# Homework Help: FDM for a 3 metal layers 3D, heat transfer

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1. Jan 30, 2016

### 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.

1. The problem statement, all variables and given/known data
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

2. Relevant equations

3. The attempt at a solution

2. Jan 31, 2016

### Staff: Mentor

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