Quantcast
  • Register
PhysicsOverflow is a next-generation academic platform for physicists and astronomers, including a community peer review system and a postgraduate-level discussion forum analogous to MathOverflow.

Welcome to PhysicsOverflow! PhysicsOverflow is an open platform for community peer review and graduate-level Physics discussion.

Please help promote PhysicsOverflow ads elsewhere if you like it.

News

PO is now at the Physics Department of Bielefeld University!

New printer friendly PO pages!

Migration to Bielefeld University was successful!

Please vote for this year's PhysicsOverflow ads!

Please do help out in categorising submissions. Submit a paper to PhysicsOverflow!

... see more

Tools for paper authors

Submit paper
Claim Paper Authorship

Tools for SE users

Search User
Reclaim SE Account
Request Account Merger
Nativise imported posts
Claim post (deleted users)
Import SE post

Users whose questions have been imported from Physics Stack Exchange, Theoretical Physics Stack Exchange, or any other Stack Exchange site are kindly requested to reclaim their account and not to register as a new user.

Public \(\beta\) tools

Report a bug with a feature
Request a new functionality
404 page design
Send feedback

Attributions

(propose a free ad)

Site Statistics

205 submissions , 163 unreviewed
5,047 questions , 2,200 unanswered
5,345 answers , 22,709 comments
1,470 users with positive rep
816 active unimported users
More ...

  Could you help me please with a mathematical model of the soil freezing process first studied by Harlan?

+ 0 like - 0 dislike
1191 views

Hello, dear colleague. Now I'm dealing with issues of modeling heat and mass transfer in frozen and thawed soils. I am solving this problem numerically using the finite volume method. Below I give an equation from Harlan for mass transfer,

∂/∂x(K(∂ψ/∂x)) = (∂θu/∂t) + (ρiw)(∂θi/∂t),

where K is the hydraulic conductivity of soil, [m/s]; θi is the volumetric ice fraction, i.e., the volume of the ice in per unit volume of frozen soil - dimensionless quantity; ψ is the soil suction potential, which controls the flow of the soil water [m]; T is the temperature, [K]; x is the position coordinate, [m]; t is the time, [s], θu is the volumetric unfrozen water fraction - dimensionless quantity, ρi - ice density [kg/m3], ρw - water density [kg/m3].


Give me please the most thorough explanation for these four questions:


What is the physical meaning of this equation?
What is the physical meaning of its left and right side?
In the right side of this equation, why has the second term a factor (ρiw)?
In which program can I put this equation to see its physical meaning?


P.S. Do you know quality and intuitive (with detailed explanations) articles, books, theses (in English language) on the subject of modeling of heat and mass transfer processes in frozen and thawed soils by the control (finite) volume method. This subject is very interesting. I am looking for the treatment one, two and three-dimensional problems, as well as software environments where you can realize the solution of these problems by “my” formulas (instead of formulas 'built into' these systems).

asked Oct 17, 2017 in Computational Physics by sashavak (15 points) [ revision history ]

Please add a reference to the context from which you obtained the equation.

The equation you cite is a continuity equation describing mass transport. See Harlan's paper

Analysis of coupled heat-fluid transport in partially frozen soil

where you can find details. There is plenty of software for solving partial differential equations, see, e.g. here, but you need to find out for yourself which package is suitable for your problem. 

Your answer

Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead.
To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL.
Please consult the FAQ for as to how to format your post.
This is the answer box; if you want to write a comment instead, please use the 'add comment' button.
Live preview (may slow down editor)   Preview
Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
If you are a human please identify the position of the character covered by the symbol $\varnothing$ in the following word:
p$\hbar$ys$\varnothing$csOverflow
Then drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds).
Please complete the anti-spam verification




user contributions licensed under cc by-sa 3.0 with attribution required

Your rights
...