Silva-Nava Valter, Hernández-Cooper Ernesto M, Chong-Quero Jesús Enrique, Otero José A
Tecnologico de Monterrey, Escuela de Ingeniería y Ciencias, Carr. al Lago de Guadalupe Km. 3.5, Atizapán de Zaragoza 52926, Estado de Mexico, Mexico.
Molecules. 2022 Feb 10;27(4):1189. doi: 10.3390/molecules27041189.
Two mass-accommodation methods are proposed to describe the melting of paraffin wax used as a phase-change material in a centrally heated annular region. The two methods are presented as models where volume changes produced during the phase transition are incorporated through total mass conservation. The mass of the phase-change material is imposed as a constant, which brings an additional equation of motion. Volume changes in a cylindrical unit are pictured in two different ways. On the one hand, volume changes in the radial direction are proposed through an equation of motion where the outer radius of the cylindrical unit is promoted as a dynamical variable of motion. On the other hand, volume changes along the axial symmetry axis of the cylindrical unit are proposed through an equation of motion, where the excess volume of liquid constitutes the dynamical variable. The energy-mass balance at the liquid-solid interface is obtained according to each method of conceiving volume changes. The resulting energy-mass balance at the interface constitutes an equation of motion for the radius of the region delimited by the liquid-solid interface. Subtle differences are found between the equations of motion for the interface. The differences are consistent with mass conservation and local mass balance at the interface. Stationary states for volume changes and the radius of the region delimited by the liquid-solid interface are obtained for each mass-accommodation method. We show that the relationship between these steady states is proportional to the relationship between liquid and solid densities when the system is close to the high melting regime. Experimental tests are performed in a vertical annular region occupied by a paraffin wax. The boundary conditions used in the experimental tests produce a thin liquid layer during a melting process. The experimental results are used to characterize the phase-change material through the proposed models in this work. Finally, the thermodynamic properties of the paraffin wax are estimated by minimizing the quadratic error between the temperature readings within the phase-change material and the temperature field predicted by the proposed model.
提出了两种质量调节方法来描述在中央加热环形区域中用作相变材料的石蜡的熔化过程。这两种方法以模型形式呈现，其中通过总质量守恒纳入了相变过程中产生的体积变化。将相变材料的质量设定为常数，这带来了一个额外的运动方程。以两种不同方式描绘了圆柱形单元中的体积变化。一方面，通过一个运动方程提出径向方向上的体积变化，其中将圆柱形单元的外半径提升为运动的动态变量。另一方面，通过一个运动方程提出沿圆柱形单元对称轴方向的体积变化，其中液体的多余体积构成动态变量。根据每种设想体积变化的方法获得液 - 固界面处的能量 - 质量平衡。在界面处得到的能量 - 质量平衡构成了由液 - 固界面界定区域半径的运动方程。在界面的运动方程之间发现了细微差异。这些差异与界面处的质量守恒和局部质量平衡一致。针对每种质量调节方法获得了体积变化以及由液 - 固界面界定区域半径的稳态。我们表明，当系统接近高熔点状态时，这些稳态之间的关系与液体和固体密度之间的关系成比例。在由石蜡占据的垂直环形区域中进行了实验测试。实验测试中使用的边界条件在熔化过程中产生了一个薄液层。通过本文提出的模型，利用实验结果来表征相变材料。最后，通过最小化相变材料内温度读数与所提出模型预测的温度场之间的二次误差，估算了石蜡的热力学性质。
