## 1 Introduction  
Solid liquid phase change materials (PCMs) have attracted increasingly more interest because of their large latent heat storage and nearly constant temperature during the phase change process [1]. PCMs are used in a number of practical applications, such as solar energy system [2; 3], electronic thermal management system [4; 5], spacecraft [6] and buildings [7]. In order to investigate the melting process of phase change materials, a great deal of studies have been carried out based on different models, including rectangular cavity [8], cylindrical container [9], tilting-wall square cavity [10] and annular cavity [11; 12]. Out of all these models, the rectangular cavity is widely investigated owing to the simple structure, which can help us to understand the melting process of PCMs. Over the past years, numerous investigations on melting PCMs have been carried out to study the melting process in a vertical or horizontal container. [PERSON] and [PERSON] [13] reported a significant effect of natural convection on heat transfer rate and phase change solid liquid interface shape during n-octadec melting. They noticed that natural convection should be considered in order to meet good agreement between numerical results and experimental data for the solid liquid interface position. [PERSON] and [PERSON] [14] presented the melting process of n-octadecane in a rectangular cavity that had an isothermal vertical wall. During the melting process, basic heat transfer data were reported. Based on the experimental results, they found that the melting rate and melting front profile were affected by the buoyancy-driven convection. [PERSON] and [PERSON] [15] studied the melting process of n-triacontane in a tall enclosure with a constant heat flux on the left vertical side wall. They discovered the influence of natural convection on heat transfer of melting. Based on this discovery, they concluded that the heat conduction played the dominant role during initial stages of melting. In later stages, the natural convection began to become the dominant role of melting. After melting, the buoyancy induced flow weakened and heat storage increased with time. [PERSON] and [PERSON] [16] presented an experiment to visualize the temperature distribution and melting interface evolution during the phase change process of lauric acid in a vertical container. They discussed the dominant heat transfer mechanisms of the melting process during different stages. In addition, they also investigated the total, latent and sensible energies in each thermal storage unit when the unit was heated at different temperatures. [PERSON] et al. [17] studied the influence of heat source temperature on heat transfer capability of paraffin in a horizontal container. Their results showed that the complete phase transformation time of PCM decreased while the heating boundary temperature increased, and the corresponding function between the complete melting time and the heating boundary temperature of pure paraffin. However, there were only a few investigators who studied the melting heat transfer of PCM in an inclined enclosure. [PERSON] and [PERSON] [18] presented a heat transfer process of n-octadec melting in an inclined rectangular enclosure. They concluded that natural convective motion was intensified when the inclination angle with respect to the vertical increased. [PERSON] et al. [19] designed a storage unit in order to respond the melting characteristics of paraffin. They discovered that melting time of paraffin was reduced by 30% if the enclosure was tilted 5\({}^{\circ}\) with respect to the vertical position. [PERSON] et al. [20] studied the heat transfer process in a solar flat-plate collector with the inclination angle of 32\({}^{\circ}\). They showed the variation of temperature distribution and heat loss coefficient of paraffin-solar collector during different times of a day. [PERSON] et al. [21] compared temperature distribution and melting time simply with three different orientations including upward, right side and downward.