Understanding unsteady state heat conduction

[dinaharchery]

Hello,

I am trying to understand one-dimensional unsteady state heat conduction for a program I am writing. The program will eventually be coded for two and three dimensional structures. Can anyone provide some basic background info./tutorial to understand the governing equation and boundary/initial conditions?

Thanks.

 

[CFDFEAGURU]

You are a little vague. What is the media that the heat conduction is taking place in? Will there be multiple media, like a solid layer then a porous layer? What programming lanquage are you planning to use? Are you assuming a lumped mass approximation? (I am assuming that you aren't because you are writing a program.) Are you looking for a finite element approach or a finite difference approach?

The more you can tell us, the more we can help you.

Thanks
Matt

 

[dinaharchery]

Sorry about being so vague.

The media is solid and there is only one. I am planning on using C++, no lumped mass matrix. I am looking for a Finite Element approach. Mainly I was looking for information on the theory, not necessarily an exact code since I would like to learn the process behind the algorithm(s).

Thanks.

 

[CFDFEAGURU]

Ok, thanks for additional information. Well the best write up I have come across for the finite element method involving heat transfer is here.

https://www.amazon.com/dp/0534552986/?tag=pfamazon01-20

Buy the old version from 2001. It is much cheaper. I have most of the problems worked out. If you would like I can post a problem with the solution later this week.

Thanks
Matt

 

[minger]

As far as a finite-element approach, it's not too difficult to understand. Basically, each element has a mass. If the net heat flux is positive into the mass, then it heats up, and vice versa.

The heat flux for an internal element is conduction. For an external element, you can apply boundary conditions such as convection and radiation to determine heat transfer.