## 1 Introduction  
Energy and environment are the two of the most significant basic factors for the development of the human society. The combustion of fossil fuels, which emit a great deal of carbon dioxide contributes to the global warming issue and effective energy saving techniques are essential for solving the energy crisis and environmental issues [1]. Building energy consumption was responsible for more than 40% of the total energy cost in China during the past seven years [2; 3]. Furthermore, the energy consumption of a building is still increasing as people's living standards improve. For this reason, developing green buildings with high energy saving characteristics has been an indispensable task for local government in order to protect the living environment and realize sustainable development. Reducing the energy release through the building envelope is an important approach for decreasing the buildings energy consumption. Due to their low thermal conductivities and latent heat characteristics, the PCMs could be inserted into the building envelope as a thermal insulation layer to decrease the building energy cost, which has attracted a lot of research attention during recent years [4; 5; 6]. As the PCMs absorb and release heat during a solid-liquid phase change process at a nearly constant temperature, it could not only increase the thermal resistance of a building's envelope but also attenuate the temperature oscillation so that the thermal comfort of the building's rooms is improved. The research methodologies for building a PCM envelope can be generally categorized as follows: Theoretical method, experimental method, and numerical method. With the fast progress of computer science and numerical modelling schemes, numerical methods have been widely used to analyze the energy saving characteristics of buildings [7]. [PERSON] applied a one-dimensional finite difference method to investigate the transient conjugate heat transfer inside the building walls contained with PCMs [8]. It was found that the integration of a PCM layer into a building wall could diminish the instantaneous heat flux magnitude through the wall when the PCM melting temperature was appropriately chosen. Besides, due to the elevated solar radiation, the wall orientation has a more obvious effect on the energy consumption of a building during the summertime. [PERSON] solved the one-dimensional transient heat equation in the multilayered wallboard using the Crank-Nicolson discretization scheme [9]. It was found that an optimum location for PCM placement existed in terms of different thermal resistances between the PCM layers and the external thermal boundary conditions. [PERSON] numerically optimized the location of the PCM layer under different parametric conditions by validating their model with experiments conducted using a dynamic wall insulator [10]. They presented that the optimum PCM layer location approaches the exterior surface of the wall when the melting temperature and the latent heat of PCMs were increased. By validating the numerical model with a PCM wallboard heat storage experiment, [PERSON] investigated the thermal performance of PCM wallboards for practical engineering [11]. Their results indicated that the PCM wallboard performance could be adverse in different seasons and the thermal analysis through an entire year is also necessary. The above research was mainly related to the heat transfer properties of PCM walls. However, the thermal loss of roofs contributes almost 70% of the total heat loss in building envelopes due to direct solar radiation and heat transfer between the roof and the exterior environment. Under this situation, the thermal performance of roofs imbedded with PCM layers deserves more scientific investigations. [PERSON] numerically analyzed the thermal performance of a roof that contained PCM in a single residential building with respect to the factors of solar radiation intensity, roof slope, PCM melting temperature and layer thickness [3].