## 4 Results and Discussion  
Figure 3 shows the axial distributions of the loop temperatures and \(\xi_{b}\) versus \(t_{w}\), where \(\theta_{w,\rho}\) represents the temperature of the outer pipe wall, \(\theta_{w,i}\) represents the temperature of the inner pipe wall, and \(\theta_{b}\) represents the local mean temperature of the suspension fluid at a given cross section of the pipe, and \(s^{*}\) is the modified dimensionless axial coordinate (=\(s^{+}/l_{L}^{+}\)). The dotted lines partition the figure into five blocks, and the point with dimensionless distance \(s^{*}\) of 0 was set at the lower-right  
Figure 2: Simulation-result comparison with (a) [PERSON] et al., and(b) [PERSON] et al. [27]. corner of the loop system (Figure 1). Except for the heating and cooling sections, all other parts in the figure are adiabatic sections. The \(s^{*}\) range of 0-0.073 corresponds to the adiabatic section before the inlet of the heating section, the range of 0.073-0.174 corresponds to the heating section, the range of 0.174-0.748 corresponds to the adiabatic section between the outlet of the heating section and the inlet of the cooling section, the range of 0.748-0.948 corresponds to the cooling section, the range of 0.948-1 corresponds to the adiabatic section after the cooling section, and \(s^{*}\) of 1 indicates the return to the starting point of the loop. Results showed that, after the fluid entered the heating section, it was heated by a constant heat flux, and temperatures started to rise. When entering the adiabatic section, temperatures decreased. After that, it remained approximately isothermal until entering the cooling section. Then, the temperatures decreased due to the cooling effect. After leaving the cooling section, it entered the adiabatic section, and the temperatures rose because the wall of the adiabatic section receives axial heat transfer from the heating section. Figure 3a-c shows that, the thicker the pipe wall was, the higher the temperatures were because thermal resistance increased with pipe-wall thickness. The distribution of the liquid fraction of PCM suspension (Figure 3d) shows that, for \(t_{w}=0.5\), the thicker pipe wall caused overall temperature to increase, which delayed the solidification of the PCM particles after complete cooling, as shown by the red arrow in the figure. In this paper, the thermal-conductivity ratio of the pipe wall \(k^{*}_{inf}=k_{w}/k_{f}\) is defined as the ratio of the wall's heat conductivity to that of the pure fluid (water), and reflects the heat-conduction capability of the wall. Figure 4 shows the effects of \(k^{*}_{wf}\) on the loop heat-transfer characteristics for fixed wall thickness (\(t_{w}=0.1\)). The smaller that \(k^{*}_{wf}\) was, the higher the thermal resistance of the pipe wall was, and the higher the wall temperature was. However, a large \(k^{*}_{wf}\) increased the heat transfer of the pipe wall, which caused preheating or precooling of the walls of the adiabatic sections near the heating and cooling sections, respectively. For \(k^{*}_{wf}=0.1\)-\(10\), the temperature at each point near the heating section remained unchanged (starting from \(s^{*}=0\)). However, for \(k^{*}_{wf}=100\), the effect of the heating section caused axial heat transfer to increase the temperature at each point before the heating section, as shown by the red arrow. Similarly, the points after the adiabatic section before the cooling section were precooled, and the temperature of each point decreased, as shown by the blue arrow. \(\xi_{b}\) distribution shows that, for \(k_{wf}^{*}=0.1,\ t_{w}=0.1\), the fluid was overheated upon leaving the adiabatic section and entering the cooling section. The fluid could only be cooled to melting point for PCM solidification T\({}_{M}\) after passing approximately 1/3 of the cooling section (as shown by the red circle in Figure 4d), leading to \(\xi_{b}<1\) (where fluid temperature = T\({}_{M}\), \(\theta_{b}=0\)).