The paper presents a formal representation for modeling function structure graphs in a consistent, grammatically controlled manner, and for performing conservation-based formal reasoning on those models. The representation consists of a hierarchical vocabulary of entities, relations, and attributes, and 33 local grammar rules that permit or prohibit modeling constructs thereby ensuring model consistency. Internal representational consistency is verified by committing the representation to a Protégé web ontology language (OWL) ontology and examining it with the Pellet consistency checker. External representational validity is established by implementing the representation in a Computer Aided Design (CAD) tool and using it to demonstrate that the grammar rules prohibit inconsistent constructs and that the models support physics-based reasoning based on the balance laws of transport phenomena. This representation, including the controlled grammar, can serve, in the future, as a basis for additional reasoning extensions.