On the treatment of plane fusion front in lumped parameter thermal models with convection

•Solid phase approximations for a two-phase Stefan fusion problem with convection are analyzed.•A reference solution combines integral conservation eqs and a FE solution of the 1D heat equation.•Numerical results are presented for a transient in light water reactor severe accident analysis.•The models performances are highlighted on fusion transients in terms of Biot and Stefan numbers. Within the framework of lumped parameter models for integral codes, this paper focuses on the modeling of a two-phase Stefan fusion problem with natural convection in the liquid phase. In particular, this specific Stefan problem is of interest when studying corium pool behavior in the framework of light water reactor severe accident analysis. The objective of this research is to analyze the applicability of different approximations related to the modeling of the solid phase in terms of boundary heat flux closure relations. Three different approximations are considered: a quadratic profile based model, a model where a parameter controls the power partitioning at the interface and the steady state conduction assumption. These models are compared with an accurate front-tracking solution of this plane fusion front problem. This “reference” is obtained by combining the same integral conservation equations as the approximate models with a mesh-based solution of the 1D heat equation. Numerical results are discussed for a typical configuration of interest for corium pool analysis. Different fusion transients (constructed from nondimensionalization considerations in terms of Biot and Stefan numbers) are used in order to highlight the potential and limitations of the different approximations.