Development of Finite Volume Shell Conduction Model for Complex Geometries

Thin, plate-like structures are often encountered in industrial heat transfer applications. Discretizing them as volumetric elements along with the rest of the domain results in a large number of elements and significantly increases the cost of computational analysis of such problems. It can also cause numerical errors and convergence difficulties because of the large aspect ratios and skewness of the mesh. On the other hand, treating the conduction in such regions separately is also unattractive because the inherent coupling of the two problems makes for very slow convergence. In this paper we present an alternative approach which treats such structures as planar elements while still maintaining full coupling between the temperature fields in the two regions. Consequently the solution for the entire domain can be obtained simultaneously without significant increase in problem complexity. The method is validated using canonical problems as well as solutions obtained by full discretization of the thin structures. Compared to the latter, the present approach is found to be significantly more efficient and robust.