  We propose a new interconnection relation for infinite-dimensional
port-Hamiltonian systems that enables the coupling of ports with different
spatial dimensions by integrating over the the surplus dimensions. To show the
practical relevance, we apply this interconnection to a model system of an
actively cooled gas turbine blade. We also show that this interconnection
relation behaves well with respect to a discretization in finite element space,
ensuring its usability for practical applications.
