Assumptions
What assumption can cancel the q-dot term in the energy equation?
No heat generation
Is bulk flow involved in conduction?
No
Estimate the diffusivity (in cm2/s) if:
J = 5 g/(cm2 s)
delta,x = 0.01 cm
c2 = 0.07 g/cm3
c1 = 0.02 g/cm2
D = 1 cm2/s
Molecular weight(s) and viscosity(/ies)
What was your favorite class this semester (CHE or non-CHE)?
Anything
(points to all teams)
(team for this question chooses again)
What assumptions can be made to simplify the continuity equation for a solid wall?
Bonus: What does the simplified continuity equation tell us?
Steady state, no velocity (all directions)
Bonus: Nothing
What is one type of energy generation included in q-dot?
Bonus: Name three types
Electrical, chemical, nuclear
Does energy from a heated pipe get included in the q-dot term for a balance over the fluid?
Bonus: What is the value of q-dot for fluid flow through a heated pipe (for a balance over the fluid)?
No
Bonus: Zero (because q-dot is only for internal heat production)
What sign does the viscous work term in the generalized energy equation always have?
Positive
Why can you not divide by r when getting a derivative from a cylindrical shell balance?
r is not constant
What is one way to cancel the viscous generation term in the energy balance?
Bonus: What is another way?
1. Have no flow/velocity
2. Have a low enough velocity that the term is given as negligible
What is the mechanism for mass transfer?
Bonus: What is the driving force?
Random molecular / Brownian motion
Bonus: Concentration gradient
Find the average sigma and epsilon/kappa values for a mixture of X and Y if:
epsilon/kappa,X = 140 K epsilon/kappa,Y = 310 K
sigma,X = 4 Angstroms sigma,Y = 2.5 Angstroms
sigma,avg = sigma,XY = 3.25 Angstroms
epsilon/kappa,avg = 208.3 K
How do you calculate an average variable in this class (ex. temperature, speed)?
integral of the variable over the volume / (integral of the) volume
When can r be factored out of a derivative?
When the derivative is with respect to something other than r
Also accept: After the derivative is taken / once the governing equation is obtained
Double Jeopardy
Can pressure be ignored in the following system and why:
Flow between two inclined plates due to the movement of one plate
Bonus: What would the alternative do to the system?
Yes, because pressure is not the driving force
Bonus: If a pressure gradient was present, some fluid would flow faster than the moving plate or move in the reverse direction
What are two types of work involved in energy generation?
Bonus: Name four types
Bonus 2: Which type of energy accounts for one type of work (also name the type of work)?
Viscous, pressure, shaft (not relevant for differential elements), and gravitational
Bonus 2: Potential energy accounts for gravitational work
Estimate the diffusivity of a mixture of X and Y (in cm2/s) using the Chapman-Enskog equation if:
T = 300 K P = 1 atm
MW,X = 20 g/mol MW,Y = 50 g/mol
Omega,D = 1.2 sigma,XY = 5 Angstroms
D,XY = 0.0851 cm2/s
What are two common boundary conditions for heat transfer?
Bonus: Provide three
Two of the following:
Temperature at a surface is specified
Heat flux at a surface is specified
Heat flux at a surface is given by the convective HT equation
Solid/solid interface continuity (q and/or T)
How does thermal conductivity generally change with:
1. Temperature
2. Pressure
1. Increases with increasing T
2. None
What are three assumptions can be made to simply the generalized equations for horizontal heat transfer through a flat vertical wall?
Bonus: Name all six (generalized)
No velocity (all directions), steady state, pressure is not a function of the direction of heat transfer, gravity = 0, temperature is only a function of the direction of heat transfer, no heat generation
What two variables are involved in the viscous work term in the energy balance?
Bonus: What mathematical operation(s) is/are used with this term and why?
Velocity and shear/momentum flux
Bonus: Gradient, because the viscous work term accounts for viscous work/shear/momentum flux in all system/flow directions
Double Jeopardy
Estimate the diffusivity of isotope X* in normal liquid X (in cm2/s) using the Stokes-Einstein equation if:
T = 400 K mu = 2 centipoise
rho = 12.5 g/cm3 MW = 100 g/mol
D,XX* = 1.856e-5 cm2/s
Write out the generalized energy balance on the board (not assuming constant properties)
grad•k(grad(T)) + q-dot + grad•[(tau,twolines)•(v,line)] = grad•rho(v,line) + (rho/2)((Dv^2)/Dt) + rho(Du/Dt) + rho(D(gy)/Dt)
(See board)
What do the two lines on top of the generalized tau mean?
Bonus: If this was multiplied with a gradient, how many terms would the product have in a 3D coordinate system?
Tau / momentum flux / shear is a tensor
Bonus: Nine