Conductance matrix for pyramid elements

The conductance matrix of pyramid element and sub-elements is derived by dividing the pyramid into two tetrahedra elements and applying the following conditions:

  • The sum of the heat flows through the adjacent side of the two tetrahedra is zero.
  • The uniform heat flux is defined on the quadrilateral face, in which the thermal gradient normal to the quadrilateral face is the same as both triangles subdividing that face.
  • The temperature at the CG of the quadrilateral face is equal to the area-weighted average temperature of the CG's of the two triangles subdividing that face.

The element conductance matrix is created by eliminating the computation point at the CG of the internal faces, using the star-delta transformation that results in a conductance matrix between the boundary elements.

When the software uses the default setting, conductance between the CG and boundary elements are balanced, similar to the previous equation.