Very high-order accurate polygonal mesh finite volume scheme for conjugate heat transfer problems with curved interfaces and imperfect contacts

Abstract

The conjugate heat transfer problem is found in non-isothermal physical systems that involve thermodynamic processes between materials that are thermally coupled through non-adiabatic contacts. A very high-order accurate finite volume scheme in general polygonal meshes is proposed to solve conjugate heat transfer problems with arbitrary curved interfaces and imperfect thermal contacts. Besides the discontinuous thermal properties, imperfect thermal contacts are challenging to address since the obtained temperature is also discontinuous on the interface as a consequence of the interfacial thermal resistance. Moreover, the arbitrary curved interfaces are discretized with polygonal meshes to avoid the shortcomings of classical curved mesh approaches, but a specific treatment is required to overcome the geometrical mismatch and properly fulfill the prescribed interface conditions. The proposed method is based on a partitioned formulation of the conjugate heat transfer problem with the appropriate thermal coupling. A generic polynomial reconstruction method is used to provide local approximations of the temperature complemented with the reconstruction for off-site data method to properly fulfill the prescribed interface conditions. A comprehensive numerical benchmark is provided to verify the proposed method and assess its capability in terms of accuracy, convergence order, stability, and robustness. The results provide the optimal very high-order of convergence and prove the capability of the method to handle arbitrary curved interfaces and imperfect thermal contacts. This contribution represents a significant step towards more efficient and versatile numerical methods for complex conjugate heat transfer problems in engineering applications.