Thermal analysis of axisymmetric domains using the polar coordinate formulation of the finite-volume theory

Resumo

Thermal analysis plays a critical role in engineering, particularly when evaluating materials and components subjected to complex operating conditions. In this context, understanding temperature distributions within axisymmetric domains, such as cylindrical structures, pipes, and circular rings, is fundamental to ensuring proper performance and structural integrity. This work presents an approach for the thermal analysis of axisymmetric domains based on a polar-coordinate formulation of the finite-volume theory. The formulation involves assembling local thermal conductivity matrices associated with surface-averaged temperature and heat flux vectors evaluated at the faces of the internal subvolumes of the discretized analysis domain. Subsequently, the global thermal conductivity matrix is assembled by satisfying the local heat flux balance and applying the local compatibility conditions regarding surface-averaged temperature and heat flux at the interfaces between adjacent subvolumes. The numerical results obtained through computational simulations demonstrate excellent agreement with analytical solutions, certifying the accuracy and robustness of the proposed polar formulation.