Understanding unsteady state heat conduction

In summary: The source code can be found here:https://github.com/MatthiasBaumann/Heat-Transfer-Problem-SolutionGood luck!
  • #1
dinaharchery
24
0
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.:smile:
 
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  • #2
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
 
  • #3
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.
 
  • #4
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
 
Last edited by a moderator:
  • #5
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.
 

1. What is unsteady state heat conduction?

Unsteady state heat conduction is the transfer of heat through a material when the temperature of the material is changing over time. This is in contrast to steady state heat conduction, where the temperature of the material remains constant.

2. How is unsteady state heat conduction different from steady state heat conduction?

In steady state heat conduction, the temperature of the material does not change over time, while in unsteady state heat conduction, the temperature does change over time. This means that there is a time component to consider in unsteady state heat conduction, while steady state heat conduction only considers the spatial component of heat transfer.

3. What factors affect unsteady state heat conduction?

There are several factors that can affect unsteady state heat conduction, including the properties of the material (such as thermal conductivity and specific heat capacity), the boundary conditions (such as temperature and heat flux at the surface), and the geometry and dimensions of the material.

4. How is unsteady state heat conduction modeled and analyzed?

Unsteady state heat conduction can be modeled using partial differential equations, such as the heat equation. These equations can then be solved using numerical methods or analytical solutions, depending on the complexity of the problem. The resulting solutions can be analyzed to understand the heat transfer behavior and make predictions about the temperature distribution over time.

5. What are some real-world applications of unsteady state heat conduction?

Unsteady state heat conduction is relevant in many practical situations, such as heating and cooling of buildings, thermal management of electronic devices, and heat transfer in manufacturing processes. It is also important in fields such as materials science, where understanding the temperature distribution in a material during processing is crucial for controlling its properties.

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