A Two-Dimensional port-Hamiltonian Model for Coupled Heat Transfer

In this paper, we construct a highly simplified mathematical model for studying the problem of conjugate heat transfer in gas turbine blades and their cooling ducts. Our simple focuses on relevant coupling structures aims to reduce unrelated complexity as much possible. Then, apply port-Hamiltonian formalism its subsystems investigate interconnections. Finally, spatial discretization system properties resulting finite-dimensional determine whether order affect semi-discrete system.