Image taken from a diagram found in the 3.185 assignments section. (Image courtesy of Prof. Adam Powell IV.)
Course Highlights
This course features a full set of lecture notes, as well as assignments and exams, both of which include solutions.
» Watch a video introduction featuring the course instructor.
(RM - 56K) (RM - 80K) (RM - 220K)
Course Description
This course deals with solid-state diffusion, homogeneous and heterogeneous chemical reactions, and spinodal decomposition. Topics covered include: heat conduction in solids, convective and radiative heat transfer boundary conditions; fluid dynamics, 1-D solutions to the Navier-Stokes equations, boundary layer theory, turbulent flow, and coupling with heat conduction and diffusion in fluids to calculate heat and mass transfer coefficients.
Special Features
- Faculty introduction video
Technical Requirements
Software to view the .tex files on this course site can be accessed via the Comprehensive TeX Archive Network (CTAN) and the TeX Users Group Web site. Microsoft® Excel software is recommended for viewing the .xls files found on this course site. Free Microsoft® Excel viewer software can also be used to view the .xls files. RealOne™ Player software is required to run the .rm files found on this course site.
*Some translations represent previous versions of courses.
Syllabus
Instructor
Adam Powell, Assistant Professor in DMSE.
Schedule
Lectures will be held three days a week for one hour. Recitations will meet two days a week for one hour. Students may attend either (or both) of the recitations.
Textbook
Welty, James, Charles E. Wicks, Robert E. Wilson, and Gregory L. Rorrer. Fundamentals of Momentum, Heat, and Mass Transfer. 4th ed. New York: John Wiley and Sons Inc., January 2000. ISBN: 9780471381495.
Optional Readings
Poirier, D. R., and G. H. Geiger. Transport Phenomena in Materials Processing. Warrendale, PA: TMS, 1994. ISBN: 9780873392723.
Incropera, Frank P., and David P. DeWitt. Introduction to Heat and Mass Transfer. New York: John Wiley & Sons Inc., July 2000. ISBN: 9780471390817.
Grading
Grades will be determined from exams and eight homework assignments as follows:
ASSIGNMENTS |
PERCENTAGES |
Problem Sets |
16% |
Math Quiz |
10% |
Test 1 |
20% |
Test 2 |
20% |
Final Exam |
34% |
General Overview
Diffusion
This section will use a phenomenon which you have already studied extensively to introduce two of the foundation methodologies of the course. The first is coupling conservation and constitutive equations to give closed-form (partial) differential equation(s) in one or more field variables. The second is dimensional analysis, which identifies the key dimensionless parameters in a given problem and allows us to quickly characterize all of its possible solutions using as few parameters as possible. The mass transfer Biot number will be used to illustrate this process.
Heat Conduction and Radiation
This section will take advantage of the mathematical similarity between diffusion and heat conduction to introduce you to a new phenomenon. Building on the principle of conservation of thermal energy, we will introduce new solutions to the (thermal) diffusion equation, define the heat transfer Biot number, and examine conduction in a solid with moving boundaries. Heat transfer by radiation will also be covered at some length, and coupled with conduction as a boundary condition. This section will close with an introduction to convection using a moving solid as an example.
Fluid Dynamics
This section will attempt to present Newtonian and non-Newtonian fluid dynamics using principles of conservation of mass and momentum in the same methodology as was used for diffusion and heat conduction. We will present the complete Navier-Stokes equations describing fluid flow, and use them to solve problems in which flow velocity varies in just one direction. The Reynolds number will be defined and related to the transition to turbulence. Boundary layer descriptions of flow near surfaces will be developed, and used to calculate the drag force on simple bodies moving relative to a fluid. Turbulence will be described qualitatively, and modeling methods based on Reynolds stresses will be developed and related to effective turbulent viscosity and eddy length scales. Finally we will discuss overall mass and momentum balances on large control volumes.
Heat and Mass Transfer
This section will begin by applying the same large control volume methodology to thermal energy and species transport, and discuss batch/continuous reactor design in this context. It will then return to the Navier-Stokes equations, and their coupling with species diffusion and heat conduction to describe heat and mass transfer in fluids. We will calculate heat and mass transfer coefficients under steady laminar and turbulent flow conditions in simple geometries, driven both by external forces and thermal/solutal buoyancy, and discuss application to materials process engineering. At least four new dimensionless parameters will be introduced to describe all of the coupling phenomena involved.
ABET Statements for 3.185
Calendar
LEC # |
TOPICS |
1 |
Introduction |
Diffusion |
2 |
1-D, Cylindrical Steady-State Diffusion |
3 |
Homogeneous Chemical Reaction |
4-5 |
Unsteady Diffusion |
6 |
Boundary Conditions, Biot Number |
7 |
Dimensional Analysis |
Heat Conduction and Radiation |
8 |
Introduction: Energy Conservation |
9 |
Transient Dimensional Analysis, Graphs |
10 |
Finite Differences and the Heat Equation |
11 |
Math Quiz, Multilayer Walls |
12 |
Moving Body (Convection) |
13 |
Phase Change, Thermal Conductivity |
14-16 |
Radiation Heat Transfer |
17 |
Test 1: Diffusion and Heat Conduction (through lecture 11) |
Fluid Dynamics |
18 |
Intro, Viscosity |
19-20 |
1-D Laminar Momentum Diffusion |
21-22 |
Navier-Stokes Equations |
23 |
Using the Navier-Stokes Equations |
24 |
Drag Coefficient on a Tube, Sphere |
25 |
Boundary Layer on a Flat Plate |
26 |
Drag Coefficient on a Flat Plate |
27-28 |
Turbulent Flow Phenomena |
Fluid Heat and Mass Transfer |
29-30 |
Heat/Mass Flat Plate Boundary Layer |
31 |
Test 2: Radiation, Fluid Flow (through lecture 25) |
32-33 |
Natural Convection, Boundary Layers |
34 |
Stream Function, Vorticity |
35 |
Inviscid Flow, Bernoulli Equation |
36-37 |
Batch and Continuous Flow Reactors |
38 |
Process Cost Modeling |
39 |
Final Review |
40 |
Final Exam Period |