Investigation of convective heat transfer performance in nanochannels with fractal Cantor structures

https://doi.org/10.1016/j.ijheatmasstransfer.2021.121086Get rights and content

Highlights

  • Fractal Cantor structures can enhance the convective heat transfer of nanochannels.

  • Fractal structures increase heat transfer areas and low potential energy regions.

  • The fractal nanochannel of n = 3 has the optimal thermal and flow characteristics.

  • Narrowest gaps in fractal structure of n = 3 induce the local hydrophobic effect.

Abstract

The micro/nanochannel cooling technology is a promising and flourishing technique of thermal management to dissipate the heat of electronic devices. Here, we apply fractal Cantor structures to construct the self-affine rough surface of the nanochannel and investigate the effect of the fractal Cantor surface on the convective heat transfer performance in nanochannels by using molecular dynamics simulation. We first find out that fractal structures can accelerate the temperature development of the fluid and improve the convective heat transfer of nanochannels in comparison with those of smooth surfaces. With the increase of the fractal number (n) and the surface wettability, both the heat transfer and flow resistance further increase. The largest comprehensive convective heat transfer performance indicator is obtained at n = 3. The results show that the expansion of low potential energy regions along with the increasing fractal number makes more near-wall fluid atoms gather at the wall-fluid interface to act as “phonon bridge” to promote the convective heat transfer in nanochannels. Meanwhile, the generation of narrowest gaps in the fractal structure of n = 3 induces the local hydrophobic effect, which can ameliorate comprehensive thermal and flow characteristics of nanochannels.

Introduction

The continuous miniaturization and increasing high power of micro/nano electronic devices are proposing an enormous challenge for the thermal management. Various researches have demonstrated that the failure rate of micro/nano electronic devices would double for the temperature increase of 10 °C [1], [2], [3]. Hence, it is urgent to improve the heat dissipation capability of these devices. Currently, numerous thermal management methods have been put forward to improve the heat dissipation for micro/nano electronics [4], [5], [6], [7]. Owing to the high heat transfer performance, compact structure and easy integration packaging, micro/nanochannel cooling technology stands out from various heat dissipation strategies.

In the past few decades, thermal and flow characteristics of microchannels have been studied thoroughly by experiments and simulations. In 1981, Tuckerman et al. first fabricated the microchannel and investigated its heat dissipation capability experimentally. They illustrated that the liquid cooling in the microchannel was an efficient method to improve the heat dissipation for planar integrated circuits at a power density of 790 W cm−3 [8]. Subsequently, many researchers further studied thermal and flow characteristics in the microchannel under different wall surface conditions [9,10], different channel structures [11], [12], [13] and different fluid styles [14], [15], [16], [17], [18], all of which devoted to reveal the convective heat transfer mechanism and optimize the heat dissipation performance for electronics at microscale. However, when the size of electronic devices decreases to the nanoscale level, the characteristics of the convective heat transfer at nanoscale become different from those at microscale because the system spatial scale becomes comparable to the molecular mean free path [19]. The traditional heat transfer and flow theories are unable to reveal the deeper physical mechanism of nanoscale convective heat transfer. Therefore, the comprehensive investigations for the convective heat transfer performance and mechanism at nanoscale are necessary to be conducted.

At nanoscale, it is difficult to conduct experiments to study the heat transfer and flow characteristics in nanochannels owing to the extremely small spatial scale. Molecular dynamics (MD) simulation, which can obtain the insight into the underlying physics of materials by directly calculating the atomistic interactions, has been proved to be an effective method to study the thermal and flow characteristics and uncover the convective heat transfer mechanism at nanoscale [20], [21], [22]. By performing the molecular dynamics simulation, Ge et al. simulated the laminar forced convective heat transfer in parallel-plate nanochannels with different surface wettabilities. They pointed out that the Nusselt number for the laminar flow in the nanochannel was smaller than its corresponding value at macroscale. Besides, the stronger surface wettability could enhance the convective heat transfer at nanoscale [20]. Marable et al. assessed the convective heat transfer of water in graphene nanochannels and observed the temperature jump and velocity slip at the interface, which played the significant roles in the convective heat transfer at nanoscale [21]. With the implement of the molecular dynamics simulation, Sun et al. comprehensively evaluated the thermal and flow characteristics in nanochannels with the tunable surface wettability. They found that the increase of the surface wettability could ameliorate the convective heat transfer but increase the flow friction, and the optimum convective heat transfer performance could be obtained when the wall-fluid coupling strength scaling parameter was about 1.00-1.75 [22].

Actually, limited by the fabrication technologies of nano electronic devices, the nanostructure surfaces are impossible to be absolutely smooth. Besides, the surface roughness has an important effect on the energy transportation at nanoscale [23,24]. Therefore, it is necessary to study the effect of surface roughness on the convective heat transfer in the nanochannel. Using the non-equilibrium molecular dynamics simulation, Chakraborty et al. structured uniformly and randomly distributed rough surfaces in nanochannels, and revealed that they had the same impact on the heat transfer for rough channels with uniform and random groove width because of the same interfacial area [25]. Another study about the effect of the wall roughness on the convective heat transfer conducted by Motlagh et al. pointed that the roughness increased the Nusselt number in the nanochannel as a result of the atom mobility increase and atom accumulation near the wall [26]. Hu et al. studied the effects of striped superhydrophobic surfaces on frictional properties under various loads in nanochannels. They confirmed that the striped superhydrophobic surfaces showed a friction reduction because of the decrease of liquid-solid contact area [27]. However, the rough surfaces of the above researches, which are composed of simple geometric structures, are hard to reflect the self-affine geometric feature of the real surfaces and cannot be highly consistent with the real rough surface profiles.

As a typical fractal method to construct the self-affine rough surface, the fractal Cantor structure has been proved to properly characterize rough surface profiles [28,29]. Chen et al. introduced the fractal Cantor set into studying the effect of surface roughness on the laminar flow in the microchannel and demonstrated that the presence of the roughness made the flow states in the rough microchannel depart more from the laminar flow behavior. This was attributed to more distorted velocity profile and larger vortex region induced by more frequent surface variation [30]. Similarly, Wu et al. studied the liquid film evaporation phenomenon on the fractal Cantor rough surface. Their results verified that the evaporation heat transfer was enhanced with the increase of the fractal dimension due to the expansion of the heat exchange area [31]. Based on the above discussions, if we introduce the Cantor fractal theory into the construction of nanochannel surface structures, it is more appropriate to uncover the effect mechanism of the surface roughness on the convective heat transfer in nanochannels.

In this work, the convective heat transfer performance in nanochannels with fractal Cantor structures is investigated by using the non-equilibrium molecular dynamics simulation. We first investigate the effect of the surface wettability on the convective heat transfer at nanoscale. Afterwards, the average Nusselt number, the Colburn factor j and friction factor f for fractal Cantor structures are used to evaluate thermal and flow characteristics in contrast with normal rough structures. Lastly, the phonon density of states (DOS), the fluid density contours, the potential energy contours, and the flow states of the near-wall fluid atoms are analyzed to gain an insight into the mechanism of the convective heat transfer. The work devotes to reveal thermal and flow mechanisms in nanochannels with fractal Cantor surfaces.

Section snippets

Simulation details

Fig. 1(a) exhibits the simulation models used in this work. The nanochannel consists of two parallel walls formed by platinum (Pt) atoms and argon (Ar) atoms are selected to be the flowing fluid in nanochannels. The Pt atoms of two walls own the face-center cubic (FCC) lattice structure with the lattice constant a = 3.923 Å. In order to simulate the simple harmonic vibration of wall atoms, the harmonic spring is applied to each Pt atom and the spring constant k is set as 179.5 N m−1 [32], which

Results and discussion

We first focus on the nanochannel with the smooth surface (n = 0) to study the influence of the surface wettability on the convective heat transfer at nanoscale. Fig. 2 exhibits the temperature and velocity profiles of smooth nanochannels with the hydrophobic surface wettability (χ = 0.025), the hydrophilic surface wettability (χ = 0.25) and the superhydrophilic surface wettability (χ = 1.00). The temperature profiles at different nanochannel cross-sections from Fig. 2(a)-(c) are parabolic with

Conclusions

In this work, we investigate the convective heat transfer performance in nanochannels with fractal Cantor structures using the non-equilibrium molecular dynamics method. We first find out the temperature jump and the velocity slip are observed at the interface for the nanoscale convective heat transfer, which can be weakened with the increase of the surface wettability. It is proved that the larger fractal number n and the stronger surface wettability can accelerate the temperature development

CRediT authorship contribution statement

Man Wang: Conceptualization, Methodology, Investigation, Software, Writing - original draft. Haiyi Sun: Investigation, Data curation, Writing - review & editing. Lin Cheng: Conceptualization, Supervision, Writing - review & editing.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

The authors declare the following financial interests/personal relationships which may be considered as potential competing interests

Acknowledgments

This work was supported by the Key R&D Program of Shandong Province, China (No. 2019GGX101030) .

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