In recent years, significant effort has been put into developing automated multi-physics simulation. The exchange of boundary conditions has lead to more realistic as well as more complex simulations with usually slower convergence rate when the coupling is being performed between two different codes. In this paper the equations of local sensitivities for element centered steady-state combined convection, conduction, and thermal radiation problems are being derived along with some implementation details. A numerical analysis on the stability of the solution matrix is being conducted. The relative importance of the heat transfer modes at various locations are investigated by their uncertainty factors and conclusions are being drawn.

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