[bigdadi]

I am trying to find the steady-state temperature distribution of a 200mm by 20 mm rectangular an-isotropic (with two different thermal conductivity kx and ky) 2D wall plate. The anisotropic plate should be insulated to prevent the heat coming from the left side. The insulation material's thermal conductivity (kins) will also be determined. I am thinking of using finite difference method, but I have problems setting up the nodal equations on the interface between the insulation material and the plate. If you have any suggestion please I need your help. Thank you for your time. Click the URL to look at the figure. https://ibb.co/hervVk

[abkahraman]

Instead trying to use finite difference method, try a little bit different version of it, the basic finite volume method. Draw rectangular control volumes around every node and equate the heat flux coming into those "cells" with the heat flux going out. This should make your discretized equations easier, especially at the interface for with the insulator and the wall.