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This paper introduces an approach for the geometric modeling of advanced cellular structures, characterized by their stochastic, conformal nature, and the ability to transition between multiple topologies. Utilizing a function representation-enhanced topological skeletal graph methodology, this approach enhances computer-aided design by encapsulating complex geometries and parameters within a versatile function representation framework. The novelty of this work lies in its operationalization through LatticeQuery, an open-source software, which demonstrates versatility in modeling stochastic cellular structures, ensures smooth topology transitions, and supports the design of conformal cellular structures. This exploration not only validates the potential of the introduced methodology but also opens new avenues in the design of cellular structures with intricate geometries and variable properties, catering to a wide range of industrial applications. [Display omitted] • A novel cellular modeling method blending function representation with skeletal graphs for enhanced design flexibility. • Seamless topology transitions in cellular structures for complex design adaptability. • Utilizes open-source tools for advanced cellular structure generation, setting a foundation for future innovation. [ABSTRACT FROM AUTHOR]

[Display omitted] • A literature review on the heat and flow properties of lattice structures is performed, and design parameters are identified. • Detailed geometric modeling and clear the knowledge gaps in the flow and heat properties of various lattices. • The results are compared with the findings obtained from existing literature and documented in detailed charts. Lattice structures are known for their capability to be tailored for achieving specific properties such as high porosity and strength, impact energy absorption and lightweight. While the mechanical properties of the strut-based and surface-based lattice structures have already been investigated in the literature, a systematic investigation of their flow and thermal properties has yet to be established. This work investigates the friction factor and convective heat transfer coefficient across strut- and surface-based lattice structures. The modeled structures are simulated in the convective heat transfer environment to gather the heat transfer coefficient and the friction factor outputs. The simulation results are documented in this work and used to generate a flow and thermal property chart to support the design process by providing a guideline for selecting lattice topologies. [ABSTRACT FROM AUTHOR]