A refined invariant subspace method and applications to evolution equations

The invariant subspace method is refined to present more unity and more diversity of exact solutions to evolution equations. The key idea is to take subspaces of solutions to linear ordinary differential equations as invariant subspaces that evolution equations admit. A two-component nonlinear system of dissipative equations was analyzed to shed light on the resulting theory, and two concrete examples are given to find invariant subspaces associated with 2nd-order and 3rd-order linear ordinary differential equations and their corresponding exact solutions with generalized separated variables.Comment: 16 page

Climate applicability study of building envelopes containing phase change materials

SUMMARY Building envelopes incorporating phase change materials (PCMs) can contribute to reducing the energy consumption of buildings and enhance indoor thermal environment comfort. In this study, two building models were developed in EnergyPlus to explore the applicability of using PCMs in different climate zones. Six significantly different cities from five climate zones in China have been investigated. The simulation results reflected that for climates with small fluctuation weather conditions, PCMs with appreciate transition temperature TR can contribute to positive influences on energy saving. For example, in Guangzhou, PCMs with TR of near 26oC and 22oC contribute to the highest energy‐saving rates of 12.0% and 12.4%, for external and internal PCMs addition. And the ideal transition temperature for each climates is subjected to its own outdoor comprehensive temperatures and its indoor set temperature, for external and internal PCMs addition, respectively. For other climates with the big fluctuation weather condition, PCMs' latent heat function to the energy savings is not significant

Development and energy evaluation of phase change material composite for building energy-saving

SUMMARY Phase change materials (PCMs) contributed to building energy‐saving and thermal comfort through increasing the thermal capacity of building envelopes. In this study, a phase change material composite was developed by using the PCMs mixture of capric acid (CA) and lauric acid (LA) as the primary phase change energy storage agent and using the solid waste fly ash as a carrier material. The results showed that for Guangdong, the ideal PCMs mixture should have a transition temperature of 25.5oC, which could be obtained by using a mass ratio of CA/LA of 4:6. Then, experiment results also indicate that the optimum adsorption ratio of 2:1 (FA/PCMs) was detected for the synthesis of this FA/PCMs composite, which has the latent heat of 45.38 J/g and exists excellent thermal reliability. Moreover, simulation results by using EnergyPlus show that the proposed composite has a good building energy‐saving effect