Transient Heat Conduction in Semi-Infinite Solid - Constant Heat Flux 1

[gianlucaf]

Every book I read regarding this topic reports just the final equation in attachment.
Is there anyone who can help me to understand the analytical steps to achieve the final equation in attachment.
Thanks in advance.

 

[ione]

I warmly suggest "Conduction of heat in Solids" Second Edition - H.S. Carslaw and J.C. Jaeger. At page 75 you should find what you're looking for.

 

[Terminus0]

Do you know how to solve Partial Differential Equations?

Because if you don't, the full derivation won't be of much help.

 

[gianlucaf]

Many Thanks ione,
in Appendix II I found what I was looking for:
what I missed was that the final equation has to be achieved by analytical solution of ierfc,
instead of developing the thermal differential equations of the heat transfer.
I am going to study this point better.
Thanks again

 

[gianlucaf]

Well Terminus0,
thank you for your reply.
Answering your question, yes I do, though maybe not very much skilled.
Anyway, there is something you could help me to understand.

Talking againg about transient heat conduction,
consider, for instance, the simple case of the constant temperature at the surface.
The heat flux through the body could be obtained:
1) calculating the partial derivative of the temperature function respect the considered direction
2) and using the Leibniz's rule for the derivative of integrals

How to express correctly the error function in terms of differentials of distance and time instead of differential of temperature penetration only?

Well, please find in attachment the exposition of the problem.

A comment from you, or from anyone else interested in this topic, would be very much appreciated.

Many thanks in advance