Comparison of the Adomian decomposition method and the variational iteration method in solving the moving boundary problem

AbstractIn this paper, a comparison between two methods: the Adomian decomposition method and the variational iteration method, used for solving the moving boundary problem, is presented. Both of the methods consist in constructing the appropriate iterative or recurrence formulas, on the basis of the equation considered and additional conditions, enabling one to determine the successive elements of a series or sequence approximating the function sought. The precision and speed of convergence of the procedures compared are verified with an example

Effect of nanoparticles on solid-liquid phase change heat transfer rate

Phase change materials (PCMs) have many engineering applications, such as thermal insulation, thermal management, and storing thermal energy. With a high latent heat of fusion, many organic PCMs such as paraffin are ideal for thermal energy storage, but their relatively low thermal conductivity makes the melting and solidification process lengthy. One way to improve this problem is the dispersion of highly conductive nanoparticles to the base PCM, making a mixture of so-called Nano-enhanced Phase Change Materials (NePCMs). However, adding nanoparticles changes many other properties of the mixture, such as viscosity, which may affect the total heat transfer rate in a complicated way. The literature on this topic shows some contradicting findings, with some studies reporting enhanced phase change heat transfer with nanoparticles, but some reporting reduced heat transfer rate. It is critically important to conduct a systematic study for a better understanding of the effects of nanoparticles on the solid-liquid phase change heat transfer rate. This thesis aims to conduct such a study. It starts with a review of the analytical models for the phase change problems, the significant parameters on the phase change rate through scaling analysis, and reported effects of nanoparticles on the phase change rate. Then, a melting problem with Rayleigh-Benard convection is investigated in a rectangular enclosure both numerically and experimentally. It is found that the effect of nanoparticles on the total heat transfer rate during this melting process is highly dependent on the level of domination of natural convection (as compared to conduction) during the phase change process. Based on the scaling analysis and the experimental results, predictive correlations are developed for the viscosity and melting rate of the NePCMs. The effects of nanoparticles on the heat transfer and phase change rate are also numerically analyzed in shell-and-tube thermal energy storage units with and without fins. The different behaviours of nanoparticles are investigated in terms of the significance and domination of natural convection in the melted regions. With a numerical and statistical approach, predictive correlations are developed for each case, and the potential interactions between the parameters in affecting the total heat transfer rate are identified. Most previous researches came up with a critical concentration of nanoparticles for higher phase change rate in a particular energy storage case. The results are often not applicable to other cases. This research systematically analyzes the effects of nanoparticles on the phase change heat transfer rate, leading to better and more general understandings of these effects. It identified the key parameters (e.g., Rayleigh number) in the heat transfer process and developed predictive correlations for phase change rate. The new findings would be useful for designers of latent thermal energy storage systems as to whether and how nanoparticles could be potentially used in the design of latent thermal energy storage units