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Heat and Mass Transfer
Published in Raj P. Chhabra, CRC Handbook of Thermal Engineering Second Edition, 2017
Robert F. Boehm, Swati A. Patel, Raj P. Chhabra, George D. Raithby, K.G. Terry Hollands, Anoop K. Gupta, N.V. Suryanarayana, Thomas F. Irvine, Massimo Capobianchi, Michael F. Modest, Van P. Carey, John C. Chen, Vasilios Alexiades, Jan Kośny, Anthony F. Mills
The Stefan problem is a mathematical model for melting a solid, or freezing a liquid by heat conduction, assuming that the phases are separated by a (locally planar) moving front, whose position at time t, denoted by x = X(t), is to be found along with the temperature field T(x, t). The phase-change front (interface) is assumed to be sharp, a surface of zero thickness, along which the temperature is the melting temperature Tm and where the latent heat is absorbed or released.
Numerical Modeling and Simulation of Melting Phenomena for Freeze Valve Analysis in Molten Salt Reactors
Published in Nuclear Science and Engineering, 2023
Davide Tartaglia, Antonio Cammi, Carolina Introini, Stefano Lorenzi
Melting and solidification of the fuel salt play a key role in the design and safety of the MSFR, such as the design of the freeze plug,[4] the analysis of accident scenarios where the solidification of the salt might be a risk,[5] or the possible formation of a frozen salt film on the reactor vessel walls, protecting them from corrosion.[6] A mathematical description of the melting and solidification problem allows for a quantitative description of a phase-change transient. The most basic mathematical description of melting and solidification phenomena is due to Josef Stefan,[7] and the respective mathematical problem is known as the Classical Stefan Problem. However, this problem does not have exact or approximate analytical solutions for many real engineering situations. For instance, most practical situations are multidimensional in nature, while analytical solutions are only available in one dimension.[8] For this reason, the urge for the development of numerical methods has been present in the scientific literature since at least the late 1980s.
Numerical investigation of a non-linear moving boundary problem describing solidification of a phase change material with temperature dependent thermal conductivity and convection
Published in Journal of Thermal Stresses, 2023
Vikas Chaurasiya, Jitendra Singh
Mathematical and theoretical modeling of the Stefan problem is of much interest in heat transfer phenomena describing phase change processes [1–5]. This type of problem commonly occurs in the liquid/solid phase transition process, in which the phase change front constitutes a moving boundary. Due to the presence of a moving boundary, such problems are known as the moving boundary problem (Stefan problem). The heat transfer process with phase change occurs widely in various engineering applications such as freeze-drying [6, 7], metal casting [8], and energy storage [9, 10]. The moving liquid/solid interface is a part of the solution of the problem that can be calculated from a liquid-solid relation often called Stefan condition. Due to the interrelation of this condition, the concerning problem is known as the Stefan problem. A detailed study of the mathematical model of phase-change problems involving melting/freezing, and their treatment is well explained in several books [11–13].
Analytical solution of the melting process of phase-change materials in thermal energy storage system
Published in Energy Sources, Part A: Recovery, Utilization, and Environmental Effects, 2020
Zhuqian Zhang, Zichen Wang, Xiande He
Thermal storage technologies have received more and more attention for its ability to match the energy supply and demand, which are also applied in the battery thermal management system to keep the working temperature in a proper range (Liu et al. 2017; Rao, Wang, and Zhang 2014). Thermal storage can be divided into two types: latent thermal storage and sensible thermal storage. Latent thermal storage takes advantages of high energy storage density and isothermal characteristics, which becomes a principal method to replace the sensible heat storage (Chinnapandian et al. 2015; Hua et al. 2019). The phase-transition forms are various, including solid–solid (Huang et al. 2016; Zhou and Liu 2018), solid–liquid (Bicer, Sari, and Lafci 2015; Rao and Zhang 2011), gas–liquid (Das, Kumar, and Sandhu 2019). Since the volume expansion ratio of solid–liquid is lower than that of gas–liquid and ga–solid, solid–liquid is the preferred phase-transition type for heat storage systems (Senthil 2019). It is essential to study the heat-transfer process of the solidification and melting of phase-change material (PCM) for the purpose of optimizing the thermal storage system. Experiment is one of the important ways to study the processes of solidification and melting. However, the temperature acquisition is restricted for the limited temperature measuring points in the experiments, which results in the limitation of understanding of the temperature distribution and the moving phase-change interface (Korti and Tlemsani 2016; Wang et al. 2019). Phase-change heat transfer has been investigated for decades and it is regarded as a Stefan problem. Great efforts have been made to solve the problems in solidification and melting.