Humidity variation over a concrete cross-section

[ridgeline]

I was hoping someone that is much more skilled at math than I could help me interpret the attached equation. Basically, I am trying to understand how humidity will vary through a cross-section of concrete. I understand concrete diffusivity 'C' will degrade with time and may be represented in units of mm^2/day.

So if I am able to choose 'C' based on some time 't', what does the variation of 'h' across 'x' look like? Do the squared terms mean 'h' varies as a square of 'x'?

 

[BAretired]

So if I am able to choose 'C' based on some time 't', what does the variation of 'h' across 'x' look like? Do the squared terms mean 'h' varies as a square of 'x'?

What I know about diffusivity would not be enough to fill a thimble, but:
The term on the left is the partial differential of h with respect to t or the rate of change in h with respect to time.
The term on the right does not involve squared terms. It is C(t) times the second partial differential of h with respect to x.



BA

 

[ridgeline]

Thanks for the response.

So, I understand this to mean that at any given time 't', 'h' is proportional to 'x'. Meaning they have a linear relationship?

 

[BAretired]

I don't think it is as simple as that, but I was never very good at differential equations.
Can you cite the reference which you are quoting? Does it contain any diagrams?

BA

 

[ridgeline]

http://www.civil.northwestern.edu/people/bazant/PDFs/Backup of Papers/164.pdf

 

[BAretired]

The article referenced above would need considerable study to develop an understanding. I believe what is meant in the snippet that you quoted originally is that the diffusion equation is linear. Nowhere does is suggest that 'h' is proportional to 'x'.

Looking at the following definitions, the equation you cited is a second order partial differential equation. It is not clear to me why the writer calls it linear. Seems to me it is non linear.

https://en.wikiversity.org/wiki/Partial_differential_equations

BA

 

[ridgeline]

Agreed. Thanks for taking a look.