Calado laser

The porosity is one of the critical parameters of aluminum foam, which could determine the effective thermal conductivity and permeability. Lafdi et al. [76] found that the heat transfer in composite is also affected by the porosity of aluminum foam. Therefore, to study the effect of porosity on the thermal behavior of LPAF/paraffin composite, the melting process and the temperature variation of the composite with different porosities are recorded for two different heat conditions.

(a) Melting process of composite heated by horizontal heat source

Fig. 3.17 shows the melting evolution of the composites with different porosities. The horizontal heat source is at the bottom and it provides the constant heat flux 3500 W m-2. Liquid phase is transparent and the solid zone is shiny white.

For the composite with ε = 67%, the solid-liquid interfaces are not distinct during the melting process, as presented in Fig. 3.17(a). The evolution of the interface is very quick and the total melting time is short, which demonstrates the temperature of the whole region rises synchronously. The melting processes of composites with ε =75% and ε = 84% are displayed in Fig. 3.17 (b) and (c), respectively. The solid-liquid interface is obvious and it keeps rising horizontally. Besides, it is seen that the interface shapes of two composites are wavy, which is maybe attributed to the natural convection in liquid phase.

Fig. 3.17. Melting evolution of the composite with different porosities for horizontal heat source (a) 67% (b) 75% (c) 84%

In order to analyze quantitatively the effect of the porosity, the temperature variations of detected points are recorded and the results are shown in Fig. 3.16. It is seen that the temperature differences between the adjacent detect points increase as the porosity increasing. This is because the large effective thermal conductivity (keff) of the composite with low porosity could improve the heat transfer process

and make the temperature homogenous. Besides, it is noted that the mushy region of the composite with ε = 67% is distinct, while this region tends to be vague for composite with ε = 84%. It is considered that the phenomenon is as a result of the change of the heat transfer mode. The permeability of aluminum foam with ε = 67% is small, which suppresses the natural convection of the liquid paraffin. In this case, the paraffin is restricted in the pores of aluminum foam and the heat transfer is governed by thermal conduction. In contrast, the aluminum foam with ε = 84% has the large permeability, and the motion of liquid paraffin in aluminum foam is less limited by metal ligaments. The natural convection of liquid phase will develop in the composite, leading to the uniform variation of temperature [134]. Therefore, it is inferred that the heat transfer in the composite with ε = 84% is affected by both thermal conduction and convection.

Fig. 3.18. Temperature variations of composite with different porosities for horizontal heat source (a) 67% (b) 75% (c) 84%

(b) Melting process of composite heated by vertical heat source

of LAPF/paraffin composite. According to the melting process of pure paraffin, the circulation flows in the liquid are different with varying the heat directions. In order to further understand the effect of the natural convection on the heat transfer, the composites with different porosities are heated by vertical heat source, and the results are shown in Fig. 3.19. Similar to the horizontal heat source, the evolution of solid-liquid interfaces of the composite with ε = 67% are parallel to the heat source due to the thermal conduction. For the composite with ε = 75%, the interface is straight at beginning. As the liquid volume increasing, the natural convection develops at 2180 s, which is confirmed by the sloping interface. However, the circulation flow does not always exist in liquid and it tends to disappear at 2700 s. This is because the thermal conduction still prevails in heat transfer, and the natural convection is suppressed during the melting process. The melting process of composite with ε = 84% is similar to pure paraffin. The sloping interface appears early, and the paraffin at the top melts quickly than that at the bottom, which is a typical phenomenon of the development of natural convection. As time progressed, the paraffin in the right corner melts lastly, as presented at 3420 s in Fig. 3.19(c). Thus, it is confirmed that the natural convection exists in the composite and the effect becomes more and more important as the increase of the porosity.

Fig. 3.19. Melting evolution of the composite with different porosities for vertical heat source (a) 67% (b) 75% (c) 84%

Fig. 3.20 displays temperature variations of composite with different porosities for vertical heat source. It is found that, although the flow patterns are different for two heating conditions, the shapes and feature of the curves for vertical heat source are similar to the horizontal heat source. This is because the thermal conduction always plays an important role in the heat transfer in spite of the heating directions, which affects the temperature distribution in whole region. However, the effect of natural convection will be influenced by the position of the heat source. Thus, the temperature rising rate for vertical heat source is slow than that for horizontal heat source.

Fig. 3.20. Temperature variations of composite with different porosities for vertical heat source (a) 67% (b) 75% (c) 84%

Fig. 3.19 presents the total melting time as the function porosity for different heating conditions. The total melting time increases as the increase of the porosity, because the composite with large porosity need more energy to melts the paraffin. Besides, the composites heated by horizontal source have the shorter melting times than that of vertical heat source, and the time differences between two heating conditions become more and more distinct with the increase of the porosity. It could be explained that the effect of convective heat transfer is more and more pronounced as the porosity increasing. The different circulations caused by heating direction lead to the different melting orders. In horizontal heating condition, the natural convection could be developed well so that it accelerates the heat transfer process. For the vertical heat source, the natural convection makes the solid paraffin in the bottom right corner melts lastly, which is responsible for the longer melting time.

Fig. 3.21. Variations of total melting time versus porosity for different locations of heat source

In the applications of the thermal energy storage (TES) system, the heat source is always vertical, such as waste heat recovery, energy storage radiator, and solar energy equipment. Besides, in order to store more energy, the volume of the phase change material should be as much as possible. In this condition, the problem of the natural convection for the vertical heat source will deteriorate the efficiency of TES system. Thus, this factor should be noted and studied further in the design of TES system.

3.5 Numerical analysis of heat transfer in the