A review of recent experimental investigations and theoretical analyses for pulsating heat pipes

Abstract

Pulsating heat pipe (PHP), or oscillating heat pipe (OHP), a novel type of highly efficient heat transfer component, has been widely applied in many fields, such as in space-borne two-phase thermal control systems, in the cooling of electronic devices and in energy-saving technology, etc. In the present paper, the characteristics and working principles of the PHPs are introduced and the current researches in the field are described from the viewpoint of experimental tests, theoretical analyses as well as practical applications. Besides, it is found that the state-of-the-art experimental investigations on the PHPs are mainly focused on the flow visualization and the applications of nanofluids and other functional fluids, aiming at enhancing the heat transfer performance of the PHPs. In addition, it is also pointed out that the present theoretical analyses of the PHP are restricted by further development of two-phase flow theories, and are concentrated in the non-linear analyses. Numerical simulations are expected to be another research focus, in particular of the combination of the nanofluids and functional fluids.

Keywords

pulsating heat pipe (PHP) / flow visualization / nanofluids / nonlinear analysis

Introduction

Pulsating heat pipe (PHP), also known as oscillating heat pipe (OHP), is a novel passive heat transfer device, which was first proposed by Akachi [1,2] in the early 1990s. It has been widely investigated by scientists and engineers all over the world for its excellent features such as small volume, low fabricating cost, simple structure and high heat transfer performance. The PHPs can be generally classified into closed end, closed loop, closed loop with check valve, and PHP with open ends [3], as shown in Fig. 1.

The operation principle of the PHP can be easily generalized as: the tube diameter is small enough (smaller than a critical value) to ensure the flow oscillations, i.e.

(1)

where d is the tube diameter, d_cr is the critical tube diameter, σ is the surface tension, g is the gravitational acceleration, and ρf and ρg are the densities for the liquid and gas phases, respectively.

Equation (1) was first proposed by Khandekar [3], who conducted a large number of experimental measurements for various PHP configurations. When the evaporation section is heated, the pressures in parallel capillary channels may be different due to the initial non-uniform distribution of vapor plugs and liquid slugs, leading to fluid transport in the direction that is inversed to the initial fluid movement. While the working fluid is transported from the evaporation section to the condensation section, heat is simultaneously transferred from the high temperature section to the low temperature section.

Zhang and Faghri [4] presented a scrutiny review on the advances and unsolved issues in the PHPs, including the working principle, the experimental and theoretical research and development, the effects of various parameters such as working fluids, charge ratios, inclination angles, number of turns etc. on the fluid hydrodynamic and heat transfer characteristics. Only in the closed loop pulsating heat pipes (CLPHPs) can the circulation be formed, thus the heat transfer capability of the PHPs will be further enhanced. However, the direction of the circulation of pulsating flow in the CLPHPs is quite difficult to be accurately predicted and very few researches have been conducted on this issue.

It is well known that the investigations on the PHPs can be categorized as either experimental measurements or theoretical analyses. Experimental studies are mainly focused on the enhanced heat transfer performances, effects of nanofluids and other functional thermal fluids and visualization of different flow patterns of the PHPs, while theoretical investigations attempt to predict analytically and/or numerically the fluid dynamics and two-phase heat transfer mechanism associated with the oscillating flow in the PHPs.

Experimental investigations

Recent experimental studies are mainly focused on the enhanced heat transfer performance, the start-up procedure and the stable operating status of the PHPs. There are many interacting factors regarding to the heat transfer capabilities of a PHP, among which the charge ratio, heating method, working fluids properties, and scale effects of tube diameter have dominating impacts on the heat transfer performance, compared to the number of turns, shapes of intersection, length of evaporation and condensation section. The heat flux and overall thermal resistance are two characteristic quantities for the measurement of the thermal performances for a PHP.

Enhanced heat transfer performance

The PHP is well recognized as one of the most promising solutions for the heat dissipation in terms of high efficient and compact. Charoensawan and Terdtoon [5] investigated the thermal performance of a horizontal closed-loop oscillating heat pipe (HCLOHP) made from copper capillary tubes with different inner diameters, evaporator lengths and number of turns. It was found that the start-up procedure was dependent on the evaporator temperature that was related to the number of turns. It was also found that the critical number of turns, which was 26 for their experiment, mainly depended on the evaporator temperature and inner diameter of the tube. The thermal performance of the HCLOHP was improved by the increase of the evaporator temperature and the decrease of the evaporator/effective length. The proper working fluids were the mixture of water and ethanol for the HCLOHP with 1 mm inner diameter, but merely water for the HCLOHP with 2 mm inner diameter.

Yang et al. [6] conducted a great deal of experimental studies on the two flat plate CLOHPs charged with ethanol in a thermal spreader configuration. Both of the two flat plates were made of aluminum with an overall size of 180 mm × 120 mm × 3 mm. One of the structures had 40 parallel square channels with a cross-section of 2 mm × 2 mm, while the other had 66 parallel square channels with a cross-section of 1 mm × 1 mm. The operations of the four different modes of the CLOHPs, as presented in Fig. 2, were obtained in their experiments. Considering their applications, the experimental study investigated the possibility of embedding the PHP as an integrated structure or a heat spreader, so as to provide a higher overall thermal conductivity to the host substrate.

Jiao, et al. [7] fabricated an oscillating cryogenic heat pipe, as illustrated in Fig. 3, which consisted of a 4×18.5 cm evaporator, a 4×18.5 cm condenser, and a 10 cm length of adiabatic section. Experimental results showed that the maximum heat transport capability of the OHP reached 380 W with an average temperature difference of 49°C between the evaporator and condenser when the cryogenic OHP was charged with liquid nitrogen at 48% (v/v) and operated in a horizontal direction. The thermal resistance decreased from 0.256 to 0.112 m²·K·W^-1 between the evaporator and the condenser. The results also showed that the amplitude of the temperature difference between the evaporator and the condenser decreased when the heat load increased due to the increase of the flow velocity.

Lin et al. [8] reported preliminary experimental results of using polydimethylsiloxane (PDMS) to manufacture a visual PHP with the length, width and internal diameter of 70, 65 and 2 mm, respectively, as demonstrated in Fig. 4. They also gave the details of the manufacturing process, and the vacuuming management for the filling and packaging. Methanol and ethanol were used as working fluids at the filling ratio of 60%. The thermal performance was tested at different heating power values (3-8 W) and the flow visualization was conducted simultaneously.

The effective range, limitations and specific heat transfer states indicated the heat transfer capabilities of the PHPs, which defined the application effectiveness in specific cases. Recent studies scrutinized these complicated issues in order to attain insightful understandings.

Yang et al. [9] experimentally studied the operational limitations of a CLPHP with the working fluid of R123. The CLPHP consisted of 40 copper tubes with the inner diameters of 1 and 2 mm, respectively. The tested filling ratios were 30%, 50% and 70%. Three operational orientations, including the vertical bottom heated, horizontal heated and vertical top heated modes were investigated. The CLPHPs with 2 mm inner diameter tubes had a lower thermal resistance in the vertical orientation with heating at the bottom, while the orientation played almost no role for the CLPHP with 1 mm inner diameter tubes. Concerning the specific performance data, the CLPHP with the inner diameter of 1 mm tubes achieved much higher dry-out heat fluxes, approximately 1242 and 32 W/cm² for axial and radial heat fluxes, respectively. While the CLPHP with the inner diameter of 2 mm tubes achieved approximately 430 and 24 W/cm² for axial and radial heat fluxes, respectively. The best thermal performance and maximum heat flux were obtained under the vertical bottom heated mode with the filling ratio of 50%.

Lin et al. [10] conducted experimental measurements on the effective range of the miniature oscillating heat pipes (MOHPs) and the results indicated that the increase of the inner diameter or the decrease of the heat transfer length was beneficial to the start-up of the MOHPs. In their experiments, the MOHP having three different heat transfer lengths (L) of 100, 150 and 200 mm consisted of 4 meandering turns and inner diameters of 0.4, 0.8, 1.3 and 1.8 mm. The effective range of the MOHPs was identified by using pure water as the working fluid. In order to measure the heat transport capability of the MOHPs, a correlation, which was well agreed with the experimental results, was proposed in terms of several dominating dimensionless parameters, including Di/L, Ja, Bo and Wa.

Khandekar and Gautam [11] found the multiple quasi-steady states in a single loop PHP. The flow visualization technique and continuous temperature measurement in crucial places, and the pressure at the inlet of the evaporator were applied in their experiments. Four distinct quasi-steady states were observed in these experimental runs. Each quasi-steady state was characterized by a unique specific two-phase flow pattern and the corresponding effective device conductance, and revealed the strong thermo-hydrodynamic coupling guiding the thermal performance.

Lips et al. [12] also applied the flow visualization technique to investigate the distinct heat transfer regimes in the PHPs. The single tube experiments were performed to highlight or reveal some phenomena usually mixed with others when they occurred in real PHPs. The wall superheat temperatures of 15 and 35 K at the evaporator of the tube were displayed in Fig. 5. The wall superheat of 35 K at the evaporator led to a faster bubble expansion that deformed the receding meniscus and broke up the liquid plug into several smaller plugs. While the wall superheat of 15 K, on the contrary, led to the nucleation of bubbles that were always lower than the tube diameter and did not affect the overall motion of the plug.

In order to enhance the heat transfer capability of the PHPs, novel structures were proposed to improve the overall thermal performance.

Thompson et al. [13] investigated a three-dimensional flat-plate oscillating heat pipe (3D FP-OHP) with staggered micro-channels. Optimal thermal performance was achieved when water was as working fluid, the bottom-heating orientation and the heating width matched that of the heat pipe, as well as the thermal resistance on the order of 0.08°C/W. Only a slight increase in the thermal resistance occurred during the horizontal orientation when utilizing a larger heating width. The reason may be partially attributed to the novel 3D design of the OHP.

The heat transfer characteristics of a coupled PHP, as depicted in Fig. 6(a), which consisted of the main PHP filled with distilled water and the synergistic oscillating PHP filled with ethanol were investigated by Liu et al. [14]. In the case of small temperature difference, the heat transfer rate of the coupled PHP was better compared to the single PHP, as sketched in Fig. 6(b), which was only made of the main PHP under the same condition. When the temperature reached 50°C, the condenser section of the synergistic oscillating PHP started oscillating, and an optimal effect of enhanced heat transfer was obtained by the two mutual incentive PHPs.

Thompson et al. [15] applied Tesla-type check valves into a FP-OHP in order to promote and sustain a desired circulatory flow for increasing the overall thermal performance. The Tesla-type check valves FP-OHP consistently possessed a lower thermal resistance than its counterpart without check valves.

Effects of nanofluids and other functional thermal fluids

Owing to the advancement in electronic technology, the demand of increasing heat loads and decreasing size of electronic devices for more effective cooling technology, nanofluids, which are engineered by dispersing nano-sized particles into base fluids, have received great attention during the past decades [16] due to their enhanced heat transfer capabilities.

Ma et al. [17] have successfully actualized heat transfer enhancement of an OHP charged with nanofluid consisted of high-performance liquid chromatography (HPLC) grade water and 1.0% volume fraction of diamond nanoparticles. When the input power approached 100 W, the temperature difference between the evaporation and the condensation sections were reduced from 42°C to 25°C, which significantly improved the heat transfer capability of the OHP.

Lin and Kang [18] carried out a detailed experimental study of the PHP with an inner diameter of 2.4 mm filled with silver nanofluid solution, and compared the result with that of pure water. They tested the PHP with 20 nm silver nanofluid at different concentrations (100×10^-6 and 450×10^-6) at various filling ratios (20%, 40%, 60%, and 80%, respectively) under different input heating power. When the heating power was 85 W, the average temperature difference and the thermal resistance of the evaporator and condenser were decreased by 7.79 and 0.092°C/W, respectively.

Qu et al. [19] conducted an experimental investigation on the thermal performance of an OHP charged with base water and spherical Al₂O₃ particles of 56 nm in diameter. The alumina nanofluids improved the thermal performance of the OHP significantly, with an optimal mass fraction of 0.9% for the maximal heat transfer enhancement. Compared with that of pure water, the maximal thermal resistance was decreased by 0.14°C/W (or 32.5%) when the power input was 58.8 W at a filling ratio of 70% and at a mass fraction of 0.9%. The change of the surface condition on the evaporator due to the nanoparticle settlement was found to be the major reason for the improvement of thermal performance of the OHP. Ji et al. [20] performed another study on the particle size effect of Al₂O₃ on the OHP. Four different size particles with an average diameter of 50 nm, 80 nm, 2.2 μm and 20 μm were experimentally tested, respectively. The OHP achieved the best heat transfer performance of a thermal resistance of 0.113°C/W when charged with 80 nm particles and water at an operation temperature of 25°C and a power input of 200 W.

Riehl and Santos [21] investigated an open loop PHP filled with water-copper nanofluids. The addition of nanoparticles resulted in the increase of the thermal conductivity of the working fluid, and the performance analysis indicated that the film evaporation effect was more predominant than the nucleate boiling at low heat loads. When the higher heat loads were applied to the PHP, the nanoparticles acting as nucleation sites improved the nucleation boiling, resulting in the appearance of the pulsating flow.

Wang et al. [22] explored the heat transfer performance of the PHPs charged with functional thermal fluids (microcapsule fluid FS-39E and nanofluid Al₂O₃), and compared it with that of pure water. Both of the functional thermal fluids significantly enhanced the heat capability of the PHP. The results exhibited that microcapsule fluid FS-39E was the best working fluid when its best concentration (wt) was 1% in the bottom heating mode, and nanofluid Al₂O₃ was the best working fluid when its best concentration (wt) was 0.1% under the specific experimental conditions.

Qiu et al. [23] conducted experiments on the heat transport performance of a PHP with water-based ferrofluids, which consisted of water and 1.39% Fe₃O₄ nanoparticles with surfactant added. An external magnetic field of 0-60 kA/m was imposed to the PHP. The results indicated that the heat resistance of the PHP charged with ferrofluid was lower compared to the working fluid of pure water and surfactant water solution. When the external magnetic fields were imposed, the heat transfer capability decreased, contributing to the impacts of ferrofluid volume force. Investigation on the ferrofluids PHP with imposed external magnetic fields was an interdisciplinary research, which revealed insightful potential application in space technology.

Flow visualization

Different thermo-hydrodynamic status results in different flow patterns, which in turn, reveal specific characteristic working conditions and heat transfer capabilities of the PHPs. Zhang and Faghri [4] briefly summarized the investigation of flow pattern as follows:

The oscillatory slug flow driven by the pressure difference between the heating and cooling sections was the dominant flow pattern in PHPs. For closed loop PHPs, the oscillatory slug flow might be combined with the circulation of working fluid. As the heat flux in a closed loop PHP increased, the circulation of working fluid might suppress the oscillating flow, and the flow pattern could change to the circulating slug flow. At even higher heat flux, the directional slug flow would change to directional annular flow. Recent experimental investigations on the flow visualization were listed in Table 1 [8,9,11,12,24-35].

Theoretical analyses

Although the PHPs have become a hot topic these years and many experimental studies have been conducted, the mechanism of the fluid flow and heat transfer behaviors of the PHPs have not yet been well understood. Most of the recent theoretical studies have been focused on the nonlinear analyses of the pulsating or oscillating processes of the PHPs.

Nonlinear behavior analyses

In order to acquire more insightful understandings of the PHPs, especially their oscillating motions in regard to the nonlinear behavior, the nonlinear analytical methods have been introduced to cooperate with the corresponding theoretical studies of the PHPs.

Ma and Zhang [36] proposed a second-order model using the central composite design method to express the relationship between the heat transfer performance of a looped copper-water OHP and the affecting factors of the charging ratio, the inclination angle, and the heat input. The data analytical results indicated that the effect of the inclination angle on the heat transfer rate was the most significant, followed by the effects of the heat input and the charging ratio. However, many other issues, such as the number of turns, the inner diameters and the effective length of the evaporator and condenser etc., have not yet been considered in their model.

A series of mathematical models including the effects of cavity size, capillary radius, heat flux level, working fluid and bubble type on the start-up characteristics of the oscillating motion were investigated by Qu and Ma [33] to better understand the heat transfer mechanism of a PHP. It was found that the cavity sizes on the capillary inner surface strongly affected the start-up performance, which can be improved by using a rougher surface, controlling the vapor bubble type, and selecting the suitable working fluids.

Based on the experiments of the flow visualization, Sakulchangsatjatai et al. [34] introduced one of the most exhaustive models for the CEPHP based on the previous work of Faghri and Zhang [37,38], by adding empirical assumptions to the nucleate boiling frequency, the bubble length and the liquid film thickness.

Arslan and Özdemir [39] conducted a series of experiments on an OHP, consisting of three interconnected columns of which the dimensions were large enough to neglect the effect of the capillary forces. A correlation function of the dimensionless numbers such as Kinetic Reynolds {\displaystyle \frac{C_p\Delta T}{h_{fg}}} (where C_p is the heat capacity, ΔT is the temperature difference, and h_fg is the heat transfer coefficient) and the geometric parameters were proposed to express the overall heat transfer coefficient.

Based on neural network, an approach of nonlinear autoregressive moving average model with exogenous inputs (NARMAX) was applied to the thermal instability of the CLPHP by Chen, et al. [40]. Their work approximated the nonlinear behavior of the CLPHP with a linear approximation method that can establish the relationship among the response temperature differences between the evaporator, adiabatic, and condenser sections. Lee and Chang [41] introduced a methodology of a nonlinear autoregressive with exogenous (NARX) neural network to analyze the thermal dynamics of a PHP in both time and frequency domains. The derived models yielded a satisfactory consistence between the measured and predicted results.

The artificial neural network (ANN), usually called neural network (NN), is a mathematical model and is inspired by the structure and functional aspects of biological neural networks. Modern neural networks are nonlinear statistical data modeling tools and are usually used to model complex relationships between inputs and outputs or to find patterns in data. The main disadvantage of using ANN is that it requires a large diversity of training for real-world operation. Another drawback of the ANN is that the algorithms are not linked to the physical phenomena heading the dynamics of the system and can only predict the PHP behavior in the range of the present experimental data.

Song and Xu [42] carried out a comprehensive study on the chaotic behaviors of the PHPs. The nonlinear analysis they used was based on the recorded time series of temperatures on the evaporation, adiabatic, and condensation sections. They confirmed that the PHPs were deterministic chaotic systems, not periodic or random systems. Three typical attractor patterns were identified. Hurst exponents and Kolmogorov entropies were applied to present the thermal performance and chaotic behavior of the PHPs.

Yuan et al. [43] proposed a model for the fluid flow and heat transfer characteristics on the liquid slug and neighboring vapor plugs in a PHP. A new energy equation for the liquid slug was proposed by the aid of Lagrange method and the latent heat was used as the outer heat input in the vapor energy equation. The gravity effect could be reasonably demonstrated by a forced vibration of the single degree of the freedom system with viscous damping.

Numerical simulation

Previous theoretical models for the PHPs were principally focused on the lumped, one dimensional, or quasi-one-dimensional, and many unrealistic assumptions were introduced [4]. Owing to the development of new theoretical models, recent numerical simulations have gained different approaches.

Hemadri et al. [44] proposed a three dimensional computational heat transfer simulation to complement their experimental study with a high resolution infrared camera to obtain spatial temperature profiles of the radiators, which were embedded with the PHP in order to conjugate heat transfer conditions on their surface. The simulation indicated that the advantage of any enhanced thermal conductivity device embedded in a radiator plate (such as the PHP) would decrease, as the absolute value of the thermal conductivity of the enhancement device/structure increased beyond a particular value. This phenomenon was in accordance with the extended surface heat transfer analogy. One of the experimental results and simulation consequence were exhibited in Fig. 7.

Liu and Hao [45] developed a mathematical model based on the volume of fluid (VOF) method to investigate heat and mass transfer behaviors in a CLOHP, by considering the effects of the vapor-liquid interface and surface tension. Under various working conditions, the proposed model could successfully simulate the initial distribution of the working fluids in the CLOHP, the sophisticated flow pattern including bubbly flow, slug flow, semi-annular/annular flow, back flow, and the flow pattern transition during the start-up processes of the CLOHP. The semi-annular/annular flow and slug flow at the initial stage of the working fluid circulation were shown in Fig. 8.

Recently, a novel numerical model was developed by Mameli et al. [46], taking into account the effects of the local pressure losses due to the presence of turns, which were neglected by previous models. The CLPHPs were simulated under different working conditions, such as different working fluids of ethanol, R123 and FC-72, different number of turns, different inclination angles as well as different inputs heat fluxes at the evaporator. Although the simulation results of the liquid momentum, the maximum tube temperature and the equivalent thermal resistances were in good qualitative and quantitative accordance with the experimental data given in literature, further direct experimental validations are still in demand to test the practical application of the numerical models.

Xu et al. [47] proposed a 3D unsteady model of vapor-liquid two phase flow and heat transfer in a flat-plate PHP (FP-PHP). A numerical simulation was conducted to study the thermal-hydrodynamic characteristics in two different type of the FP-PHP, of the traditional FP-PHP having uniform channels and the FP-PHP with micro grooves incorporated into the evaporator section. The one with micro grooves was effective for the heat transfer enhancement and possessed a smaller thermal resistance at high heat loads.

In order to better understand the enhanced heat transfer behaviors of the PHP/OHP by the magnetic fluids, Tang et al. [48] developed a 2D numerical model based on COMSOL Multiphysics software combined with user defined function. Preliminary numerical simulations were carried out in coupling with three fields of thermal, fluid flow and magnetic. The additional volumetric force caused by the external static magnetic fields was imposed to the magnetic fluids of the numerical model. The influences of the single-phase magnetic fluid on the enhanced heat transfer characteristics for two parallel plates were simulated under non-uniform static magnetic field [48]. The typical distributions of the magnetic flux density and the magnetic vector potential were displayed in Fig. 9. The pressure profiles inside the two parallel plates were presented in Fig. 10, at the inlet velocity of 3 m/s and at the heating flux of 20 W/cm² on both top and bottom plates.

The numerical results showed the heat transfer coefficient of the magnetic fluids between the two parallel plates can be enhanced by the external static magnetic fields, as given in Fig. 11. The fluid flow was in the range of laminar (Re<10⁵) at various inlet velocities from 1 to 3 m/s. It showed that the heat transfer enhancement by the external magnetic field was obvious at lower inlet velocity and decreased as the inlet velocity increased because of incomplete heat exchanging.

Applications of PHPs

The PHPs/OHPs are now mainly applied in the cooling of electronic devices and superconducting magnets, in energy saving systems for heat recovery [49-51] and other fields demanding highly efficient heat transfer rates. However, the commercial availabilities are still quite limited [4]. According to previous reviews and reports, few manufactured PHPs, regarded as standard items, have been commercialized up to the present.

Maydanik and Dmitrin [52,53] investigated a compact CLPHP cooler made of a copper tube with an inner diameter of 1.2 mm for the application of electronic cooling. The CLPHP, charged with R141b, water and methanol respectively, was equipped with a light copper radiator, as shown in Fig. 12.

The experiments conducted by Nuntaphan et al. [54] indicated that the heat transfer rate of the wire-on-tube heat exchanger can be enhanced by using an OHP. Mito et al. [55] proposed a highly effective cooling technique for a superconducting magnet incorporating the cryogenic OHP as the cooling panels in the coil windings.

As reported by Srimuang and Amatachaya [51], the PHP had already been applied in energy saving systems. Recently, Supirattanakul et al. [56] applied a CLOHP with check valves (CLOHP/CV), as illustrated in Fig. 13, in order to reduce the energy consumption in the split type air conditioning system. The CLOHP/CV was fabricated with the copper tube having an inner diameter of 2.03 mm and charged with the working fluids of R134a, R22 and R502. Compared to the conventional air conditioning system without CLOHP/CV, the system coupled with CLOHP/CV achieved the highest value of 14.9% and 17.6% for COP and EER, respectively.

Considering the increasing practical demands and huge potential markets for highly efficient heat transfer rates, it can be concluded that the PHPs/OHPs will definitely attract more interest and applications in the cooling of electronic devices and superconducting magnets, in energy saving systems for heat recovery.

Conclusions

Owing to their outstanding heat transfer capabilities and simple structure, the PHPs/OHPs have received worldwide focus in academic and engineering fields. Meanwhile, the complicated operational pulsating behavior and two-phase flow mechanism in the channels of the PHPs have also gained much attention.

As mentioned above, a great deal of experimental studies indicated that the visualization technique combining the scrutiny investigated images of the flow patterns and the experimental data of heat transfer performance, contributed a lot to further understanding of the thermo-hydrodynamic mechanism within the PHPs. The characteristics of the start-up procedure and dry-out phenomena are presently the main research topics. With the applications of nanofluids and other functional thermal fluids to the heat transfer enhancement of the PHPs/OHPs, the outstanding heat transfer capabilities of the PHPs will gain more attentions in various fields.

Many practical and sophisticated mathematical models of the PHPs are expected to be proposed for theoretical analyses, in particular of the nonlinear behavior analytical method. Owing to the limitations of the two-phase flow theories, the mundane of the pulsating or oscillating flow behaviors and heat transfer mechanisms are required further development. Moreover, numerical simulations will definitely attract extensive attention with the fast development of supercomputers.

It is worth mentioning that the PHPs will be gradually expanded from high-tech fields, like aerospace and electronics cooling to commercial and civilian fields.

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