International Journal of Thermal Sciences 156 (2020) 106496 Available online 1 June 2020 1290-0729/© 2020 Elsevier Masson SAS. All rights reserved. An improved layered thermal resistance model for solid-liquid phase change time estimation Mohammad Parsazadeh a , Zhichun Liu b , Xili Duan a, * a Faculty of Engineering and Applied Science, Memorial University of Newfoundland, St. John’s, Newfoundland, A1B 3X5, Canada b School of Energy and Power Engineering, Huazhong University of Science and Technology, Wuhan, Hubei, 430074, China A R T I C L E INFO Keywords: Heat conduction Phase change Solidifcation time Layered thermal resistance model Approximate semi-analytical solution ABSTRACT This work improves a layered thermal resistance (LTR) model for the prediction of phase change times in solid- liquid phase change heat transfer. A combination of analytical and numerical approaches is applied in 1-D and 2- D solidifcation problems where heat conduction is dominant. In the improved layered thermal resistance (ILTR) model, the domain is discretized to layers. Based on its thermal resistance, the solidifcation time of each discrete layer is obtained by calculating the heat fux across the boundaries and the sensible and latent heat transfer. Unlike the quasi-steady heat conduction approach and linear temperature distribution assumption in the LTR model, the ILTR model considers transient heat conduction in each layer thus providing a better estimation of the average temperature distribution. The total solidifcation time is obtained by adding the solidifcation time of all the discrete layers. In several validations, the ILTR model shows a good agreement with the exact solution (1-D), experimental results (1-D), and numerical results (2-D). It is demonstrated that the ILTR model provides better predictions of phase change times than the LTR model, particularly under large Stefan numbers. This model could be further developed for more complicated (geometry or boundary conditions) phase change problems. 1. Introduction Solidifcation and melting of materials widely occur in various en- gineering applications, such as latent heat thermal energy storage [1], thermal management in space equipment [2], building materials [3], freezing of food or water [4], solidifcation of metals in casting [5], just to name a few. During a liquid-solid phase transition, thermal energy is released or stored almost isothermally at the melting temperature. These phase change heat transfer problems are diffcult to model because of the transient nature and the inherent moving boundary condition at the solid-liquid interface. In modeling ice formation, early analytical works [6,7] solved the parabolic heat conduction equations in a region a moving boundary. This was later named the Stefan problem [7]. The integral method, an approximate solution, was implemented to solve a one-dimensional transient melting problem by Goodman [8], and later by many other researchers [9–12]. The moving heat source (or integral equation) method is another method for the solution of phase change problems, where the latent heat transfer is treated as a moving heat source or sink. This method was analytically implemented in one-dimensional phase – change problems and later numerically developed for other conditions [13,14]. The approximate perturbation method and variable eigenvalue method were also studied widely [15–17]. These analytical methods are limited to the one-dimensional and semi-infnite domain. In the real world, however, solidifcation problems are rarely one-dimensional. To solve more complicated phase change problems, researchers have come up with various innovative methods. In one study, Myers and Mitchell [18] analyzed the accuracy of the heat balance integral method with a time-dependent boundary condition. They developed a loga- rithmic approximating function to capture the moving peaks in the temperature profle; then they [19] utilized their method for the Stefan problem and reported that their new method was more accurate than the second-order perturbation solution in a wide range of Stefan numbers. He [20]introduced the homotopy perturbation method, which is another approximate analytical solution. This method was implemented by Singh et al. [21] to model solidifcation using time-space fractional derivatives in a fnite slab and to study the effects of a different order of fractional time and space derivatives on the freezing process. Bauer [22] developed an approximate analytical solution based on the effective medium properties of the fn and the phase change material (PCM). The method was implemented to calculate the solidifcation time of a PCM in a fnned plane wall and a radially fnned tube. The method is limited to * Corresponding author. E-mail address: xduan@mun.ca (X. Duan). Contents lists available at ScienceDirect International Journal of Thermal Sciences journal homepage: http://www.elsevier.com/locate/ijts https://doi.org/10.1016/j.ijthermalsci.2020.106496 Received 1 January 2020; Received in revised form 21 April 2020; Accepted 18 May 2020