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Abstract: The transient performance of a phase change material (PCM)-based heat sink may be affected by its inclination angle because natural convection usually occurs and dominates melting during the operation of the heat sink. An experimental setup was designed and used in this study that allows for the alternation of the inclination angle of the heat sink. The inclination angle was varied from 0° to 90° at increments of 15°, while two pulsed heat loads (20 and 40 W) were adopted. 1-hexadecanol of a nominal melting temperature of 49 °C was selected as the PCM. The transient performance of the heat sink was characterized by the temperature variations at the center of the heat spreader under various conditions. The results showed that the transient performance of the heat sink is able to be improved by simply increasing its inclination angle which then facilitates the natural convection during melting. However, the variation in the performance is not a monotonous function of the inclination angle. Although the time-averaged thermal resistances of the heat sink were shown to be only marginally lowered, the maximum operation times may be greatly extended under the given thermal conditions. For a heat load of 40 W and the maximum allowable temperature of 75 °C, the operation time of the heat sink is extended by up to nearly 67% at an inclination angle of 75° when compared to that of the horizontal case. Based on the cases tested, the optimal inclination angle was found to lie between 60° and 75°.

倾斜角度对基于相变材料的散热器在脉冲式热负荷作用下瞬时性能的影响

研究目的：通过实验方法定量研究在相变材料较为剧烈的熔化传热过程中散热器倾斜角度的改变对其瞬时性能所产生的影响。
创新要点：定量研究在倾斜角度从水平到垂直时，储能式散热器在脉冲式热负荷作用下瞬时性能的变化规律，并在所研究的工况范围内给出了最优的倾斜角度参考值。
研究方法：采用电加热方法模拟电子器件所产生的热源，通过调节电压改变脉冲式热负荷的强度和作用时间，并根据热电偶测量所得的加热表面温度变化来表征储能式散热器的瞬时性能。
重要结论：在一定的倾斜角度下工作，可以有效提升基于相变材料的储能式散热器的瞬时性能。在加热功率为40 W、以75 °C为目标时，其有效保护时间的相对增长可达约67%。
散热器；倾斜角；相变材料；储热；热管理

1.  Introduction

 Highly-efficient thermal management technologies are of great practical interest in improving the safety and reliability of electronic devices (Garimella, 2006) and power batteries (Rao and Wang, 2011) with increasing power and the shrinking of the packaging. These should also be diverse to meet unique requirements for a variety of operating conditions in the heat sources. As opposed to the active cooling options, air-cooling for example (Etemoglu, 2007; Fan et al., 2013b), a thermal energy storage (TES)-based thermal management technique enables a more energy-efficient passive or hybrid solution to the cooling of electronics/batteries. This technique is often implemented by employing a phase change material (PCM). The presence of a PCM serves as an energy buffer that is capable of rapidly extracting the excess heat from the target electronics/batteries before its final dissipation to the surroundings. Featuring reduced temperature rise and improved temperature uniformity, the thermal issues of electronics/batteries subject to intermittent (e.g., pulsed or cyclic) loads may be well addressed by PCM-based thermal management techniques (Vesligaj and Amon, 1999; Al Hallaj and Selman, 2000; Evans et al., 2001; Krishnan and Garimella, 2004; Yoo and Joshi, 2004; Krishnan et al., 2005; Mills and Al-Hallaj, 2005; Kizilel et al., 2008; 2009; Sabbah et al., 2008; Faraji and El Qarnia, 2009; Duan and Naterer, 2010; Rao et al., 2011; Saha and Dutta, 2012).

 Considering the low thermal conductivity associated with common PCM candidates, internal fins have been routinely introduced into PCM-based TES systems in an effort to improve their transient performance through enhancement of heat conduction (Fan and Khodadadi, 2011). The effects of internal fins on the performance of PCM-based heat sinks have thus been extensively studied in the literature with applications to electronics cooling (Akhilesh et al., 2005; Shatikian et al., 2005; 2008; Nayak et al., 2006; Kandasamy et al., 2008; Saha et al., 2008; Saha and Dutta, 2010; Hatakeyama et al., 2011; Hosseinizadeh et al., 2011; Baby and Balaji, 2012; Jaworski, 2012; Fan et al., 2013a). Natural convection, however, generally occurs in the molten PCM during operation (energy charging) of the PCM-based heat sinks (El Omari et al., 2011; Saha and Dutta, 2011). The random positioning of portable electronic devices indicates that if a PCM-based heat sink is equipped for such devices (Hodes et al., 2002; Alawadhi and Amon, 2003; Tan and Tso, 2004; Setoh et al., 2010; Wang and Yang, 2011; Tan and Fok, 2012), its cooling performance may not be constant due to its natural convection transient nature. The variations are mainly because of the inclination angle of the heat sink. Few studies have addressed the inclination-dependent melting behaviors (Webb and Viskanta, 1986; Ye et al., 2012; Kamkari et al., 2014) and the resulting performance of PCM-based heat sinks (Kandasamy et al., 2007; Wang et al., 2007; Fok et al., 2010; Yang and Wang, 2012). Among these studies, however, Kandasamy et al. (2007) and Fok et al. (2010) seem to be the only ones who have presented experimental efforts where these three inclination angles being examined were horizontal (0°), inclined at 45° to horizontal, and vertical (90°). The exerted heat loads were up to 12 W that corresponds to a maximum heat flux of only about 0.5 W/cm² (neglecting the heat losses), indicating that the natural convection effects were relatively weak in their experimental studies.

 In view of the existing studies on relatively low heat loads and limited inclination angles, exploration of the effects of a wider range of inclination angles and more intensive heat loads on the performance of PCM-based heat sinks is of great interest. Hence, to extend the existing knowledge in this area, this study aims at examining experimentally the influence of the inclination angle on the transient performance of a PCM-based heat sink subjected to intensive pulsed heat loads.

2.  Experiments

2.1.  Experimental setup

 A prototype PCM-based heat sink was designed and tested. The core component in this experimental setup was the heating unit used to mimic the heat source. The heating unit was assembled into a sandwich-like structure in such a way that the top side of a round mica-insulated electric heater (Minco HM6807, with a diameter of 38.1 mm) was attached to a round copper plate, while its bottom was attached to an insulated pad made of ceramic fabric paper. The mica heater, round copper plate, and insulated pad were of identical size. A square copper plate with a slightly larger size (side of 40 mm) serving as the heat spreader was attached to the top surface of the heating unit (i.e., the top surface of the round copper plate), as shown in Fig. 1a. The heating unit was packaged with a bulk rectangular base made of Teflon®. Such an integrated design of the heating unit enabled convenient installation and replacement of the heat sink.




 The packaging was fixed on top of a motorized goniometer stage (WN04GA45, Winner Optics), which allows for an adjustment of the inclination angle from −45° to 45° with an accuracy of ±0.1°. As shown in Fig. 1b, the heating unit, along with the heat sink, may be installed on an L-shaped steel plate to extend the range of the inclination angle. In this way, the inclination angle (relative to horizontal) was able to be varied from −45° to 135°. A heat sink made of aluminum was mounted on top of the heating unit (not explicitly shown in Fig. 1a) and was firmly held in place by the two clamps. The structure of the heat sink is shown in Fig. 1c. The outer dimensions (length×width×height) of the heat sink were 80 mm×80 mm×30 mm. A perspex plate lid was fabricated to cover the heat sink, which allows for visualized observation of melting occurring inside the heat sink. The lid was sealed carefully with a silicone sealant after the heat sink was filled with a PCM. The entire cooling system was actually of a hybrid type with a cooling fan being mounted on top of the heat sink and being operated at a constant air flow rate. The detailed assembly process and specifications of the various components were presented by Fan et al. (2013a).

2.2.  Experimental procedure

 In the present work, 1-hexadecanol (C₁₆H₃₄O) with a nominal melting point of 49 °C was chosen as the PCM. As concluded by Fan et al. (2013a), a PCM with a relatively high melting point is preferred because of its better performance primarily due to faster recovery (re-solidification) for subsequent use. The selected PCM was pre-melted and degassed in a vacuum oven for 3 h prior to use. The molten PCM was then poured into the heat sink. The weight of the adopted PCM was (60±0.1) g for all experiments. Several type-T thermocouples (TCs), which were calibrated to have an accuracy of ±0.2 °C prior to use, with a diameter of 1.0 mm, were employed to monitor the temperature variations at various locations of the setup. The TC that was mounted at the center of the heat spreader was identified as the junction temperature of the heat source. The mica heater was powered by a digital DC power supply (RXN-3010D, Shenzhen Zhaoxin Electronic Instrument Equipment Co., Ltd., China) at two different power input levels of approximately 20 and 40 W. The uncertainty of the exerted heating power was less than ±0.1 W. As mentioned above, such powers are much greater than the maximum value (about 12 W) examined in related studies and are closer to the intensive heating conditions encountered in practical electronics cooling applications. During the entire course of pulsed heating, the power was kept constant at a set point and was then turned off after a prescribed heating duration. Transient temperature variations were monitored by TC readings that were logged by a digital data acquisition system (Agilent 34970A) at a frequency of 0.1 Hz. All experiments were carried out in an air-conditioned room maintained at a temperature of (21±1) °C. The inclination angle was varied from 0° to 90° in increments of 15°. According to the combinations of input powers (Q≈20 and 40 W) and inclination angles (α=0°, 15°, 30°, 45°, 60°, 75°, and 90°), a total of 14 different cases were considered. The definition of the inclination angle α (with respect to horizontal) is illustrated in Fig. 2.




 It is evident that the inclination angle is equal to the angle between the heat flux q″ (perpendicular to the heat spreader surface) and gravity vectors. The two extreme cases, i.e., α=0° and 90°, may be classified into melting above a heated horizontal wall and melting along a heated vertical wall, respectively. The heat fluxes q″ on the heat spreader surface and the heating durations are listed in Table 1 for the two heat loads.




 Neglecting the heat losses, the surface heat flux was as high as about 2.5 W/cm² which was much greater than those adopted in the previous experimental studies (Kandasamy et al., 2007; Fok et al., 2010). The heating durations were carefully chosen to assure that complete melting was achieved for all cases and that the maximum temperature rises were within a rational range. The cooling (re-solidification) periods were not monitored in the present study, because natural convection effects are expected to be negligible during solidification in such a configuration. Each case was repeated twice and excellent consistency was observed between the two runs of each case. The maximum discrepancies of the transient temperature variations were found to be less than 1 °C. Therefore, the experimental data from the single runs are presented herein.

3.  Results and discussion

3.1.  Transient temperature rises

 As mentioned, temperature readings of the TC mounted at the center of the heat spreader were considered as the cooling target. Comparisons of transient temperature variations among the various inclination angles are presented in Fig. 3 for the heat load of 20 W within a total duration of 50 min.




 Based on the slope of the curves, several representative phases during the entire heating may be identified, i.e., pre-melting, melting, and post-melting. Initially, temperature rises rapidly prior to the onset of melting. After heating for about 12 min (corresponding to 58 °C), the energy buffer began to play its role as the slope of the curves became much lower. At this time instant, the temperature of the TC was about 10 °C higher than the melting temperature of the PCM (about 49 °C) because of the presence of thermal resistance between the heat spreader and the heat sink. Melting then lasted for about 30 min, followed by a rapid temperature rise again after completion of melting.

 As shown in Fig. 3, during the pre-melting phase, the curves corresponding to the various inclination angles almost converges to a single one. This clearly resulted from the fact that conduction was the dominant mode of heat transfer during this phase, which is not influenced by inclination. The curves then start departing from one another during the melting phase. This phase may be further separated into two stages, i.e., initial and developed, which can be indicated by the change of slope. For the horizontal case (α=0the slope became much lower at around 22 min. Th), the slope became much lower at around 22 min. This inflection point roughly separates the two sub-stages during melting and indicates the transition of melting from conduction-dominated to convection-dominated. During the initial melting stage, the slope of the curves became smaller with increasing the inclination angle, until it reached 45the slope became much lower at around 22 min. Th, and vice versa during the developed melting phase. This suggests that the effect of natural convection is more pronounced at greater inclination angles. In other words, melting tended to become convection-dominated at the initial stage for an inclined heat sink. This discrepancy can be interpreted in relation to the intensity of natural convection during melting. As it is well known, the intensity of natural convection can be measured by the Grashof number (Gr), which may be defined as (1) , where g is the gravitational constant; β, k, and ν are the thermal expansion coefficient, thermal conductivity, and kinematic viscosity, respectively; and L stands for the characteristic length. A pertinent characteristic length may be chosen as the height of the liquid phase along the direction of the heat flux. Hence, the characteristic length grows as melting proceeded, leading to the intensifying of the convection effect.

 Given the geometric configuration, thermal boundary condition, and thermophysical properties of the PCM, the instantaneous value of the Gr number is only determined by the inclination angle and the characteristic length. Despite a lack of direct visualized observation on the melt patterns (through the lateral walls of the heat sink), it is rational to speculate that during the initial stage of melting, the molten PCM was in the form of a thin layer along the bottom of the entire heat sink for the horizontal case (α=0°), whereas if the heat sink was inclined (α>0°), the molten PCM tended to rise and concentrate in the upper corner of the heat sink. Even if the amounts of molten PCM for the two cases were close (at the beginning of melting), the instantaneous characteristic lengths for the inclined cases were much greater than that for the horizontal cases. This leads to much greater instantaneous Gr numbers for the inclined cases, despite the slight lowering of the effective gravitational acceleration that is scaled by cosα (cosα<1 for α>0°). The discrepancy of the melt patterns is thus understood to be the primary cause of the departure of the curves for different inclination angles during melting. When the inclination angle became greater than 45°, the curves are rather consistent with one another, suggesting that the melt patterns for those inclination angles (α=45°, 60°, and 75°) were similar, except for the vertical case (α=90°) which likely resulted from the uniqueness of the melt pattern. The instantaneous characteristic lengths of the horizontal and inclined cases became closer as melting proceeded and the curves finally converge together again, as shown in Fig. 3. Approaching completion of melting (around 42 min), local troughs (undershoots) are found on the curves for α≥30°. This is attributed to the falling of a small piece of PCM that was previously attached to the transparent cover of the heat sink. Such phenomena were always observed in repeated experiments for these cases. The natural convection-induced melt patterns seem to be responsible for the formation of such isolated pieces of PCM in inclined cases when α≥30°. Therefore, this phenomenon is expected to be accompanied with intensive natural convection.

 As shown in Fig. 3, after completion of melting, the slope of the curves become almost identical again and the maximum temperature rises are consistent with the end of heating. This is in accordance with the findings presented by Kandasamy et al. (2007) that the final temperature rise is almost independent of the inclination angle. This can be understood through the intensity differences of natural convection among the various inclination angles becoming negligible in fully molten PCM. The maximum relative difference is determined to be approximately 0.71 (=cos45°/cos0°), in light of the fact that the instantaneous characteristic lengths were all equal to the height of the heat sink.

 Comparisons of transient temperature variations among the various inclination angles for the heat load of 40 W within a total duration of 23 min are presented in Fig. 4. It is clear that the general trends are similar to what have been presented before, regardless of the heating power exerted. However, the curves deviate from one another to some extent during the pre-melting phase, which is likely due to variations of convective heat transfer coefficients along the lateral walls of the heat sink at the various inclination angles. The local troughs occurring at the end of melting are also found on the curves for all the inclined cases (α>0°), except for the vertical configuration (α=90°) where such a local trough is absent. The magnitudes of the troughs seem to be greater than those for the previous cases with the lower heat loads, which can be attributed to the inherently more intensive convection effect associated with the higher heat loads.

3.2.  Time-averaged thermal resistances

 Based on the above analysis on the transient temperature rises, a conclusion may be drawn qualitatively that the transient performance of the PCM-based heat sink tends to be better as the temperature rise is clearly suppressed during the melting phase with increasing the inclination angle. To provide a quantitative evaluation, the effective thermal resistance (R) of the heat sink may be evaluated by (2) , where T _∞ is the ambient temperature. It is noted that the thermal resistance defined in this way actually characterizes the performance of the hybrid system including both the PCM-based heat sink and the cooling fan. The average values of the time-dependent thermal resistances for the two heat loads over their respective heating periods were calculated, as presented in Fig. 5.




 At constant inclination angles, the thermal resistances of the heat sink at the higher heat load are consistently lower than those at the lower heat load, because the natural convection effect during melting was much more pronounced in the former case which improves the performance of the heat sink. It is shown that within the entire spectrum of the inclination angle, the variations of the time-averaged thermal resistances are not monotonous. For the case of Q=20 W, the time-averaged thermal resistance gradually decreases and then rises with increasing the inclination angle. The minimum thermal resistance is found at α=60° for this case. In contrast, two local troughs (α=30° and 75°) are seen for the case of Q=40 W with the one at α=75° being the minimum.

 However, the relative variations of the thermal resistances are less than 10% for both heat loads. That is, at a constant heat load, the thermal resistance of the PCM-based heat sink may be considered as nearly independent of the inclination angle. It is also interesting that the thermal resistances for the two extreme cases (horizontal and vertical) are nearly identical, regardless of the heat load applied, although their transient temperature rises and the associated melt patterns were essentially different.

3.3.  Maximum operation times

 In real-world applications, it is often required that the cooling target temperature is able to be maintained below a set point (the maximum allowable temperature) as long as possible. This serves as a measure to characterize the performance of heat sinks. If the set point is 75 °C (for commercial portable electronic devices), for the lower heat load (20 W), the various curves exceed this point at almost the same time instants around the end of melting (around 42 min), as shown in Fig. 3. For this heat load, the maximum operation times of the heat sink at various inclination angles are compared in Table 2, where the extensions of operation time relative to that of the horizontal case (α=0°) are also given. The resolution of the measured times is 10 s due to the interval of data logging.




 It is shown that the operation time was only extended by a maximum of 5.4% while being placed at α=60°, which is consistent with the lowest thermal resistance for this case, whereas the operation time was shortened by 4.6% for the vertical case (α=90°). On the contrary, the time to reach this set point spreads within a much wider range (during melting) for the heat load of 40 W, as can be seen in Fig. 4. The measured operation times for this case are listed in Table 3.




 It is shown that the operation time is significantly extended by inclining the heat sink. The maximum extension by a factor of nearly 67% is found at α=75° that is also consistent with the lowest thermal resistance as previously seen in Fig. 5. As discussed, such improvement on the transient performance of the PCM-based heat sink is primarily caused by the enhancement of natural convection during melting by altering the inclination angle. If the electronic device being cooled is operated within the melting phase of a PCM-based heat sink with pertinently chosen combinations of heat load and heat storage capacity, the performance of the heat sink can be intensified by simply inclining it to a certain angle to facilitate natural convection. As suggested by the present results, the optimal inclination angle may be around 75°. The enhanced performance, however, is strongly dependent on the given thermal conditions, especially the heat load, as well as the cooling target criteria.

4.  Conclusions

 The transient performance of a PCM-based heat sink was investigated experimentally in this paper with an emphasis on the effect of its inclination angle, which was also supplemental to the previous study (Fan et al., 2013a). The inclination angle of the heat sink was varied from 0° to 90° relative to horizontal, while two relatively intensive heat loads (20 and 40 W) were adopted. It was shown that by facilitating natural convection, the temperature rises for the inclined cases were greatly suppressed during the initial stage of the melting phase, regardless of the heat load exerted. This was interpreted to be related to the instantaneous melt patterns during melting. Comparison of the time-averaged thermal resistances of the heat sink at various inclination angles was shown to be consistent with that of the temperature rises. In general, the thermal resistance decreases with increasing the inclination angle for both heat loads, except for cases approaching the vertical configuration (α=90°). The minimum thermal resistances were found at an inclination angle of 60° and 75° under the heat loads of 20 W and 40 W, respectively. However, the minimums were only up to 10% lower than their respective baseline values for the horizontal cases, because the inclination effect was negligible during both the pre-melting and post-melting phases.

 On the contrary, for a given combination of heat load and maximum allowable temperature of the electronic device being cooled, the maximum operation time may be extended by simply inclining the heat sink. It was shown that such an extension can be achieved by a factor up to nearly 67% for the heat load of 40 W and a set point of 75 °C. The optimal inclination angle was found to lie between 60° and 75° based on the cases studied. The enhanced performance of the PCM-based heat sink, however, was only able to be realized when the target devices were operated within the melting phase. The performance was strongly dependent on the given thermal conditions including both the heat load and the cooling target.

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* Project supported by the National Natural Science Foundation of China (No. 51276159)