An approximate approach of heat transfer accompanied by phase transition

Low temperature heat (solar energy, geothermal energy, industrial and domestic waste heat) is widely available for many applications. Energy storage of that heat is now of great importance because the key to the effective and widespread use of low temperature heat is its adaptation to the energy requirements. From this point of view, storage tanks based on the phase change principal are one interesting alternative. Phase change material (PCM) is particularly attractive due to its ability to provide a high-energy storage density and its characteristics to store heat at a constant temperature corresponding to the phase transition temperature of the heat storage material. That is why the problem of the heat transfer accompanied by phase transition is of mine interest to the practice. Heat storage system with the PCM and shell-and-tube type is analysed by Lacroix [6]. Several authors, using mathematical models of different complexity, studied this type of. latent heat storage unit. Heat-of-fusion storage materials for law temperature storage in the temperature range 0-120oC are reviewed by Abhat [5] and Reiter and Rota [4]. Hamdan and Elweer [3] have investigated a melting process of a solid phase. In the present study, the phase change problem of the PCM is analysed in another type of heat storage system. We use closed tubes (capsules) filled with PCM and the heat transfer fluid (HTF) flowing in the shell space of the heat exchanger (Fig.1). The heat process is analysed in terms of both radial and axial direction and is linked to the convective heat transfer from the HTF. As it is known [2,3] the transient heat transfer in PCM can be described by the well-known heat conduction equation applied for various phase conditions and the energy balance on the interface given by the Stephan's equation. The later determines the rate of moving of the interface and in this manner the space areas where the heat conduction equations have corresponding coefficients. The application of this approach is related to the use of two space areas of solutions and leads to considerable difficulties in the algorithm and programming in the cases of two and three-dimensional problems. Another method for the solving of this kind of problems is the use of equivalent characteristics of the substances [3,4]. This approach is based generally on the evaluation of the equivalent specific heat capacity of the substance in the phase change area summarizing in this manner the heat capacity effect and the heat for the phase transition. This treatment has the advance to obtain a homogeneous mathematical problem having a common space solution area. It should be mentioned that the equivalent specific heat capacity is strongly temperature depending and so a supplementary dependence between space and time increment can arise during the discretization of the equations. The aim of this study is therefore to propose a new approach to the problem, using a source member in the heat conduction equation that takes in account the effect of phase transition. (Authors)