Abstract

This paper addresses the melting of phase change solid sphere, which motivates researchers to develop new thermal energy storage (TES) systems techniques. Phase change materials can store or release large amounts of heat in short intervals of time, thus improving the thermal performance of cooling and heating systems in buildings and regulate the temperature of PV systems, batteries and other electronic components. We have considered a convective spherical Stefan problem with thermal conductivity as a function of time and temperature. The heat balance integral method (HBIM) is used to find the problem’s solution numerically. The temperature profile is approximated by using n degree polynomial. The influence of governing parameters on the location of melting front and temperature profile is discussed thoroughly. The parameters depict that transition from solid to liquid phase becomes fast for higher values of Stefan number while the transition rate slows down for larger values of Peclet number. The melting rate increases from 20% to 80% when Stefan number rises from 0.1 to 1.0 at a particular time. Moreover, a comparative study of the proposed model with some existing models is being done. It is observed that moving melting front for the assumed problem undergoes a fast melting process.

中文翻译：

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变导热球形相变材料熔化过程的数值研究

摘要

本文讨论了相变固体球的熔化问题，这促使研究人员开发新的热能存储（TES）系统技术。相变材料可以在短时间内储存或释放大量热量，从而提高建筑物中冷却和加热系统的热性能，并调节光伏系统、电池和其他电子元件的温度。我们考虑了热导率随时间和温度变化的对流球形 Stefan 问题。热平衡积分法 (HBIM) 用于数值求解问题。温度分布通过使用 n 次多项式来近似。深入讨论了控制参数对熔化前沿位置和温度分布的影响。这些参数表明，对于较高的斯特凡数值，从固相到液相的转变变得更快，而对于较大的佩克莱特数值，转变速率减慢。当Stefan数在特定时间从0.1上升到1.0时，熔化率从20%增加到80%。此外，正在对所提出的模型与一些现有模型进行比较研究。据观察，假设问题的移动熔化前沿经历了快速熔化过程。