Abstract

Boundary controlled irreversible port-Hamiltonian systems (BC- IPHS) defined on 1, 2 and 3-dimensional spatial domains are defined by extending the formulation of reversible BC-PHS to irreversible thermodynamic systems controlled at the boundaries of their spatial domain. The structure of BC-IPHS has a clear physical interpretation, characterizing the coupling between energy storing and energy dissipating elements. By extending the definition of boundary port variables of BC-PHS to deal with the irreversible energy dissipation, a set of boundary port variables is defined so that BC-IPHS are passive with respect to a given set of conjugated inputs and outputs. As for finite-dimensional IPHS and 1-D infinite-dimensional IPHS recently defined in [Ramirez et al., Chem. Eng. Sci. (2022)], the first and second laws of Thermodynamics are satisfied as a structural property of the system. As a common thread, the 3D compressible fluid example is worked out to illustrate the proposed approach: both the reversible case of the isentropic fluid and the irreversible case of the non-isentropic fluid are presented.Copyright (c) 2023 The Authors.