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Instantaneous solid-liquid interface of the PCM at different cross-section along axial direction with two different times (after 600s and 1200s) are presented for pipe model and cylinder model in Fig.5. The region of liquid fraction between 0 (blue) and 1 (red) indicates the positions of solid-liquid interface region. As can be seen from the figure, in the cases without natural convection, heat conduction dominates the heat transfer process in PCM strictly, and the solid-liquid interface presents obvious concentric distribution along the center of the tube. Compared to the two models for the same cross-section, at start, very thin layer of liquid is formed around the hot inner tube of cylinder model firstly. As time processes further, for the pipe model, the radius at solid-liquid interface is increasing, and for the cylinder model, the radius at solid-liquid interface is decreasing. In the cases with natural convection, solid-liquid interface moves no longer symmetrically along the center of the tube. For the pipe model, the solid-liquid interface moves upwards due to the high temperature liquid PCM flow upside and the high density solid PCM moves downside. And only heat conduction occurs between the hot tube wall and solid PCM, which causes PCM melted very slowly at the bottom region. For the cylinder model, the heat transfer performance between the hot tube wall at the bottom sections and solid PCM is better, and the completely melting time is lower.
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genhunter

ÖÁ×ðľ³æ (ÖøÃûдÊÖ)

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ÔÚ·ÉÏhenu: ½ð±Ò+20, ·­ÒëEPI+1, ¡ï¡ï¡ï¡ï¡ï×î¼Ñ´ð°¸, ·Ç³£Ð»Ð» 2015-05-13 18:33:01
Real-time images of solid-liquid interface of the PCM at different cross-sections along axial direction at two different time points (after 600s and 1200s)  for the pipe model and the cylinder model are presented in Fig.5. The liquid fraction between 0 (blue) and 1 (red) indicates where the solid-liquid interface region locates. As can be seen in the figure, in the absence of natural convection, heat conduction dominates the heat transfer process in the PCM portion strictly, and the solid-liquid interface presents obvious concentric distribution that radiates (or gradually changes) along the center of the tube. A side-by-side comparison is made between two models at the same cross-section, initially, a very thin layer of liquid is formed around the hot inner tube, which appears first for the cylinder model( I feel like that you are missing something for the tube model). Later on,  the (liquid?) radius at solid-liquid interface is increasing for the pipe model, while the opposite is true for the cylinder model, the radius at solid-liquid interface is actually decreasing. when natural convection is present, the solid-liquid interface moves asymmetrically along the center of the tube. For the pipe model, the solid-liquid interface moves upwards due to the fact that hot liquid PCM flows upward and the high density solid PCM moves downward. The only heat conduction occurs between the hot tube wall and the solid PCM, which melts PCM very slowly at the bottom. For the cylinder model, the heat transfer between the hot tube wall at the bottom sections and solid PCM is more efficient, and the time for a complete melting is shorter.

Suggestion: Natural convection seems can be simplified as convection.
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