CHE 406
Homework #2
6
1. Given the scalar field s and vector field v below (where A,B,C and are constants), derive an
expression for the material derivative of the scalar field, Ds/Dt.
2. Consider the velocity field for the flow for an incompressible ( =
CHE 406
Homework #5
Consider the equations governing energy transport during the Czochralski Crystal Growth (CZCG)
process. Using the quasi-steady state approximation (QSSA), the equations for the temperature
distribution T(r,z) in a solid crystal of leng
CHE 406
Homework #1
1. Evaluate the following in terms of RC components:
2. Prove, using RC components, that the following is valid for any scalar field s and vector field v :
3. Prove, using RC components, that the following is valid for any scalar s fie
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CHE 406
Final Exam - Open Textbook (BSL) Only
Fall2007
1. A thin metal sheet with thickness 2B and uniform temperature T0 enters a heating chamber with
velocity V. The heating chamber contains a hot gas having uniform temperature Tg. A schematic
of
CHE 406
Transport Phenomena
Fall 2011
Instructor:
Professor David C. Venerus
venerus@iit.edu
105 Wishnick Hall (7-5177)
Office Hours: TR 10:00 - 11:30 am
Teaching Assistant:
Ms. Fatemeh Rahmaninejad
frahmani@hawk.iit.edu
115 Perlstein Hall
Office Hours: W
CHE 406
Homework #6
1. Show that for a binary system of A and B the following is true:
2. Problem 18B.2 (parts a and b only) in BSL
3. Problem 18B.7 in BSL (simplify species continuity equation rather than derive shell balance)
4-5. A thin solid disk with
CHE 406
Homework #4
6
6
6
6
@
1. For incompressible Newtonian fluids where J = -: ( = -:[L v + (L v )T], show that
66
@
J :L v = -:( (:()
2-3. Problem 10B.1 (9.H)
4-5. Problem 10B.4 (part a. only) (9.J)
6-7. Problem 10D.1 (9.Q)
8-9. Problem 10B.2 (10.H)
CHE 406
Homework #3
6
6
1. For potential flow, the velocity potential N is related to the velocity field as follows: v = - L N.
For potential flow around a sphere, N is given by the following
where V is the approach velocity and R is the radius of the sph
Review of Differential Equations
1. Basic Definitions for second order Partial Differential Equations (PDEs)
In the above equation, x and y are the independent variables and u is the dependent variable. A, B,
C, D, E and F are coefficients that depend in
E. Boundary Conditions for Mass Transfer
As before, we consider a phase interface where two distinct phases (+/ ) are separated
by a surface S* having velocity u unit normal n *:
1. Jump Species Mass Balance
Application of the species I continuity equatio
C. Constitutive Equations for Mass Transport
1. Thermodynamic Constitutive Equations
For purely-viscous, multi-component mixtures, we assume the following for the specific
internal energy:
Caloric Equation of State
Since 1 = w1, we can write this as
Comme
IV. Mass Transport
A. Concentrations, Velocities and Fluxes
1. Concentrations (See Table 17.7-1 BSL)
Variable
mass density of I
Symbol
I
total mass density
molecular wt. of I
molar density of I
MI
cI
total molar density
c
molar avg. mol. wt.
M
M = /c
mass
III. Energy Transport
E. Boundary Conditions for Heat Transfer
As in fluid mechanics, we consider a phase interface where two distinct phases (+/-) are
separated by a surface S* with unit normal n *:
1. Jump Energy Balance
Application of the energy equati
III. Energy Transport
D. Forms of the Thermal Energy Equation
In this class, materials described by the caloric equation of state U = U (V ,S )
and by Fouriers Law
will be designated at Thermally Simple Materials (TSMs).
Substitution into the Thermal en
III. Energy Transport
A. Forms of Energy and Energy Transmission
1. Forms of Energy
Kinetic Energy- associated with macroscopic fluid motion: Dv2 [energy/volume]
Internal Energy- associated with molecular motion and interactions: D
[energy/volume], where
II. Momentum Transport
F. Boundary Conditions for Fluid Mechanics
The solution of a fluid mechanics problem requires the specification of velocity and/or
stress boundary conditions. Boundary conditions at phase interfaces are formulated
using two-dimensio
II. Momentum Transport
E. Special Forms of the Equations of Motion
The continuity equation
and equations of motion
represent 4 equations that contain 11 unknowns and, hence, can not be solved. We now
combine the equations of motion and rheological constit
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CHE 406
E xam #1
O PEN B OOK ( Fllillsport P hcnomCllo) O NLY
b 1l2009
A n Incompressible Newtoni:m Fluid ( INF) o f constant viscosi! YI-l t lows in a cylindrical c,lvit y h(\ving
a cyJindnl:JI r od that m oves t hl\'ngh If w ith cunstant v elocity V as