A graph theory-based modelling framework for thermal response analysis of polar ship superstructure with arbitrary compartment layouts

Polar ships experience extreme temperature gradients and prolonged cold exposure, necessitating stable thermal environments for crew and equipment. Accurate prediction of heat transfer and compartment thermal responses is critical for cold-proof design and heating strategies. This paper develops a generalized heat transfer modelling framework for polar ship superstructure with arbitrary compartment layouts. A graph theory-based description approach is proposed to represent compartment adjacency relations via undirected graphs. An adjacent matrix and vectorized elements are proposed to quantify complex inter-compartment heat transfer based on polygon-clipping algorithm. A generic-form heat transfer model is established to predict coupled thermal responses of compartments and wall structures for arbitrary spatial configuration. Validations against both single- and multi-compartment cases indicate the consistency and robustness of the proposed modelling framework. A practical case study simulating 71 compartments across 5 decks reveals significant spatial heterogeneity in compartment thermal responses to cold environments, highlighting model capability to describe and simulate complex heat transfer in ship compartment group. The results demonstrate the model utility in designing precise heating strategies that enhance temperature uniformity while reducing energy consumption, offering application potential for cold-proof design and thermal management of polar ships.