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Example showing how the heat transfer with Robin boundary conditions is solved using the iron library.

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Heat Transfer in a Cylinder with Robin and Neumann Boundary Conditions

This example solves heat transfer in a cylinder. The purpose of this example is to implement Robin boundary conditions in the OpenCMISS and enable it for convection or radiation heat transfer.

The boundary conditions at one end of the cylinder are Neumann boundary conditions and over the rest of the boundary are Robin boundary conditions. The dimensions of the cylinder are about the same as an adult human arm. The temperature for the whole cylinder initially is 37 Celcius, and suddenly air with 10 Celcius blows over it and cools it down. Because the heat flux is higher at the skin, in the beginning, skin temperature drops quickly, but the in-depth temperature remains the same.

A tetrahedral mesh for the cylinder was generated, and tri-linear simplex interpolation was used for temperature interpolation in the elements.

Running the example

Python version:

cd ./src/python
mkdir output
mpiexec -n 4 python3.4 heat_transfer.py

Results

Results can be visualised by ParaView or running visualise.cmgui with the Cmgui visualiser.

The following figures show the temperature distribution in the cylinder.

docs/images/transparentCyl.png

Figure 1: Temperature distribution.

docs/images/CrossSection.png

Figure 2: Temperature distribution in the cylinder cross-section.

The expected results from this example are available in expected_results folder.

Prerequisites

There are two files describing the mesh in the input folder.

License

License applicable to this example is described in LICENSE.

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Example showing how the heat transfer with Robin boundary conditions is solved using the iron library.

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