FDM for a 3 metal layers 3D, heat transfer

[Federico Navarrete]

Dear members,

Some days ago, I received the following exercise but I have never studied thermodynamics before and I don't know very well where to start, the exercise is about Heat Transfer and the Finite Difference Method and I must program the solution using Petsc and C++.

About the Finite Difference Method (FDM) and the Laplace equation, I have used it before and I know how to implement it but I have few clues about this. I have read and watched many tutorials in YouTube about the topic but most of them are for one layer, 2D and different temperatures around it. Nevertheless, in this exercise, I have 3 different metals and it's in 3D.

I'd like to get some recommendations or tips about what I should do or where to read. Thanks for your valuable help, sorry because I don't have any equation or relevant information but my knowledge about this is minimal.

Homework Statement

Get the heat transfer of the following figure using the Finite Difference Method and finally, implement it with Petsc and C++:

The ambient temperature is 0 degrees Celsius.

Thermal conductivity:

• Aluminum : 205 W/mK
• Copper: 385.0 W/mK
• Iron: 79.5 W/mK

http://hyperphysics.phy-astr.gsu.edu/hbase/tables/thrcn.html

Homework Equations

The Attempt at a Solution

 

[Chestermiller]

The first step is to write the equations for the boundary conditions at the 3 junctions between the materials.