functionbiotAndUniformGrid

Information

This functions gives the position of the vertices that form segments. The position is computed to insure an equal distance between all the vertices, expected for one of the boundary segment (x[2] - x[1]) if symmetricalMesh is false and both otherwise, where the size of the segment is computed for having a Biot number equal to 0.1.

For the special case where the number of segments N equal 2, the length of the segment is half of the length of the domain and biot layers are ignored.

In order to compute the size of the 'Biot' layer, the user has to supply as input of the function a decouple value for the heat transfer coefficient at the boundary(ies) and the thermal conductivity of the material.

The distance between vertices derives:

Where :

• x is the vector of size N+1 of position of the vertex that form the segment of the mesh of the domain
• N is the number of segments
• L is the length of the domain to mesh
• dx is the thickness of the 'Biot layer'
• Biot is the Biot number
• λ is the thermal conductivity of the material
• h is the heat exchange coefficient at the boundary(ies)

A mesh divided into N segments contains N+1 vertices. That is why the size of x is N+1.

Inputs

Outputs