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
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 tem
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 compo
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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
CHE 406
Transport Phenomena
Fall 2011
Instructor:
Professor David C. Venerus
[email protected]
105 Wishnick Hall (7-5177)
Office Hours: TR 10:00 - 11:30 am
Teaching Assistant:
Ms. Fatemeh Rahmaninejad
f
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
CHE 406
Homework #4
6
6
6
6
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1. For incompressible Newtonian fluids where J = -: ( = -:[L v + (L v )T], show that
66
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J :L v = -:( (:()
2-3. Problem 10B.1 (9.H)
4-5. Problem 10B.4 (part a. only) (9
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
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 variabl
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
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 Equ
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
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 *:
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 Si
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 molec
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 condition
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
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CHE 406
E xam #1
O PEN B OOK ( Fllillsport P hcnomCllo) O NLY
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