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Summary: The current latent heat storage (LHS) units are usually poor in energy charging and discharging efficiency. Given this, a two dimensional (2D) numerical model of the energy discharging process is presented and comprehensively analyzed to predict the role of metal foam in the solidification performance of LHS units. In the model, the fractal geometry reconstructed by the fractal Brownian motion is utilized for the pore characterization of the metal foam. The proposed model is validated through a melting experiment in copper foams from the reference. The temperature dynamic response and the solidification front evolution in metal foam are analyzed and compared to those in a corresponding cavity. The roles of the fractal dimension and porosity in the solidification behaviors are quantitatively analyzed. The results report that the presence of metal foam enhances the solidification performance. For the main goal of maximizing the latent storage, the appropriate porosity of an LHS unit is dependent on the duration time for the heat discharging process in the real application of thermal energy storage. Even if the porosity is the same, the fractal dimension also affects the solidification performance. A decrease in the fractal dimension (lower degree of disorder for pore distribution) provides greater access to heat flow through the phase change material‐foam composite and thus leads to improvement in the interstitial heat transfer, which in turn accelerates the rate of heat release. The fractal dimension is expected to be less than 1.5 for superior solidification performance. [ABSTRACT FROM AUTHOR]

This paper is concerning the asymptotic behavior of solutions to the fast diffusive non-Newtonian filtration equations coupled by the nonlinear boundary sources. We are interested in the critical global existence curve and the critical Fujita curve, which are used to describe the large-time behavior of solutions. It is shown that the above two critical curves are both the same for the multidimensional problem we considered. [ABSTRACT FROM AUTHOR]