A Comparison of Different Solution Methodologies for Melting and Solidification Problems in Enclosures

On the importance of solid deformations in convection-dominated liquid/solid phase change of pure materials

“…The analysis of the past (till very recent) literature on the two-dimensional numerical simulation of this Gau & Viskanta experiment leads to the following significant considerations: i) the multicellular flow structure of the melt convection meets expectations from fluid dynamics (Lee & Korpela [38], Derebail & Koster [17]), and from ad hoc stability analysis of melting from a side (Le Quere & Gobin [39]), ii) the multicellular flow structure of the melt convection appears combined with unphysical wavy shaped phase fronts (Dantzig [14], Stella & Giangi [48], Hannoun et al [27]), iii) certain low order numerical schemes yield one main cell melt flow and produce smoother phase fronts, surprisingly closer to experimental observation (Brent et al [6], Viswanath & Jaluria [55]), iv) some specialists, counting on highly accurate numerical discretizations, have started to explain the inconsistencies by conjecturing that the mathematical models in use for phase change with convection are not adequate for this experiment (Hannoun et al [26], Tenchev et al [51]). …”

“…The paper by Hurle [32] deals with the transitions of the horizontal convective flow of the melt in artificial crystal growth systems. On this issue a bunch of papers have been published throughout the following years to nowadays (e.g., more recently, Viswanath & Jaluria [55], De Groh III & Lindstrom [16], Rady & Mohanty [44], Voller [57], Yeoh et al [58], Chen et al [9], Bertrand et al [5], Sampath & Zabaras [45], Bansch & Smith [4], Kim et al [35]). The applicative interest in this specific matter is due to the fact that oscillatory instabilities in the melt flow are one of the main causes of the appearance of dishomogeneities and defects in the final crystal.…”

Influence of the Fin Design on the Melting and Solidification Process of NaNO3 in a Thermal Energy Storage System

“…The balance equations for momentum and energy are solved in each phase in the multi-domain method [39,41,44]. Between the two phases, a time dependent interface (phase change boundary) is arranged, which is modeled by a porous zone.…”

A Finite-Volume/Newton Method for a Two-Phase Heat Flow Problem Using Primitive Variables and Collocated Grids

“…[1][2][3][4][5][6][7]) have been proposed to solve these prob-velocity decoupling can be avoided, the collocated allocalems. Among them, they can be categorized, from the for-tion seems to be a good candidate for two-and threemulation point of view, by streamfunction/vorticity (/Ͷ) dimensional free boundary problems, and even for [2][3][6][7] and primitive (UVP) variables [1,[4][5], and multigrid methods. Interestingly, to the UVP formulation from solution point of view, by decoupled [2][3][4][5][6] and global Newton's method has not been used based on the collo-(coupled) [1,7] iteration approaches.…”