27216 Transport in Materials

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27-216 Transport in Materials

• Anthony Rollett
• Wean Hall 4315
• Phone [phone]
• Email rollett_at_andrew.cmu.edu

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Outline

• Course details
• Grading
• Office hours
• Course materials
• Mock quiz
• Why do we need to study transport and kinetics?
• Driving force, materials properties/structure and
  conditions

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Grading
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• Participation 5, Home Works 20, Each of 2 Exams
  15, Final Exam 20, Lab reports 25
• Participation show up to class, warn instructor
  in advance of absences, answer questions (not
  expected that you will know all answers!),
  prepare for student presentations, professional
  attitude to class.
• Grading will be done on a curve however, final
  grade will reflect performance and a superior
  performance will earn an A.
• Grader Jason Gruber

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Office hours
Come and see me at any time that I am in my
office if Im too busy we will make an
appointment. I will make myself regularly
available after class on Wednesdays also on
Fridays when I do not have another commitment
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Homework will be due on Thursday
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Course material
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• (GL) M. E. Glicksman (2000). Diffusion in Solids.
  New York, Wiley, ISBN 0-471-23972-0.
• (K) S. Kou (1996). Transport Phenomena and
  Materials Processing. New York, Wiley, ISBN
  0-471-07667-8.
• (GA) D. R. Gaskell (1992). An Introduction to
  Transport Phenomena in Materials Engineering. New
  York, Macmillan. ISBN 0-02-340720-4.
• (PG) D.R. Poirier and G.H. Geiger (1973).
  Transport Phenomena in Materials Processing TMS,
  Warrendale, PA, ISBN 0-87339-272-8.
• (PE) D.A. Porter, K.E. Easterling (1992), Phase
  transformations in metals and alloys, Chapman
  Hall, London, ISBN 0-412-45030-5, call no. 669.94
  P84P2.
• Home http//neon.materials.cmu.edu/rollett/27216/
  27216.html
• Slides include lecture notes with derivations
  etc.
• Homeworks
• Homework solutions
• Blackboard site http//www.cmu.edu/blackboard/
• Announcements
• Grade book

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Mock quiz
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• Not graded
• Intended to help the instructor understand what
  students are comfortable with, and where help
  will be needed.

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Labs

• Transport is primarily an analytical and not
  practical class and the objectives of the labs
  are to
• To learn characterization techniques in materials
  science
• Learn how to communicate technical information
• Transport will be an integral part of your
  analysis and discussion of the laboratory results

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Todays objectives

• Why do we need to study transport and kinetics?
• What is a driving force and what does it cause?

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Why do we need to study transport and kinetics?
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• Thermodynamics has taught you that systems will
  evolve towards a most energetically favored
  state.
• However, most engineering questions can not be
  answered by Thermodynamics alone!

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Example 1 Materials degradation
Expose a piece of Al and a piece of Fe to air at
room temperature
PO2 0.21 atm T 298 K
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After a few days.
Why has the Fe rusted? Why does the Al appear to
have not? Would the Al ever degrade/corrode?
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Remember the Ellingham diagram?
Fe
Al
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Example 2 Transport through nano-porous materials
From the web site of Prof. David Sholl, Chemical
Eng., CMU Molecular Adsorption and Transport in
Microporous Materials Zeolites are crystalline
inorganic materials that are permeated by
ordered pores of molecular dimensions. The size
of zeolite pores and the fact that the pores
form highly ordered structures make zeolites
ideal materials for a host of industrial
processes involving shape-selective catalysis or
separations. One of the challenges in the
successful use of zeolites is that the behavior
of adsorbed species in zeolite pores is
typically strongly dependent on the atomic-scale
structure of both the adsorbate molecule and the
pore itself. As a result, any truly predictive
theoretical treatments of adsorption and
transport in zeolite pores must include this
atomic-scale information.
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Example 3 Materials performance
Furnace walls have to provide heat insulation.
How much heat is leaking through?
298oC
1300oC
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Example 4 Materials performance
Nano-electrical-mechanical systems (NEMS).
Reducing the size of electrical devices.

• Current flow is essential but also liberates
  heat because of the electrical resistance.
• Therefore heat has to be removed from the
  materials.

http//www.aip.org/physnews/graphics/html/tubefet.
htm (7 May 1998 issue of Nature, Cees Dekker)
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Summary Kinetics and Transport tells us

• How fast does a reaction, process or
  transformation take place?
• How does it take place?

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Rate of transport Flux (J)
Rate of Reaction/transformation (r)
H21/2O2 ? H2O Si(l) ?S(s)
moles.s-1.m-2 grams.s-1.m-2
Volumetric moles.s-1.m-3 Interface
grams.s-1.m-2
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Driving force, materials properties/structure and
conditions
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Rate of transport Flux (J) or Reaction/transformat
ion (r)
?
?
?
Driving Force
Structure/properties
Conditions
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Learning Approach
What is the result that we want? For a solved
problem, we quote the equation or concept.
How do we find solutions for the differential
equations, and what are they?
What are the variables?
How do we visualize the solution - what graphs
are appropriate?
How do we set up the differential equations?
What do worked solutions corresponding to
physical situations look like?
How do we determine the boundary conditions?
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Example 1D diffusion

• Desired an equation that allows us to predict
  how quickly a given component will diffuse into a
  material.
• Important variables concentration, distance
  time. To set up the appropriate differential
  equation, think of a series of boxes and relating
  the change in the contents of a box during an
  increment of time to the difference in contents
  between a given box and its neighboring box.
• Boundary conditions concentration at timezero
  as a function of distance.
• BCs determined by inspection of the problem -
  e.g. the temperatures inside outside the
  furnace in Ex. 3.

• How to find solutions? We have to seek equations
  that have the right properties to satisfy both
  the basic differential equation and the boundary
  conditions.
• Visualization? Use a math package (Mathematica,
  Maple) or spread-sheet (Excel) to obtain values
  of the dependent variable (concentration) for a
  series of values of the independent variables
  (time, distance). Plot/graph the result.
• Worked solutions several will be given during
  the course!

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Differential Equations
Flow rate ? ?(height)
h1
h2
2R
dx
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Example of boundary conditions absorption
CASE I
Cs
Ci
L
X0
Boundary conditions (i) t0, -LltxltL , CCi (ii)
t gt0, x 0 CCs (iii) Any t, xL, J0 (since
dc/dx0)
CCASEII(x,t)
CCASEI(x,t)
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Parallels between fluid flow/ heat flow/ mass
transfer

• Note the similarities of the equations used to
  describe the basic characteristics of these three
  phenomena

Kou p269
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What do I need to know?

• As a student, of course there are many items that
  you are expected to learn and know about. Here
  are a few key concepts and ideas.
• Ficks 1st and 2nd laws.
• Analogues to Ficks laws in heat flow, fluid
  flow.
• The difference between steady state and transient
  flows.
• How to identify solutions to problems in
  mass/heat/fluid transport, based on the
  applicable differential equations and boundary
  conditions.

• The meaning of order of reaction.
• Mechanisms of diffusion in the solid state.
  Differences between metals and ceramics.
• Kirkendall effect.
• Viscosity of fluids.
• How to construct a 1D numerical model (finite
  difference) for heat/mass transport.
• How to use a standard boundary value problem
  solver (finite element model, ANSYS).

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Schedule
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Schedule
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ABET targets
?
?
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Summary

• Kinetics and transport tells us about the speed
  and mechanism with which systems move towards
  equilibrium.
• The speed is dependent on driving force,
  materials properties and conditions.