All Questions
12 questions
0
votes
2
answers
168
views
How to modify single phase fluid/solid coupled PDEs to account for a phase change?
I have two PDEs that model both fluid and solid temperature change due to fluid flow through a packed bed. Schematic and equations here (where the f and s subscripts are for the fluid and solid ...
- 15
0
votes
0
answers
108
views
How to calculate convection between a hot and a cold area through a circular hole?
Consider the below problem:
where we have two half infinite worlds with $T_2 < T_1$ and a circular hole with the diameter of $D$ in an infinite isolating wall. There is no ...
- 373
0
votes
0
answers
40
views
Can one model fluid flow only by using the convection–diffusion equation?
Modeling fluid flow in a coil seems very complicated, especially for turbulent flow. Having Navier-Stokes equations seems to be the right way to go, but I was wondering... can one use the convection-...
- 564
6
votes
0
answers
300
views
Why is the Fokker-Planck equation only valid for the forward and backward velocities but not for the flux velocity?
I noticed that the Fokker-Planck equation is often only written for the forward velocity $\vec b$ and the backward velocity $\vec b^*$:
\begin{align}
\partial_t \rho + \nabla (\vec b \rho) &= D \...
- 10.3k
0
votes
1
answer
486
views
Confusion about Fick's first law
Consider a binary system of mass transport (A, B). Some of mass transfer books (Skelland and Welty) say that the relation $$J_A= -C D_{AB} \frac{dx_A}{dz} \tag{I}$$ is more general than $$J_A= -D_{AB} ...
- 261
0
votes
1
answer
483
views
What is the maximum flux in Fick's diffusion?
Solving the Fick's second law with common boundary conditions and applying to the first law will result in a common expression of one-dimensional diffusion as
$$J_{(x=0)} = D\frac{\partial c(x,t)}{\...
- 55
1
vote
1
answer
550
views
How to measure percentage of nitrogen present in Nitro Coffee
Starbucks had launched nitro coffee. Unlike carbonated, this coffee contains nitrogen gas which makes that peculiar down draft waviness in the drink. In carbonated beverages, the gas effervescence and ...
- 977
0
votes
0
answers
94
views
Diffusion of solute in a dynamic solvent
Consider this hypothetical equipment.
A pipe made of semi-permeable membrane (permeable only to the solute)
has a streamline flow of pure water going from A to B ($P_A>P_B$). Midway, another
...
- 3,168
3
votes
0
answers
146
views
How does air going through silica gel change its humidity
Assume that the properties(temperature,humidity,velocity and so on) of the incoming air flow stay constant. The air flow goes through a silica gel plate. Humidity of the air will decrease, but how to ...
- 31
4
votes
2
answers
102
views
The validity of constitutive diffusive fluxes
In transport phenomena the diffusive fluxes for mass, energy and momentum are the constitutive laws:
$$\boldsymbol{j}_c=-D\boldsymbol{\nabla}c \quad \boldsymbol{j}_T=-k\boldsymbol{\nabla}T \quad \...
- 3,489
1
vote
4
answers
3k
views
How does the dissolution of salt affect the solution density?
Suppose you have a container of water as a solvent and you a certain amount of salt as a solute sitting at the bottom of the container that has yet to start dissolving. Supposing temperature and ...
- 289
1
vote
0
answers
343
views
How does fluid velocity affect the dissolution of some solute in the fluid?
Suppose we have a perfect sphere of some solute such as sugar and we place it in a fluid such as water, at a certain temperature, that is not moving. It will dissolve and diffuse into the water due to ...
- 289