Assumptions
What assumption removes terms that are functions of time?
Steady state
What is the driving force for heat transfer?
Temperature gradient
What two properties can be estimated using similar forms of the mixture correlation?
Viscosity (dynamic) and thermal conductivity
Where does maximum velocity occur with laminar flow inside a pipe?
At the center
What is one thing you're looking forward to after project/exam season is over?
Anything
(points to all teams)
(team for this question chooses again)
What area element variable can you not divide by when deriving balances in cylindrical coordinates and why?
r (initial/inner radial distance)
Because r is not constant (like 2*pi) and can not be chosen to be constant (like delta(z))
What are the key assumptions in molecular gas theory?
What properties are used in finding phi in the mixture property equations?
Molecular weight and (dynamic) viscosity
Where does no shear occur with laminar flow inside a pipe?
At the center
Name one isotropic material
glass, non-rolled metal, or any other applicable
What is a common scenario where pressure drop can be ignored?
Open to atmosphere (pressure drop in the direction of movement is negligible)
May also accept: if pressure is not the driving force (not always true, but usually true)
What mechanism does conduction use?
Molecular (heat transfer)
Estimate k through a flat wall if:
Tc = 300 K
Th = 500 K
delta(x) = 0.1 m
q = 5000 W
A = 1 m2
k = 2.5 W/(m K)
What four variables are used in Fourier's Law?
Bonus: What kind of heat transfer does this law describe?
q (heat flow), A (cross-sectional area), k (thermal conductivity), T (temperature, used in gradient)
Bonus: Conduction
Name 2 anisotropic materials
wood, rolled metal, carbon fiber, or any other applicable
Name three common assumptions used to simplify the Navier-Stokes equation
Bonus: Name five
Any three of the following:
steady state, constant properties, laminar flow, no end effects, two of the directional velocities being 0, Newtonian fluid
What mechanism does gaseous conductive heat transfer use?
Brownian motion
Calculate the thermal conductivity of a gas if:
T = 1000 degC
MW = 500 g/mol
OmegaK = 1
sigma = 2 Angstrom
(use the Chapman-Enskog k equation)
k = 0.03307 W/(m K)
What does a partial derivative assume and/or tell us?
How a function (f) changes with respect to one variable (x), assumes all other variables (not x) are fixed
What does a mass balance usually prove?
Bonus: What is another possible result?
Momentum in a given direction is not a function of position in that direction
Bonus: It could provide nothing (if there is no momentum in the system)
For the following system, which terms would cancel and why?
(board)
1. Steady state
2. v,r = 0
3. v,theta = 0
4. v,z =/= f(z) or dv,z/dz = 0 (continuity equation)
5. no
6. no
7. v,z =/= f(theta)
8. v,z =/= f(z) or dv,z/dz = 0 (continuity equation)
9. no
Double Jeopardy
What kinds of materials can be used with the:
1. Chapman-Enskog k equation
2. Eucken correlation
1. monoatomic gases
2. (low-density) polyatomic gases
Calculate the thermal conductivity of a gas if:
MW = 100 g/mol
T = 300 K
sigma = 3.5 Angstrom
OmegaMu = 1.08
c,p = 10 J/(mol K)
R = 8.314 J/(mol K)
(Use Chapman-Enskog viscosity and Euken tc equations)
(viscosity = 3.4946e-5 Pa s)
k = 0.00713 W/(m K)
What can a differential area of a curved surface be approximated as if the differential thickness delta(r) is very small? (What type of shape?)
A flat surface / rectangle
Double Jeopardy
What is the value of the Dirac delta if i is not the same as j?
0
(used to determine directional transfer of all directional shears in a Newtonian fluid)