tools.

- Perform control volume (or macroscopic) balances
- Derive and use a macroscopic mass balance (continuity equation) [4.1, 4.2]
- Derive and use a macroscopic momentum balance [5.1, 5.2]
- Derive and use a macroscopic energy balance [6.1, 6.2]

- Use the General Mechanical Energy Balance Equation to perform
calculations on simple pipe networks and/or process problems [6.3]
- Explain the connection between a macroscopic energy balance and Bernoulli's Equation
- Use Bernoulli's Equation to calculate velocities, pressures, or height changes in flowing fluid systems
- Extend the Bernoulli's Equation for more general cases (i.e., write and use the mechanical form of the macroscopic energy balance equation)

- Solve heat transfer problems on macroscopic bodies [p241-243]

- Determine the efficiency of a fin
- Calculate the heat flow through a fin from the fin's efficiency

Differential balances, although more complex to solve, can yield a tremendous wealth of information about ChE processes. General balance equations for each of the modes of transport can easily be derived either directly from shell balances or via control volume analysis. Understanding the origin and meaning of the terms that make up these balance equations lies at the heart of posing and solving complex transport problems.

- Describe the physical meaning of each of the terms within a
general thermal energy balance
- Simplify the general thermal energy balance equation (identifying assumptions)
- Identify reasonable boundary conditions in a conduction problem (explain when each is most useful)

- Describe the physical meaning of each of the terms within a
differential mass balance equation
- Simplify the mass balance equation (identifying assumptions)
- Identify reasonable boundary conditions in a mass transport problem (explain when each is most useful)

- Describe the physical meaning of each of the terms within the
momentum balance
- Explain the physical meaning of the terms in the differential Continuity and Navier-Stokes Equations
- Simplify both the differential Continuity and Navier-Stokes Equations
- Identify proper boundary conditions for use with the Navier-Stokes equations