A channel layout of a micro pulsating heat pipe for an excessively localized heating condition
Introduction
Thermal management in electronics is one of the most significant factors affecting performance and reliability. As electronics are getting thinner and their performances are getting higher, thin heat spreaders having high thermal conductivity are being demanded for appropriate thermal management. Traditionally, a heat pipe, which is comprised of a hollow tube with a wick structure attached to the inner surface, is used. In the heat pipe, the working fluid is evaporated in the heating section, and the condensed working fluid in the condenser section is returned to the heating section through a wick structure. Recently, as a different type of heat spreader, a pulsating heat pipe (PHP) has received attention as an effective heat spreader due to its simple structure [1]. A PHP consists of a serpentine channel and transfers heat from the heating section to the condenser section by the thermally-driven oscillating motion of the liquid slugs. Even though its structure is simple due to the absence of a wick structure, the flow and the heat transfer characteristics are very complex because of the thermo-hydrodynamic coupling. In the last few decades, numerous studies have focused on the fundamental aspects of PHPs, such as their oscillating mechanisms [2], [3], heat transfer mechanisms [4], [5], and the effect of the working fluids [6], [7] including nano fluids [8], [9], [10], [11]. Based on the understanding of PHPs from these studies, there have been many attempts to apply PHPs to various applications including cryogenic systems [12], heat recovery systems [13], [14], solar thermal systems [15], satellites [16], and flexible devices [17], [18]. However, there still exist some challenges for a PHP to overcome if it is to be used in practical applications. One of them is associated with localized heating conditions where heat is dissipated from a small component. Various types of channel layout have been investigated to make PHPs applicable to various heating conditions [19], [20], [21], but as of now, there is no study to apply PHPs to excessively localized heating conditions.
Under localized heating conditions, only a few channels of PHPs overlap the heating section, while the remaining channels are isolated from it. Because the heat input is required to induce the oscillating motion of the liquid slugs in PHPs, in thermally-isolated channels, liquid slugs tend not to oscillate actively, so they do not directly participate in the cooling of the heating section. In previous studies [22], [23], under localized heating conditions, a significant decrease in the thermal performances of PHPs because of the non-oscillating liquid slugs in the thermally-isolated channels was experimentally observed. To overcome this limitation, there have been a few attempts. In authors’ previous work [23], non-uniformly arranged channel layout was proposed to induce the active oscillating motion of all liquid slugs under the localized heating condition. Non-uniformly arranged channels in which all the channels overlap the heating section without any thermally-isolated channel provided much higher thermal performance than the uniformly arranged channels. This method is applicable when the perimeter of the heating section, into which channels can penetrate, is larger than the channel pitch multiplied by the number of channels. However, under an excessively localized heating condition, it is extremely difficult to make all channels overlap the heating section because of its small perimeter, and this results in thermally-isolated channels. To overcome this problem, Kelly et al. [24] developed a radial PHP with a boiling chamber. Although there were no thermally-isolated channels due to a boiling chamber under the excessively localized heating condition, they reported that the oscillating motion of the liquid slugs was not strong enough to transfer heat from the localized heating section to the condenser section. The low performance of their PHP seems to indicate there was an insufficient driving force to maintain the oscillating motion of the liquid slugs. It is well known that the driving force for the oscillating motion in the PHP is the pressure difference between the adjacent vapor plugs [2], [25]. In the radial PHP, because all channels were connected through a boiling chamber, the pressure difference between the adjacent vapor plugs was evened out, so the oscillating motion of the liquid slugs would have been significantly reduced. Therefore, to use PHPs in various applications with excessively localized heating conditions, there is a need to suggest a novel channel layout that can induce the active oscillating motion of all liquid slugs.
The objective of this study is to propose a method for designing a channel layout of a flat-plate micro pulsating heat pipe (MPHP) under an excessively localized heating condition. To simplify the heat transfer characteristics in MPHPs, the channel regions are modeled as a region with the high effective thermal conductivity, and a distribution of the channel regions is determined using the topology optimization method in the design domain. To take into account the operational characteristics of MPHPs, the constraints on the maximum length scale and the minimum solid volume fraction in local regions are imposed. Using this method, the channel layout is suggested for the case with the excessively localized heating condition, in which the size of the heating section is about 2% of the total area. To verify the effectiveness of the proposed channel layout, silicon-based MPHPs are fabricated, and their flow characteristics and thermal performance are compared.
Section snippets
Design domain
The design mothed is implemented for the MPHP, which has a width of 30 mm and a length of 47 mm. An excessively localized heating condition is implemented using a 5 mm × 5 mm heater in the middle of the bottom part. In this domain, as shown in Fig. 1, the channel pitch multiplied by the number of channels (27 mm) is much larger than the perimeter of the heating section (15 mm) into which the channels can penetrate due to the small size of the heating section. Thus, there must be
Results of topology optimization
The channel layout of the MPHP is designed using the method proposed in the previous section. Fig. 9(a) shows the history of the distribution of relative densities and Fig. 9(b) shows the histories of the objective function and the average temperature difference between the heating section and the condenser section in the design domain during the optimization procedure. As shown in Fig. 9(b), minimizing the thermal compliance leads to minimization of the average temperature difference. Fig. 10
Conclusion
In this study, a method for designing a channel layout of a flat-plate MPHP under an excessively localized heating condition is proposed. The channel regions are modeled as a region with the high effective thermal conductivity, and using the topology optimization method, a distribution of the channel regions are determined to minimize the average temperature difference between the heating section and the condenser section in the design domain. The constraints on the maximum length scale and the
CRediT authorship contribution statement
Jonghyun Lim: Conceptualization, Validation, Formal analysis, Investigation, Resources, Writing - original draft, Writing - review & editing. Sung Jin Kim: Writing - review & editing, Supervision, Project administration, Funding acquisition.
Declaration of Competing Interest
The author declare that there is no conflict of interest.
Acknowledgement
This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No. 2021R1A2C3011944).
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