lecture01 spring05 transfer phenomena

8/8/2019 Lecture01 Spring05 Transfer Phenomena

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CE 389/ENVE 310CE 389/ENVE 310 Environmental Transport PhenomenaEnvironmental Transport Phenomena

Spring 2005Spring 2005

Introduction to Transport PhenomenaIntroduction to Transport Phenomena Mass TransportMass Transport


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Course objectives

CE 389/ENVE 310 provides theoretical and practical basis forunderstanding and quantifying mass, momentum and energytransport motivated by examples and applications relevant toenvironmental engineering problems.

We will explore both molecular and macroscopic principleshighlighting unifying principles underlying transport processesand properties.

Students are expected to develop proficiency in formulation oftransport problems, making simplifying assumptions, and using anarray of analytical and numerical solution methods.

Synthesis and addressing coupled transport processes will beexplored primarily through student self-study via class project.


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General Information and Grading Instructor: Dr. Dani Or (CAST 313, 6-2768) [email protected]

TA: Mr. Tao Long (CAST 101, 6-0467) [email protected]. Inst.: Dr. Ross Bagtzoglou (CAST 327, 6-4017) [email protected]

Time: T;Th 3:00-4:30 pm Location: CAST 206 Office Hrs: T+Th 2:00-3:00 pm

Text: Transport Phenomena (Bird, Stewart and Lightfoot )2nd ed.; Additional materials posted on course webpage;Supplemental textbook: Welty et al 2001 4 th ed.

Webpage: www.engr.uconn.edu/environ/envphys/courses/transport/

Grades:30% homework assignments (1 week after assignment)20% each two exams30% class project (10% presentation; 20% report)

A>90%; B=80-89%; C=70-79%; D=60-69%; F


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Expectations and observations

Use office hours as needed (PRIOR to last week of semester). No late HW returns

Exams are open book You are expected to use ALL available information and makeassumptions regarding missing parts dont get stuck due tolack of information check, estimate, approximate, & assume

Pay attention to rules of thumb to develop a sense for orderof magnitude estimation

Check if results make sense no negative volumes, please!

Use SI units to report results & HW (scientific currency) Dimensional inspection key to success... Class project an opportunity for guided self exploration.


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Class Project Steps & Milestones Identify a topic of interest discuss with instructor Be definitive, original synthesis (no google-projects!)

Develop 1-2 page proposal by week 3 Read, study, explore 1 st draft report by week 6 Project report and presentation ready by week 10

Format:Title Introduction: a brief discussion of the topic, problem formulationand objectives.

Theoretical basis: governing equations, definitions, parameters.Solution or Proposed design: key results and figures.Discussion: discuss assumptions, limitations, significance, broader applications; integrate transport & engineering challenges.Literature Cited


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Class Project Topics Coupled transport processes in PEM (Polymer Electrolyte

Membrane/Proton Exchange Membrane) fuel cells Kinetic aspects of microbial colony growth Why are microorganisms small? Analysis of microprocessor heat control Modeling tumor growth (analytical or numerical) Design of slow-release fertilizer capsules Lattice Boltzmann method - diffusion or flow modeling Energy balance on a single plant leaf Gas separation techniques Analysis and design of evaporative coolers Drug delivery patches


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Week 1-3: Introduction & Mass Transport Basic Mass, Momentum and Energy transport processes; micro and

macroscopic views; phenomenological laws; driving forces(gradient); transport coefficients.

Definition of fluxes; conservation principles (divergence);differential elementary volumes and coordinate systems; boundaryconditions; dimensionless numbers.

Molecular mass transport Ficks law of binary diffusion (BSL Ch.16); binary gaseous diffusion coefficient kinetic theory(molecular dynamics); diffusion in liquids and solids.

Effective transport properties (diffusion in suspensions andthrough pack of spheres).

Steady and transient diffusion processes in 1-D and higherdimensions examples and application to transport problems.(diffusion through stagnant film; diffusion from a point source;spherical dissolution; diffusion with 1st order reaction; transient

diffusion into infinite medium; and more)


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Environmental Transport Phenomena - Scope Three closely related topics:

Mass transport of chemical species - diffusion

Energy transport - heat transfer and radiationMomentum transport fluid dynamics

They frequently occur simultaneously They obey similar basic laws/equations The mathematical tools for describing these

phenomena are similar and enable analogy

The molecular mechanisms underlying thesethree phenomena are closely related


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ui

n i dA

dV

Transport Phenomena - Scales Three scales of system description:

Macroscopic scale system representationusing measurable changes in inputs and

outputs no attempt to resolve details.

Microscopic scale examine in detail whathappens at a small region within thesystem (DEV, a pore or a grain, etc.)

Molecular scale fundamental description

of intermolecular motions and forces givingrise to micro- & macroscale behavior.

Convective transport is due to bulk fluid motion;Molecular transport is due to molecular or aggregate

of molecules independent of bulk motion.


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Definition of fluxes (macro) A flux J M of property M is the quantity of extensive property,

M, which crosses a unit area per unit time (Thomson, 2000)E xtensive properties are dependent on system size or total quantities

involved [Mass, Energy, Momentum]; The flux of intensive propertiessuch as temperature and pressure is meaningless.A flux may expressed as volumetric concentration of M multiplied by thevelocity of transport perpendicular to area A:

Energy flux (KE, heat)

Mass flux of A (or molar)

Momentum flux (in x direction) -

; x x vv

vVolumemv

22

22 = xref p x vT T cvVolume

H m)( =

)

x A x A vC or v

( )x x x

x vvvVolume

mv =


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Phenomenological laws of transport Transport processes:

Excited by molecular level (random) motions

Respond to spatial inhomogeneities (gradients)

Obey linear relationships: Flux = coefficient x gradient

Ficks law:

Fouriers law: Newtons law:

x D J A AB Ax

=

xT

k q x

=

z

v y zy

=


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Scalars, vectors, and tensors Scalar is a quantity invariant under rotation of the coordinate

system (does not operate in any particular direction) temperature, density.

Vector is a directional quantity represented as 1 st order tensorwith 3 1 components: velocity, force . Stress or momentum transport is represented by 2 nd order Tensor

with 3 2 components:

Because momentum is a vector quantity it is difficult to envision itstransport to other directions. The ij double index for ij indicates

j-momentum is being transported in the i direction.

k u juiuu z y xrrr

r ++=

=

333231

232221

131211

r


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Gradient and divergence The spatial derivative of a scalar, is the gradient, a vector

defined is Cartesian coordinates as:

and in cylindrical coordinate system:

The spatial derivative of a vector (e.g., velocity) is known as thedivergence: it is a scalar .

k zT

j yT

i xT

T rrr

+

+

=

z

T T

r r

T T

+

+

=

1

zu

y

u

xu

u z y x +

+= r

z z x

y y xr

=

=

+=1

22

tan

)(


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Derived SI-UnitsVELOCITY: Rate at which position changes with time

SI Unit = [m/s]

Distance per Time

]TL[]T[]L[

tsv 1==

ACCELERATION: Rate of change of velocity with time

SI Unit = [m/s 2]

Velocity per Time

]TL[]T[

]TL[

t

v'a 2

1

==

FORCE: (Newtons second law of motion)

SI Unit = Newton [nt] or [N]

Mass times Acceleration

]TL[]M['amF 2=


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Derived SI-Units

PRESSURE:

SI Unit = Newton/m 2 [nt/m 2] = Pascal [Pa]

Force per Unit Area

]LTM[]L[

]LTM[

A

FP 12

2

2

==

WORK:

SI Unit = Newton m [nt m] = Joule

Force times Distance

[ ]222 TLM]L[TLM

sFW=

==


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The International System of Units SI

Table 1-1 continued: Base Units in the Systeme International and their Prefixes

Fraction Prefix Symbol Multiple Prefix Symbol

10 -1 deci d 10 deca da

10 -2 centi c 102 hecto h

10 -3 milli m 103 kilo k

10 -6 micro 106 mega M

10 -9 nano n 109 giga G

10 -12 pico p 1012 tera T

A dimension is a qualitative expression of a physical quantity or anattribute. It may be a basic dimension such as length [L], time [t], or mass[M], or a derived dimension such as volume [L 3], or density [ML -3].

Dimensional inspection is an important step in verifying the validity of anequation; the dimensions of all terms must be consistent.

Writing the equation in dimensional form only, leaving out real values(numbers), enables algebraic manipulation of dimensions, i.e., dimensionsmay be divided, multiplied, and cancelled to simplify the dimensionalequation in terms of basic dimensions.


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Dimensions and Unit ConversionExample 1-1: Dimensions and Unit Conversion

Dimensions: Find the dimensions of pressure in basic units

Solution: Pressure is force divided by the area of its action. The dimensions of force are[MLt-2] and those of area are [L 2]. Thus, the dimensions of pressure are

]tML[]L[

]MLt[

A

FP 21

2

2

===

Units: Convert a pressure of 2.7 kg/cm 2 into SI units (Pa = N/m 2)

kPa7.264Pa264762kg

N806.9

m

cm100

cm

kg7.2

cm

kg7.2

2

22

22==

=

http://www.digitaldutch.com/unitconverter/


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Differential and integral equations

Homework problems to refresh basic ordinarydifferential equations

Integral equations definite and indefinite Use of boundary conditions

Units and dimensions For definitions and hints please consult:

MathWorld - A Wolfram Web Resource.http://mathworld.wolfram.com/PartialDifferentialEquation.html


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Partial Differential Equations

A partial differential equation (PDE) is an equation involvingfunctions and their partial derivatives ; for example, the waveequation

(1)

in general, partial differential equations are much more difficultto solve analytically than are ordinary differential equations .They may sometimes be solved using a Bcklund transformation ,

characteristics , Green's function , integral transform , separationof variables , or--when all else fails (which it frequently does)--numerical methods such as finite differences .

Fortunately, partial differential equations of second-order are

often amenable to analytical solution. Such PDEs are of the form(2)

2

2

22

2

2

2

2

2 1

t v z y x

=

+

+

Eric W. Weisstein. "Partial Differential Equation." From MathWorld--A Wolfram Web Resource.

http://mathworld.wolfram.com/PartialDifferentialEquation.html

02 =+++++ F Eu DuCu Bu Au y x yy xy zz


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Partial Differential Equations (2)

Fortunately, partial differential equations of second-order areoften amenable to analytical solution. Such PDEs are of the form(2) Linear second-order PDEs are then classified according to the

properties of the matrix

as elliptic , hyperbolic , or parabolic . If Z is a positive definite matrix , i.e. det(Z)=AC-B2>0; the PDE is

said to be elliptic . Example: Laplace's equation :(also classified as a Boundary Value Problem ) If det (Z) < 0 , the PDE is said to be hyperbolic . The wave equation

or is an example.

If det (Z)=0, the PDE is said to be parabolic. The heat conductionequation and other diffusion equations are examples.

(also classified as an Initial Value Problem y t) )

02 =+++++ F Eu DuCu Bu Au y x yy xy zz


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Diffusion molecular to macroscopic transport Ficks (1855) first law of diffusion:

x X

CD J x

D J A AB Ax A

AB Ax =

= ;

Random molecular motions(thermal agitation/Brownian motion) result innet flow (diffusion) in thedirection of negative localconcentration gradient.

Examples: (1) LBMsimulations 2-D diffusion;(2) particle simulation ofmulti-component mixture;(3) Brownian motion of 1mparticles in water & viscoussolution.


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Drug capsules and patches - diffusion Modern methods of drug

delivery ensure a constantconcentration of desiredcompound in patients bloodstream or in treated tissue.

Knowledge of diffusioncoefficients & rates throughcapsule and tissues.

Prescribed amounts andconcentrations for effectiveand sustainable treatment.

Similar applications forfertilizer slow release capsulesused to supply nutrients forplant growth.

Micro and macroscopic scales


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Contaminant transport Hanford Site

The Hanford site near the ColumbiaRiver in southeastern Washington is theworlds largest cleanup operation.

Nuclear waste from the Manhattan project leaks from corroded tanks andmigrates towards the Columbia river.

Environmental transport issues

diffusion, convection, flow pathways,interactions with rock, transformations,kinetics, buoyancy.


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Macroscopic nutrient mass balance - Eutrophication

The transport of excess nutrients into water bodies can causealgae bloom resulting in the death of aquatic organisms.

Solution Reduce nutrient load (input) using macroscopic balance principles.

lecture01 spring05 transfer phenomena

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