Power-saving exploration for high-end ultra-slim laptop computers with miniature loop heat pipe cooling module

# Power-saving exploration for high-end ultra-slim laptop computers with miniature loop heat pipe cooling module

Author links open overlay panelGuohuiZhouaJiLibZizhouJiachttps://doi.org/10.1016/j.apenergy.2019.01.258Get rights and content

## Highlights

• A 1 mm thick mLHP module with 30 W cooling capacity was first developed.

• A lowest system thermal resistance of 2 °C/W was obtained at 25 W.

• Fan voltages and working orientations impact the performance indistinctively.

• Cooling energy saved with the proposed module was up to 80%.

• Coefficient of performance based on cooling power was increased by six times.

## Abstract

In this paper, an active air-cooling module based on a 1-mm-thick ultrathin miniature loop heat pipe with a flat evaporator for high-end ultra-slim laptop computers is presented and studied. Systematic experimental investigations were conducted under natural air convection and forced air cooling conditions with different fan voltages. The results indicated that the miniature loop heat pipe module could effectively dissipate a heat load of 12 W at all test orientations under natural convection with zero power consumption when the chip-junction temperatures were below 85 °C. Under forced air cooling, the proposed miniature loop heat pipe module had almost identical cooling performance at all test orientations when the fan input voltages were changed from 5 V to 2 V. Aided by infrared photography and theoretical analysis, the unique operation mechanism for the module was revealed. Finally, in a 35 °C temperature humidity chamber, the module could dissipate 25 W at a fan voltage of 5 V (22 W at 2 V) with the chip-junction temperature below 85 °C, showing a promising and energy-saving thermal management solution for high-end ultra-slim laptop computers. The results indicate that by using the proposed module, cooling energy savings of up to 80% could be realized compared to the current applied miniature heat pipe module in a laptop computer.

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## Keywords

Miniature loop heat pipeUltra-slimThermal managementEnergy savingLaptop-computer cooling

## Nomenclature

• A

• cross-section area, m2

• d

• hydraulic diameter, m

• D

• diameter of copper wire, m

• H

• height, m

• ${h}_{\mathit{fg}}$

• latent heat of evaporation, J/kg

• I

• current, A

• ID

• inner diameter, m

• K

• permeability, m2

• L

• length, m

• l

• thickness, m

• n

• number of vapor removal channels

• OD

• outer diameter, m

• P

• pressure, Pa; power, W

• Q

• R

• thermal resistance, °C/W

• r

• T

• temperature, °C

• U

• voltage, V

• W

• width, m

### Greek symbol

• $\beta$

• aspect ratio

• $\sigma$

• surface tension, N/m

• $\delta$

• thickness, m

• $\lambda$

• heat conductivity, W/(m·K)

• $\mu$

• dynamic viscosity, Pa·s

• $\rho$

• density, kg/m3

• $\epsilon$

• porosity

• Γ

• perimeter, m

### Subscripts

• a

• ambient

• c

• condenser

• cap

• capillary

• $\mathrm{c}\mathrm{i}$

• condenser inlet

• $\mathrm{c}\mathrm{o}$

• condenser outlet

• e

• evaporator

• $\mathrm{e}\mathrm{i}$

• evaporator inlet

• $\mathrm{e}\mathrm{o}$

• evaporator outlet

• g

• gravity

• j

• junction

• l

• liquid

• $\mathrm{l}\mathrm{l}$

• liquid line

• $\mathrm{v}$

• vapor

• vc

• vapor removal channel

• $\mathrm{v}\mathrm{l}$

• vapor line

• w

• wick

## 1. Introduction

As predicted by Moore’s law, the number of transistors per square inch on a processor doubles every 18 months [1]. Moreover, Feng coined “Moore’s law for power consumption” to describe the electricity used by computing nodes: the power consumption of compute nodes doubles every 18 months [2]. As a most significant aspect, central-processing-unit (CPU) temperatures not only affect the operational reliability [3], but also the power consumption of computers, including fan power consumption and total power consumption [4]. The computational performance and computation speeds that reduce energy use go hand in hand with reducing CPU temperature [5]. In order to further address this issue, DeVogeleer et al. [6] proposed a practical model to estimate the CPU power consumption at a given temperature with arbitrary CPU configurations. The exponential behavior is affected by, among other factors, temperature-dependent leakage currents, physical properties and the voltage regulator.

Driven by the continuous miniaturization of high-performance electronics, the dramatic increase of heat fluxes generated by semiconductor components urges the development of more effective cooling methods to ensure the reliability, stability and performance of these components [7]. As proposed by Bar-Cohen et al. [8] and Chen et al. [9], the stability and reliability of electronic chips decrease by 10% for every 2 °C increase above the permissible operating temperature. In particular, thermal management of portable electronics (for example, laptop computers) is becoming a more challenging task due to the difficulty of the problem in such a narrow space being on the order of millimeters, and ultrathin and high-performance cooling devices are urgently in demand [10]. Fig. 1 shows the inner structure of an ultra-slim laptop computer with a widely adopted, flattened heat pipe cooling module [11].

As shown in Fig. 2, the power of CPU processors for laptop computers has continued to decline in the most recent 10 years. Meanwhile, in the last five years, the power of CPU processors has undergone almost no change, with a thermal design power (TDP) of 15 W (low end) to 28 W (high end). Table 1 summarizes the TDP for laptop computers, which shows that total heat loads dissipated by CPU processors are in excess of 15 W. For example, the latest Intel CPU processor, i7-8550U, has a full-load power consumption of 15 W and a configurable power load of up to 25 W [12].

Table 1
Intel Core CPU processors
SoCCoresBase frequencyMax turbo frequencyTDP (W)
i7-8550U41.80 GHz4.00 GHz15
i7-7660U22.50 GHz4.00 GHz15
i7-8559U42.70 GHz4.50 GHz28
i5-8250U41.60 GHz3.40 GHz15
i5-8269U42.60 GHz4.20 GHz28
i3-8109U23.00 GHz3.60 GHz28

To efficiently cool CPU processors, two-phase passive cooling devices based on conventional heat pipes (HPs) have been widely used [13], [14], [15], [16] for laptop computers. Mochizuki et al. [13] presented a hinged HP system for cooling notebook computer CPUs. The testing results showed that the hinged HP system could dissipate 10–12 W with the CPU surface temperature below 95 °C. Nguyen et al. [14] fabricated and tested three cooling solutions using HPs for cooling a notebook PC. The results showed that at an ambient temperature of 40 °C, the cooling solutions could dissipate a maximum heat load of 13 W with a CPU surface temperature of 95 °C. To cool the Pentium processors, searches for a thermal solution were conducted by Xie et al. [15]. The results showed that two thermal solutions using HPs exhibited high heat transfer performance. Moon et al. [16] presented a miniature HP for cooling a notebook PC that could transfer a thermal load of 11.5 W with the junction temperature below 100 °C. However, owing to the heat transfer capacity limit of a single HP, for high heat fluxes and high power loading, thermal control devices may require multiple HPs or the aid of phase-change material (PCM) to meet the cooling demands, and more space is needed to integrate large cooling modules inside laptop computers. For example, Li et al. [17] proposed a novel sintered wick structure for the improvement of ultrathin HPs (UTHPs), and the effects of various parameters on the thermal performance of the UTHPs were evaluated experimentally. The results showed that the maximum heat transport capability could reach 25 W, and the thermal performance decreased rapidly with decreasing thickness. In addition, to improve the maximum heat transfer capacity for laptop computers cooling, HPs with PCM cooling modules were also studied [18], [19]. For example, Weng et al. [18] designed a HP module with PCM for electronic cooling, in which the adiabatic section of the HP was covered by a storage container with PCM, and investigated the thermal performance. The cooling module could save 46% of the fan power consumption compared with a traditional HP. However, the problems with using phase change materials are their limited heat-storage capacity and the need for additional space [20].

However, the development trends of laptop computers are faster, thinner, and lighter. For example, the thickness of the Lenovo ThinkPad X1 ultra-slim computer series has been reduced from 18.85 mm in 2012 to 15.95 mm in 2018, and the weight has been reduced from 1.347 kg to 1.13 kg, correspondingly. Another case is the Apple MacBook laptop computer, which has a total thickness of less than 13.1 mm. If the available space for cooling-module implementation is strictly limited, e.g., approximately 4–5 mm total thickness inside the chassis or less in the future, a powerful fan is required to deliver more waste heat out of laptop computers based on the conventional flattened HP configurations, which results in extra power consumption and a significant amount of noise. In this situation, novel miniature two-phase heat transfer devices with higher heat transport capacity are expected to be developed for laptop computers cooling.

A loop heat pipe (LHP), first developed in 1972 [21], is a highly effective two-phase heat transfer apparatus that uses the phase change of the working fluid to transfer heat from a heat source to a heat sink, and relies on capillary force generated in a porous wicking structure to circulate the working fluid inside the closed loop [22]. Owing to their advantages, such as the flexibility in packaging, high heat transfer capacity, low thermal resistance, and antigravity operation, many LHPs have been widely used in the thermal control of spacecraft[23], [24], electronics cooling [25], [26], [27], [28], [29], [30], [31], and solar-energy utilization [32], [33]. In recent decades, with the development of the microelectronics industry, application of LHPs in cooling mobile electronics, such as laptop computers or smartphones, has attracted special attention. However, because of the limited available space inside the cabinet for installing such heat transfer devices, conventional LHPs with large cylindrical evaporators may not meet the requirements of laptop computers or other portable devices. Therefore, ultrathin miniature loop heat pipe (mLHP or ULHP) coolers with flat evaporators are expected to be urgently developed and investigated.

Singh et al. [34], [35], [36] designed three different miniature loop heat pipes for compact computers and notebooks, one with a disk-shaped evaporator, 30 mm in diameter and 10 mm thick, another one with a rectangular evaporator, 45 × 35 mm plan area and 5 mm thick, and a third with a rectangular evaporator, 47 × 37 mm plan area and 5 mm thick, which showed that the potential for the compact computers cooling. Lin et al. [37] presented a miniature loop heat pipe with a 3-mm-thick rectangular evaporator for laptop PCs. The test results indicated that the mLHP could dissipate a heat load of 45 W with a heat source temperature of 63.1 °C under forced liquid cooling at the condenser side. However, the mLHPs mentioned above [24], [25], [26], [27], [28], [29], [30], [31], [32], [33], [34], [35], [36], [37] may not actually be installed due to the limited available space in the latest ultra-slim laptop computers if considering the extra space needed for the fins attached to the LHPs. In the Ref. [38], a 1.5-mm-thick looped type heat pipe was developed for thermal management of a power battery, but it only worked in a gravity-assisted situation, which is not feasible for laptop computers.

In the very latest review literature [39], the ultrathin micro heat pipe technologies for electronics cooling have been summarized. Presently, the publicly-reported miniaturized loop heat pipes with thickness of less than 2 mm for mobile electronics are very few. One is developed by Fujitsu Laboratories in 2015, specifically a novel ULHP with a 0.6-mm-thick evaporator for thermal management of smartphones. Compared to highly thermal conductive sheets (copper or aluminum), the ULHP exhibits approximately five times larger heat transfer capacity with a maximum heat transfer capacity of 15 W before burnout [40]. Another work is from the authors’ group [29], in which a novel copper–water miniature loop heat pipe with a flat 1.2-mm-thick evaporator and a 1.0-mm-thick condenser was designed, which has a capacity of more than 12 W at natural convection without any further heat transfer enhancement emendation. Basically, the thermal performance of a fanless ultrathin heat pipe module as illustrated in [29], [40] is very limited, which can only be aimed at less than 10 W cooling requirements [29], [39], [40].

Owing to the limited capacity of a conventional HP module and the very small size of attached fins, a dynamic fan is needed to meet the requirement of a large amount of waste heat dissipation from laptop computer CPUs, e.g., 15–28 W, as shown in Table 1. However, within 5 mm of available space height in an ultra-slim laptop computer, or even less, the complexity for the cooling module installation and the heavy fan usage will induce possible long-term failure and significant noise issues due to the very limited air flow rate from the usual small centrifugal fan. Meanwhile, even the power consumption of a laptop computer fan is very small (1–2 W), owning to the large number of laptop computers in use and their long operating time, the aggregate power consumption is still very large on a global scale. Therefore, the development of a simply-structured, ultrathin but high-performance heat dissipation module capable of handling 30 W or so with extremely low power consumption (or light fan usage) is the ideal solution for the next generation of ultra-slim laptop computers, while LHP technology could most likely meet the requirements due to its many unique advantages compared to conventional HPs as explained above. Unfortunately, to the best of our knowledge, no such a loop heat pipe apparatus has been reported in literatures or used commercially so far.

In the present work, a unique active cooler based on a 1-mm-thick miniature loop heat pipe (mLHP), aimed at handling 30 W for a high-end ultra-slim laptop computer, was developed and tested successfully for what we believe is the first time. Its thermal characteristics, both under natural convection and forced air cooling conditions, were fully investigated. Furthermore, the effects of different test orientations and air flow velocities flowing through the condenser on the thermal performance of the proposed LHP were systemically examined by adjusting the fan voltages from 5 V to 0 V. It was found that the proposed mLHP module can work fairly well even at a 2 V fan voltage over a heat load range of 15–30 W. At the same time, a detailed theoretical model was established to provide an insight in understanding the operation mechanism of the proposed mLHP module, and also serve as a very useful guide for developing practical applications. In addition, the power consumption and the power savings were calculated based on the experimental findings. Finally, the operational performance of the proposed mLHP module in a temperature humidity chamber was evaluated and compared with the latest advanced ultrathin HP module. The results indicate that the present mLHP module is superior to the conventional HP module in the aspects of space, weight, and power savings, in addition to achieving higher cooling performances. Compared to the current ultrathin HP module applied in the latest ultra-slim laptop computers, the proposed mLHP module is approximately 11.10 g lighter, and the cooling energy consumption is reduced by 80%.

## 2. Description of the experimental prototype

As shown in Fig. 3, the proposed mLHP mainly has a flat evaporator, a vapor line, a liquid line, a fin-and-tube type condenser, and a charging line for vacuuming and liquid charging. The mLHP module also includes a slim centrifugal fan attached to the fin assembly by tape. The main geometric parameters of the proposed mLHP module are summarized in Table 2.

Table 2
EvaporatorL × W × H (mm)60 × 23 × 1.2
Primary wickOverall dimensions (L × W × H) (mm)50 × 21 × 0.8
Porosity (%)65.2

Secondary wickL × W × H (mm)105 × 1.5 × 0.43
Porosity (%)61.2

Vapor lineInitial tube ID/OD (mm)3.5/4
Final external height (mm)1.0
Length (mm)132

Liquid lineInitial tube ID/OD (mm)3.5/4
Final external height (mm)1.0
Length (mm)132

Fin assemblyOverall dimensions (L × W × H) (mm)72 × 32 × 5

Working fluidWater

Filling ratio40%

Centrifugal fanL × H (mm)72 × 5

The mLHP flat evaporator was formed by two 0.2-mm-thick upper and lower copper plates and a primary capillary wick through a sintering process under 850 °C for 30 min in a vacuum sintering furnace with nitrogen shielding gas. The primary capillary wicking structure was 0.8 mm thick, and was fabricated from 500 mesh copper wire mesh. The primary wick geometric parameters, a SEM photograph, and the wettability of deionized water are shown in Fig. 4, respectively. As illustrated in Fig. 4(a), there are 10 rectangular grooves with 1 mm wide machined through the entire thickness of the primary wick at 1 mm intervals using wire-electrode cutting, which functioned as the vapor flow passages. Fig. 4(b) shows that the microstructures of the 500 mesh copper mesh, which increased the hydrophilic property of the copper mesh and the capillary force of the primary wick according to the Young-Laplace law. Fig. 5(c) presents the wettability demonstration of a 7 μl water droplet on the primary wick, showing that the droplet penetrated the sintered copper mesh completely only within 15 ms.

As shown in Fig. 3(a), a 0.43-mm-thick secondary wicking structure fabricated from 150 mesh copper wire mesh was employed in the liquid line, which was integrated with the primary wick through another sintering process, to develop additional capillary force to promote working fluid circulation. The transport lines, including the vapor and liquid lines and the pipeline of the condenser, were fabricated from Φ4 mm × 0.25 mm copper tubing that was uniformly flattened to an external height of 1 mm using a flattening mill. The length of both the vapor and liquid lines was 132 mm. For the fin-and-tube-type condenser, an aluminum fin assembly was soldered on the pipeline using lead-free solder paste. The volume of the condenser encompassing the pipeline and fin group was 72 × 32 × 5 mm3, and a DC centrifugal fan was mounted on the condenser.

Deionized water was used as the working fluid, and the filling ratio was calculated to be 40%, where the filling ratio is defined as the volume percentage of the total inner space of the LHP, including the porosity of the capillary wick shared by the working fluid.

## 3. Experimental setup

To evaluate the thermal performance of the mLHP, a copper block containing a cartridge heater served as the heat source, which was provided by a variable DC power supply (accuracy of $±$0.5%). The heating block with an active heating area of 12 mm × 10 mm was mounted on the flat evaporator surface, and wrapped with a layer 10-mm thick adiabatic foam made of NBR/PVC, the thermal conductivity of which is about 0.034 $\mathrm{W}/\left(\mathrm{m}·\mathrm{K}\right)$, to minimize the heat loss of the heater. A very thin layer of thermal grease (thermal conductivity of about 8.5 $\mathrm{W}/\left(\mathrm{m}·\mathrm{K}$)) was used to fill the air gap between the heating block and the mLHP evaporator to minimize the contact thermal resistance. As shown in Fig. 5(b), a K-type Omega thermocouple was embedded into the top surface of the heating block to measure the junction temperature${T}_{j}$ of the heater. In the condenser cooling system, the centrifugal fan was powered by a variable DC power supply, and the fan voltage could be adjusted to attain different air flow velocities flowing through the condenser to fully examine the effects of air flow velocity on mLHP thermal performance.

For the data acquisition system, an Agilent 34970A data acquisition with measurement accuracy of $±$0.1 °C was used to monitor and record the temperature data obtained from the K-type Omega thermocouples with an uncertainty of $±$0.3 °C at a time interval of 1 s. Fig. 5(a) illustrates the locations of 11 K-type Omega thermocouples, including 10 thermocouples attached to the mLHP surface and the thermocouple measuring the junction temperature ${T}_{j}$. Thermocouples #101 and #102 were located on the heated surface of the evaporator, and the evaporator temperature ${T}_{e}$ was determined as the average value of the two thermocouples, where ${T}_{e}=\left({T}_{101}+{T}_{102}\right)/2$. Thermocouples #103 and #110 were used to measure the temperatures of the evaporator outlet ${T}_{\mathit{ec}}$ and inlet${T}_{\mathit{ei}}$, respectively. Thermocouples #104 and #109 were employed to measure the temperatures of the vapor line ${T}_{\mathit{vl}}$ and liquid line${T}_{\mathit{ll}}$, respectively. Thermocouples #105 and #108 were employed to measure the temperatures of the condenser inlet ${T}_{\mathit{ci}}$ and outlet ${T}_{\mathit{co}}$, respectively. Thermocouple #106 and #107 were used to measure the temperatures on the pipeline and the fin group of the condenser, respectively. Finally, another K-type Omega thermocouple was employed to measure the ambient temperature${T}_{a}$. Moreover, an infrared camera (Fluke Ti32) with an uncertainty of $±$2 °C was used to visualize the temperature distribution of the mLHP at steady state under different heat loads.

To fully evaluate the heat transfer performance of the proposed mLHP, two different cooling mechanisms, natural convection (fan input voltage = 0 V) and forced air cooling, were employed in the experimental investigations. For the forced air cooling, the fan input voltages were maintained at 2 V (the minimum voltage for the operation of the centrifugal fan), 3 V, 4 V, and 5 V (the rated voltage) to examine the effects of the air flow velocity on the thermal performance of the proposed mLHP. An anemometer (Testo 425) with an accuracy of $±$0.03 m/s was used to measure the air flow velocities flowing through the condenser under the fan voltages of 2 V, 3 V, 4 V, and 5 V, and the corresponding mean air flow velocities were 1.54 m/s, 2.48 m/s, 3.59 m/s, and 4.67 m/s, respectively.

In addition, the mLHP was tested in three different orientations, as shown in Fig. 6. Fig. 6(a) illustrates three common positions in which the laptop computers are used. Thus, three typical orientations, $\phi =0Â°$$\phi =90Â°$ (vapor flowing upward) and $\phi =-90Â°$ (vapor flowing downward), were studied here. It should be noted that for the two above-mentioned cooling methods, the ambient temperature was maintained at 23 ± 1 °C.

## 4. Pressure balance and temperature analysis in the mLHP

In a loop heat pipe, the capillary force provided by the capillary wick should be larger than the total pressure losses along the loop, mainly including the vapor flow pressure drop, the liquid flow pressure drop, and the hydrostatic pressure loss, for the continuous operation. This can be mathematically expressed as follows:

(1)$\mathrm{\Delta }{P}_{\mathit{cap}}=\frac{2\sigma }{{r}_{\mathit{cap}}}\ge \mathrm{\Delta }{P}_{v}+\mathrm{\Delta }{P}_{l}+\mathrm{\Delta }{P}_{g}$where $\mathrm{\Delta }{P}_{\mathit{cap}}$ is the capillary force; $\sigma$ is the surface tension of the working fluid; ${r}_{\mathit{cap}}$ is the mean effective pore radius of the capillary wick, which might be approximately calculated as ${r}_{\mathit{cap}}\approx \frac{1}{2N}$ ($N$ is the mesh number per meter), and $\mathrm{\Delta }{P}_{v}$$\mathrm{\Delta }{P}_{l}$ and $\mathrm{\Delta }{P}_{g}$ are the pressure losses for the vapor flow, liquid flow, and the pressure loss caused by hydrostatic resistance of a liquid column in the gravitational field, respectively.

In the horizontal orientation, where the hydrostatic pressure loss $\mathrm{\Delta }{P}_{g}$ is zero, the relationship for the proposed mLHP could be expressed as

(2)$\mathrm{\Delta }{P}_{\mathit{cap}}=\frac{2\sigma }{{r}_{cap1}}\ge \mathrm{\Delta }{P}_{v}+\mathrm{\Delta }{P}_{l}$where σ is the surface tension of the working fluid and ${r}_{cap1}$ is the mean effective pore radius of the primary capillary wick.

For the proposed mLHP, the vapor flow pressure drop $\mathrm{\Delta }{P}_{v}$ includes the pressure drops due to the vapor flow in the vapor removal channels $\mathrm{\Delta }{P}_{v,vc}$, in the vapor line $\mathrm{\Delta }{P}_{v,vl}$, and in the condenser pipeline $\mathrm{\Delta }{P}_{v,cond}$. The liquid flow pressure loss $\mathrm{\Delta }{P}_{l}$ mainly consists of two parts, namely the pressure drop due to the liquid flow in the liquid line $\mathrm{\Delta }{P}_{l,ll}$, and the pressure drop due to the liquid flow through the wick $\mathrm{\Delta }{P}_{l,w}$.

As indicated by Li and Peterson [41], [42], the vapor flow drop in the rectangular vapor removal channels $\mathrm{\Delta }{P}_{\mathit{vc}}$ can be calculated as

(3)$\mathrm{\Delta }{P}_{v,vc}=\frac{Q·{\mu }_{v}·{L}_{\mathit{vc}}}{{h}_{\mathit{fg}}·{\rho }_{v}·{n}_{\mathit{vc}}·H·W·{{d}_{\mathit{vc}}}^{2}}\left[9.4+39.28\frac{1+{\beta }^{2}}{{\left(1+\beta \right)}^{2}}\right]$

In the vapor line,

(4)$\mathrm{\Delta }{P}_{v,vl}=\frac{128·Q·{\mu }_{v}·{L}_{\mathit{vl}}}{\pi ·{h}_{\mathit{fg}}·{\rho }_{v}·{{d}_{\mathit{vl}}}^{4}}$

And for the vapor pressure loss in the condenser,

(5)$\mathrm{\Delta }{P}_{v,c}=\frac{128·Q·{\mu }_{v}·{L}_{c}}{\pi ·{h}_{\mathit{fg}}·{\rho }_{v}·{{d}_{c}}^{4}}$

Here, $Q$ is the applied heat load; ${\mu }_{v}$ is the dynamic viscosity of vapor; ${L}_{\mathit{vc}}$${L}_{\mathit{vl}}$, and ${L}_{c}$ are the effective lengths of the vapor removal channel, vapor line, and condenser pipeline, respectively; ${h}_{\mathit{fg}}$ is the latent heat of evaporation; ${\rho }_{v}$ is the vapor density; ${n}_{\mathit{vc}}$ is the number of vapor removal channels; $H$ is the height of the vapor removal channel; $W$ is the width of the vapor removal channel; ${d}_{\mathit{vl}}$ and ${d}_{c}$ are the effective hydraulic diameters of the vapor line and the condenser pipeline, respectively, which can be calculated from $d=4A/\mathrm{\Gamma }$, and $\beta$ is the aspect ratio of the vapor removal channel, which may be defined as Eq. (6),

(6)$\beta =\frac{H}{W}$

It should be noted that the vapor flow pressure losses above were calculated for the fully-developed laminar flow.

For the liquid flow pressure loss in the liquid line, $\mathrm{\Delta }{P}_{l,ll}$ can be calculated using the following equation:

(7)$\mathrm{\Delta }{P}_{l,ll}=\frac{128·Q·{\mu }_{l}·{L}_{\mathit{ll}}}{\pi ·{h}_{\mathit{fg}}·{\rho }_{l}·{{d}_{\mathit{ll}}}^{4}}$where ${\mu }_{l}$ is the dynamic viscosity of liquid; ${L}_{\mathit{ll}}$ is the effective length of the liquid line; ${\rho }_{l}$ is the liquid density, and ${d}_{\mathit{ll}}$ is the effective hydraulic diameter of the liquid line.

According to the Dancy’s law, the pressure loss due to the liquid flow through the wick $\mathrm{\Delta }{P}_{l,w}$ can be determined as:

(8)$\mathrm{\Delta }{P}_{l,w}=\frac{Q·{\mu }_{l}·{\delta }_{w}}{{h}_{\mathit{fg}}·{\rho }_{l}·{A}_{w}·K}$where ${\delta }_{w}$ is the thickness of the wick, ${A}_{w}$ is the cross sectional area of the wick, and $K$ is the wick permeability, which may be calculated by the following equation according to the modified Black-Kozeny equation,(9)$K=\frac{{D}^{2}·{\epsilon }^{3}}{122{\left(1-\epsilon \right)}^{2}}$where $D$ is the diameter of the copper wire and $\epsilon$ is the porosity of the capillary wick.

Thus, for the proposed mLHP, the pressure loss across the wick $\mathrm{\Delta }{P}_{l,w}$ is established as,

(10)$\mathrm{\Delta }{P}_{l,w}=\mathrm{\Delta }{P}_{l,w1}+\mathrm{\Delta }{P}_{l,w2}=\frac{Q·{\mu }_{l}·{\delta }_{w1}}{{h}_{\mathit{fg}}·{\rho }_{l}·{A}_{w1}·{K}_{1}}+\frac{Q·{\mu }_{l}·{\delta }_{w2}}{{h}_{\mathit{fg}}·{\rho }_{l}·{A}_{w2}·{K}_{2}}$where subscripts 1 and 2 represent the primary capillary wick and the secondary capillary wick, respectively.

As presented by Chernysheva et al. [43], for an LHP, the evaporator wall temperature ${T}_{e}$ under a certain heat load $Q$ is,

(11)${T}_{e}={T}_{a}+\left(\frac{1}{{\alpha }_{c,ext}·{S}_{c,ext}}+{R}_{c,wall}+\frac{1}{{\alpha }_{c,int}·{S}_{c,int}}+\sum _{i}\mathrm{\Delta }{P}_{i}·\frac{\mathit{dT}}{\mathit{dP}}{|}_{\overline{T}}+\frac{1}{{\alpha }_{e}·{S}_{e,active}}\right)·Q$where ${\alpha }_{c,ext}$ is the convective heat transfer coefficient at the external surface of the condenser and ${S}_{c,ext}$ is the total surface area of the condenser; ${\alpha }_{c,int}$ is the condensation heat transfer coefficient and ${S}_{c,int}$ is the internal surface area of the condenser pipeline; ${\alpha }_{e}$ is the evaporation heat transfer coefficient and ${S}_{e,active}$ is the active area of the condenser to which heat load $Q$ is supplied. ${R}_{c,wall}$ is the thermal resistance of the condenser wall, where ${R}_{c,wall}=\frac{{\delta }_{\mathit{wall}}}{k·{S}_{\mathit{wall}}}.$ Due to the thin thickness of the condenser pipeline wall ${\delta }_{\mathit{wall}}$ and the high heat conductivity $k$ of the wall material (copper), the thermal resistance of the condenser wall ${R}_{c,wall}$ can be neglected, regardless of the surface area of the condenser pipeline wall ${S}_{\mathit{wall}}$${\sum }_{i}\mathrm{\Delta }{P}_{i}$ is the total pressure drop of the vapor, which mainly consist of the pressure drops due to the vapor flow in the vapor removal channels $\mathrm{\Delta }{P}_{v,vc}$, in the vapor line $\mathrm{\Delta }{P}_{v,vl}$, and in the condenser $\mathrm{\Delta }{P}_{v,cond}$, as given by Eqs. (3), (4), (5), respectively. Thus,(12)$\sum _{i}\mathrm{\Delta }{P}_{i}=\mathrm{\Delta }{P}_{v}=\mathrm{\Delta }{P}_{v,vc}+\mathrm{\Delta }{P}_{v,vl}+\mathrm{\Delta }{P}_{v,c}$

The derivative $\frac{\mathit{dT}}{\mathit{dP}}{|}_{\overline{T}}$ is a thermophysical characteristic of the working fluid that describes the characteristics of the liquid-vapor saturation line at the temperature $\overline{T}=\frac{{T}_{v}-{T}_{c}}{2}$. The derivative $\frac{\mathit{dT}}{\mathit{dP}}{|}_{\overline{T}}$ could be approximately calculated by the Clausius-Clapeyron equation at the reference temperature.

Owing to the nonideal thermal contact between the heating block and the LHP evaporator, a temperature drop always exists in the heat-supply zone $\mathrm{\Delta }{T}_{j}={T}_{j}-{T}_{e}$. For the proposed mLHP, the thermal resistance of the contact zone ${R}_{\mathit{cont}}$ is caused by the very thin layer of thermal grease, which may be written by the following relation:

(13)${R}_{\mathit{cont}}=\frac{l}{\lambda ·{S}_{e,active}}$

Here, $l$ is the thickness of the thin layer of the thermal resistance (in the study, the thickness $l$ is about 0.1 mm), and $\lambda$ is the thermal conductivity of the thermal grease.

The temperature drop $\mathrm{\Delta }{T}_{j}$ can be calculated using Eq. (14),

(14)$\mathrm{\Delta }{T}_{j}=Q·{R}_{\mathit{cont}}$

Therefore, the junction temperature ${T}_{j}$ can be determined as follows:

(15)${T}_{j}={T}_{e}+Q·{R}_{\mathit{cont}}$

With an allowance for Eq. (11), Eq. (15) for the junction temperature is developed herein,

(16)${T}_{j}={T}_{a}+\left(\frac{1}{{\alpha }_{c,ext}·{S}_{c,ext}}+{R}_{c,wall}+\frac{1}{{\alpha }_{c,int}·{S}_{c,int}}+\sum _{i}\mathrm{\Delta }{P}_{i}·\frac{\mathit{dT}}{\mathit{dP}}{|}_{\overline{T}}+\frac{1}{{\alpha }_{e}·{S}_{e,active}}+{R}_{\mathit{cont}}\right)·Q$

Therefore, for the proposed mLHP, all the equations above may be calculated theoretically under a certain applied heat load $\mathrm{Q}$.

## 5. Results and discussion

It is should be noted that all the tests described in this section were carried out with the temperature humidity chamber shutdown, and its door opened to facilitate infrared (IR) detection.

### 5.1. Heat transfer characteristics of the proposed mLHP module

#### 5.1.1. Natural convection

Fig. 7 shows the heat load dependence of the junction temperature of the proposed mLHP at steady state under natural convection condition for the test orientations. It is clearly shown that for the test orientations, the junction temperature ${T}_{j}$ nearly linearly increased with increasing heat load. It can be also be seen from Fig. 7 that the experimental results approximately demonstrated that, only using natural convection as the cooling mechanism, the mLHP could effectively dissipate approximately 12 W at all test orientations with the junction temperatures below 85 °C.

It can be found that for the test slope $\phi =-90Â°$, the junction temperatures were slightly lower than those obtained for the other test orientations. Referring to the steady-state surface temperature IR detection of the mLHP and the schematic of the two-phase flow inside the mLHP as given in Fig. 8, it is shown that at the slope $\phi =-90Â°$, the average temperature of the condenser and the liquid line temperature at 15 W were both higher than those obtained for $\phi =90Â°$, showing a more uniform temperature distribution. Moreover, based on the temperature distributions in Fig. 8(a), the schematic of two-phase flow inside the mLHP was illustrated approximately in Fig. 8(b), which clearly shows the distribution of the vapor phase and liquid phase of the working fluid inside the mLHP.

Fig. 9 presents the steady-state temperature distributions measured by the IR camera at 2 W, 5 W, 10 W, and 15 W in the horizontal orientation under natural convection condition. It is clearly shown that the surface temperature distribution of the mLHP became increasingly more and more uniform with increasing heat load. At 15 W, the temperatures of the evaporator, vapor line, and the condenser were very close, indicating a good heat transfer performance from the evaporator to the condenser.

As an important reference, the “heat source-ambient” system total thermal resistance ${R}_{\mathit{total}}$, which is the most interesting parameter for industrial applications, may be defined as

(17)${R}_{\mathit{total}}=\frac{{T}_{j}-{T}_{a}}{Q}$

Here, $Q$ is the applied heat load.

Fig. 10 presents the total thermal resistances of the mLHP under different heat loads for the test orientations. It can be seen that for all test orientations, the total thermal resistance ${R}_{\mathit{total}}$ of the mLHP gradually decreased with the increasing heat load. A minimum value of 4.59 °C/W was obtained at 15 W for $\phi =-90Â°$. In general, it can be concluded from Fig. 7, Fig. 10 that the proposed mLHP is an active cooler for mobile electronics cooling under natural air convection, which could effectively dissipate a maximum heat load of 15 W.

#### 5.1.2. Forced air cooling

Fig. 11 shows the transient temperature evaluations during the startup process at a heat load of 2 W in the horizontal orientation at a fan voltage of 5 V. Fig. 11 clearly showed that when the heat load was applied to the evaporator, the temperatures, i.e., evaporator temperatures (101 and 102), evaporator outlet temperature (103), and the vapor line temperature (104), rapidly increased. It should be noted that a sudden rise and drop was observed for the vapor line temperature (104) between 500 s and 1500 s, which may be a sign of the fluid periodic circulation in the mLHP. At 2 W, the junction temperature had a value of 41 °C at steady state. In addition, it is evident that the evaporator inlet temperature (110) was higher than the liquid line temperature (109) due to the heat leakage.

Fig. 12 presents the transient temperature evaluations during the startup process at a heat load of 25 W in the horizontal orientation at a fan voltage of 5 V. It is shown that the proposed mLHP started up and operated smoothly with negligible fluctuation in the temperature curves. The startup process of the proposed mLHP needs approximately 500 s, after which a stable operation condition was achieved with a steady-state junction temperature of 79.3 °C.

Fig. 13 shows the heat load dependence of the junction temperature under different fan voltages for all test orientations. It can be seen from Fig. 13 that, under forced air cooling condition, when the voltage of the centrifugal fan was 2 V, the steady-state junction temperatures were highest for the heat load ranging from 2 W to 25 W at all test orientations. However, when the heat load was over 25 W, the mLHP exhibited a higher thermal performance at 2 V owing to the more uniform temperature distribution. In addition, it is shown that under forced air cooling condition, the proposed mLHP cooler could efficiently dissipate a maximum heat load of 25 W with the maximum allowable junction temperature of 85 °C for all test orientations, and the junction temperatures nearly decreased with the increasing fan voltage from 2 V to 5 V. Finally, it is demonstrated that the mLHP could still function well at 30 W with the maximum junction temperature of about 110 °C for all fan voltages and test orientations.

Fig. 14 shows the steady-state IR measurements of the temperature distribution of the mLHP at 10 W, 20 W, and 30 W for different fan voltages of 2 V and 5 V in the horizontal orientation. It is shown that at heat loads of 10 W and 20 W, the measured temperatures at the evaporator outlet were higher at 2 V than those at 5 V. In addition, for a high heat load case of 30 W, the uniformity of the temperature distribution at fan voltage of 2 V was comparatively better than that at 5 V, which may explain the phenomenon that the mLHP had a lower junction temperature at a fan voltage of 2 V, as shown in Fig. 13(a) beyond 25 W.

Under forced air convection, the total thermal resistance could also be estimated using Eq. (17), and for the proposed mLHP, the uncertainty of the total thermal resistance ${R}_{\mathit{total}}$ was calculated to be approximately 4.71–1.11% in the range of the heat loads from 2 W to 32 W, which can be estimated by the following equation:

(18)$\frac{\mathrm{\Delta }{R}_{\mathit{total}}}{{R}_{\mathit{total}}}=\sqrt{{\left(\frac{\mathrm{\Delta }{T}_{j}}{{T}_{j}-{T}_{a}}\right)}^{2}+{\left(\frac{\mathrm{\Delta }{T}_{a}}{{T}_{j}-{T}_{a}}\right)}^{2}+{\left(\frac{\mathrm{\Delta }Q}{Q}\right)}^{2}}$where $\mathrm{\Delta }{T}_{j}$$\mathrm{\Delta }{T}_{a}$, and $\mathrm{\Delta }Q$ are the measurement errors of the junction temperature ${T}_{j}$, the ambient temperature ${T}_{a}$, and the heat load $Q$, respectively.

Fig. 15 plots the heat load dependence of the total thermal resistance ${R}_{\mathit{total}}$ under different fan voltages for all test orientations. It can be seen that, for the fan voltages higher than 2 V, ${R}_{\mathit{total}}$ initially decreased with increasing heat load from 2 W to 25 W, and then slightly increased at 30 W. While for a fan voltage of 2 V, ${R}_{\mathit{total}}$ decreased with the increasing heat load from 2 W to 30 W, and then slightly increased at 32 W. A minimum value of ${R}_{\mathit{total}}$ was 2.17 °C/W, which was obtained at 30 W for $\phi =-90Â°$ at the fan voltage of 2 V. It is demonstrated by Fig. 13, Fig. 15 that, for the proposed mLHP, the high fan voltage of 5 V was contributed to the lower junction temperatures at heat loads not exceeding 25 W, while at the low fan voltage of 2 V, the mLHP showed a higher heat transfer performance when the heat load was over 25 W.

### 5.2. Performance analysis and power consumption

#### 5.2.1. Pressure balance and temperature analysis

Fig. 16 shows the pressure balance analysis in the mLHP in the horizontal orientation. It is shown that both the vapor and liquid pressure drops gradually increased with increasing heat load. As shown in Fig. 14(a), the junction temperature ${T}_{j}$ exhibited an unusual increase at 30 W at a fan voltage of 5 V, reaching a value of 108.6 °C. Based on Fig. 16, a possible explanation for this phenomenon may be that at 30 W the total pressure drop increased to be 5045 Pa, which was slightly lower than the capillary force of 5412 Pa, and the capillary limit was nearly reached (considering the real situation, the capillary limitation was reached).

For the present mLHP, the evaporation heat transfer coefficient ${\alpha }_{e}$, condensation heat transfer coefficient ${\alpha }_{c,int}$, and convective heat transfer coefficient ${\alpha }_{c,ext}$ may be calculated according to the following respective definitions [44],

(19)${\alpha }_{e}\approx \frac{Q}{{S}_{e,active}\left({T}_{e}-{T}_{v}\right)}$${\alpha }_{c,int}\approx \frac{Q}{{S}_{c,int}\left({T}_{\mathit{ci}}-{T}_{\mathit{co}}\right)}$${\alpha }_{c,ext}\approx \frac{Q}{{S}_{c,ext}\left({T}_{c}-{T}_{a}\right)}$where ${S}_{e,active}$${S}_{c,int}$, and ${S}_{c,ext}$ are the evaporation active area, condensation active area, and total surface area of the condenser, respectively; ${T}_{v}$ is the vapor temperature, which may be approximately defined as the evaporator outlet temperature ${T}_{\mathit{eo}}$, i.e., ${T}_{v}\approx {T}_{\mathit{eo}}$${T}_{c}$ is the average temperature of the condenser, ${T}_{c}=\left({T}_{105}+{T}_{106}+{T}_{107}+{T}_{108}\right)/4$. In this study, ${S}_{e,active}=1.2×{10}^{-4}$ m2${S}_{c,int}=3.384×{10}^{-4}$ m2, and ${S}_{c,ext}=2.125×{10}^{-2}$ m2.

Fig. 17 plots the values of the heat transfer coefficients calculated from Eqs. (19), (20), (21), including the evaporation heat transfer coefficient ${\alpha }_{e}$, condensation heat transfer coefficient ${\alpha }_{c,int}$, and convection heat transfer coefficient ${\alpha }_{c,ext}$, under different heat loads in the horizontal orientation at 5 V. It is shown that ${\alpha }_{e}$ increased initially and then decreased with the increasing heat load, which had a value from 68,990 W/(m2 K) to 168,029 W/(m2 K). However, ${\alpha }_{c,int}$ initially decreased and then increased slowly with increasing heat load. Similarly, ${\alpha }_{c,ext}$ varied between 29.4 W/(m2 K) and 68.5 W/(m2 K) for the different heat loads. Here we assumed the averaged values of ${\alpha }_{e}$${\alpha }_{c,int}$, and ${\alpha }_{c,ext}$, namely, ${\alpha }_{e}=110,191$ W/(m2 K), ${\alpha }_{c,int}=1531.5$ W/(m2 K), and ${\alpha }_{c,ext}=52.5$ W/(m2 K), as the values employed in Eq. (16) for the simplified temperature analysis of the mLHP in practice.

Fig. 18 shows a comparison of heat load dependence of the junction temperature between experiments and theoretical calculations in the horizontal orientation at 5 V. It is evident that the theoretical curve had a near-linear shape due to the constant heat transfer coefficients adopted hereinabove, while the experimental curve showed a nonlinear characteristic. If the varied values of ${\alpha }_{e}$${\alpha }_{c,int}$, and ${\alpha }_{c,ext}$ are employed, the theoretical results may be much closer to the experimental results.

#### 5.2.2. Energy savings calculation

The power consumed by the centrifugal fan at different voltages was determined from ${P}_{\mathit{fan}}=U·I$ and is presented in Fig. 19(a), which demonstrates that the consumed powers at fan voltages of 2 V and 5 V were 0.2 W and 1.45 W, respectively. Moreover, as shown in Fig. 19(b), the total energy consumption of a single centrifugal fan in one year (365 days) operating for 8 h per day was 2102.4 kJ at 2 V voltage, in contrast to an energy consumption of 15242.4 kJ at 5 V voltage, with a more than sevenfold difference.

Fig. 20(a) summarizes the global unit shipments of laptop computers in a 5-year period (2013–2017). For example, in 2017, 164.7 million laptop computers were shipped worldwide. Therefore, taking 2017 as an example, the total energy consumption of the laptop computers per year due to the centrifugal fans operation was calculated, which is shown in Fig. 21(b). Thus, it could be approximately estimated that a little bit more than 600 million kW·h in energy consumption could be saved by using the proposed mLHP module as the cooling system for the laptop computers, which is nearly one-fifth of the annual power production of a large-scale power plant.

The coefficient of performance (COP) of the proposed mLHP cooling module could be calculated approximately by using the following equation:

(22)$\mathit{COP}=\frac{{Q}_{h}}{{P}_{\mathit{fan}}}$

Here, ${Q}_{h}$ is the heat transfer capability of the proposed mLHP module; ${P}_{\mathit{fan}}$ is the consumed power of the centrifugal fan.

It can be easily obtained that the COP gradually increased with the decrease of fan power. For a fan voltage of 2 V, a maximum COP of 150 was achieved at 30 W, compared to a COP of 20.7 at a fan voltage of 5 V.

### 5.3. Performance comparisons in a temperature humidity chamber

#### 5.3.1. Test results

Aimed at evaluating the thermal performance on board, the proposed mLHP was tested in a temperature humidity chamber as commonly required by the laptop PCs dealers. To better evaluate the thermal performance of the proposed mLHP, its results in the temperature humidity chamber were compared with those obtained from a dual-HP module (with a TDP of 25 W) used in a latest and thinnest laptop PC produced by a leading international PC maker under the same testing condition. In this case, a very high-performance 1.2-mm-thick dual-HP module was selected from a world-famous company in this field, which includes two Φ8 mm flattened HPs: one is 1.2 mm thick with a length of 163 mm with a similar fin group at the fan side, and the other is a 1.0-mm-thick flattened HP with a length of 145 mm without fins to further improve the heat transfer ability of the module in such a small space. The experimental results of this commercialized HP cooling module from a third party could be used to gather benchmark data to better understand the potential heat transfer characteristics of the proposed mLHP module. Table 3 presents a comparison of several parameters between the dual-HP module and the proposed mLHP module for evaluation of actual implementation. The data shows that the proposed mLHP module has a 25% weight reduction at a cost increase of only approximately 20%.

Table 3
Cooing modulesHeat pipe size (Length × Thickness) (mm)Total weight without fan (g)Production cost ($) Dual-HPone: 163 × 1.2; the other: 145 × 1.038.304.5 mLHP(loop ∼ 4 × ) 132 × 1.027.205.0 (estimated) As shown in Fig. 21(a), when placed at the room temperature of 23 °C, the mLHP exhibited the lowest junction temperatures at a fan voltage of 5 V when the heat load was between 15 W and 25 W. At a fan voltage of 2 V, the junction temperature for the mLHP was higher than that at 5 V, but within 5 °C. However, the conventional HP module exhibited a 15 Celsius degree junction temperature difference between 2 V and 5 V. Fig. 21(b) presents a comparison of the junction temperatures of the dummy heater separately cooled by the proposed mLHP module and the HP module respectively in the horizontal orientation, and placed in the temperature humidity chamber at 35 °C. It can be seen that for both the proposed LHP and the HP coolers, the junction temperatures at a fan voltage of 2 V were higher than those obtained at a fan voltage of 5 V for all heat loads, and the temperature differences increased with increasing heat load. A maximum temperature difference of 7.8 °C at 25 W between 2 V and 5 V was registered for the proposed mLHP. In contrast, the same temperature difference for the HP module was totally unacceptable. Even at a lower rated CPU power of 15 W, the junction temperature differences between 2 V and 5 V were approximately 5 °C for the proposed mLHP module and 15 °C for the HP module, respectively. In addition, when the fan voltage was set at 5 V, the mLHP exhibited lower junction temperatures and a better heat transfer performance than the HP cooler when the head load was over 15 W. #### 5.3.2. Further discussion on power saving using the proposed mLHP module Fig. 21 demonstrates the present mLHP module exhibits similar performance at 2 V as the conventional double-HP module at 5 V. Taking the product cost into account, the annual profit from implementing the proposed mLHP module can be summarized in Table 4 (the unit electricity price is about 0.1$/(kW⋅h)). It can be seen that if the operation time of a laptop computer is longer than 8 h per day, the net profit will arise, and will be up to 0.1 billion USD. Another derived benefit from low fan voltage operation is that the battery will last a little bit longer.

Table 4
Cooing modulesProduct cost (million $)Cooling power cost (million$)Total cost (million \$)
Dual-HP74170 (5 V, 8 h/day)–210(5 V, 24 h/day)811–951
mLHP82310 (2 V, 8 h/day)–30 (2 V, 24 h/day)833–853

On the other hand, Refs. [4], [5], [6] indicated that improving the computational performance of laptop computers with reducing the CPU temperatures also invariably increased the electrical efficiency of computing as well as energy efficiency. For a certain computing case, the electricity consumption could be saved with higher computation speeds and shorter computing time. It is well known that there are several main factors contributing to the CPU power consumption, which include dynamic power consumption, short-circuit power consumption, and power loss due to transistor leakage currents [6], [45],

(23)${p}_{\mathit{CPU}}={P}_{\mathit{dyn}}+{P}_{\mathit{short}}+{P}_{\mathit{leak}}$

There existed different models to analyze the CPU power consumption in the literatures. DeVogeleer et al. [46] provided both theoretical and experimental evidence for the existence of an energy/frequency convexity rule, which relates energy consumption and CPU frequency on mobile devices. However, they just conducted the analysis at a fixed core temperature. As indicated by Shen et al. [47], the temperature, performance and energy have different nonlinear relationships with frequency/voltage scaling ratio and this relationship was closely related to the characteristics of hardware and applications. They designed a reinforcement learning algorithm to tackle the problem of simultaneous temperature, performance and energy management. But, the proposed approach mainly dealt with continuous tradeoff among these three quality measurement of a computer system. For a real situation, it is very complicated for energy consumption evaluation. Ref. [6] introduced an experimentally validated new macro-level model of the CPU temperature/power relationship. Unfortunately, the data provided were out of date, and their exponential expression (${p}_{\mathit{CPU}}={e}^{\left(T-{C}_{1}\right)/{C}_{2}}+{C}_{0}$) to evaluate the temperature-induced bias on power measurements is too case-sensitive.

It is no doubt that the computing speed of CPU is a function of its temperature (e.g., in [48], if the averaged CPU temperature increases from 70 °C to 85 °C, the CPU performs about 2.5% slower),

(24)$\varpi =f\left({T}_{\mathit{CPU}}\right)$

For a certain computing task X, the total energy needed is,

(25)$E\approx \left({P}_{\mathit{CPU}}\left(T\right)+{P}_{\mathit{cooling}}\right)·\frac{X}{\varpi \left(T\right)}$

However, to find the actual expression for the above equation is a very hard topic since there are many factors which affect the expression, and furthermore, is out of the scope of the present study. Even for 3% computing speed drop, globally the annual economic loss will be 46 million USD (for 8 h operation per day) or 138 million USD (for 24 h operation per day) if other factors do not change with temperature. Besides, from the publicly reported latest data as given in [48], [49], for a given computing task on a certain computer, we plotted the relationship between the normalized CPU (INTEL or AMD) computing time and its temperature as shown in Fig. 22.

It can be found that if CPU temperature is below 85 °C or so, the computing speed does not change much (<3%). if="" the="" temperature="" is="" higher="" than="" that="" system="" will="" reduce="" its="" speed="" or="" even="" turn="" off="">90 °C). Fig. 22 shows when the ambient temperature increases to an allowable high temperature (35 °C) the advantage of the mLHP is much more notable. For a high-end laptop CPU with TDP ≥ 25 W, the conventional double-HP module cannot sustain the heating power and the system is overheated (CPU temperature >85 °C). It is well acknowledged that the conventional double-HP module has approached to its heat dissipation limit within such a small thickness, which was also demonstrated by the tests hereinbefore. The promising alternative solution is miniature loop heat pipe technique as explored in this work. That is the most interesting and important contribution of the present study to the community.

## 6. Conclusions

In this work, an active cooling module based on an ultrathin miniature loop heat pipe was developed for high-end ultra-slim laptop computers cooling. The heat transfer performance of the proposed miniature loop heat pipe was experimentally investigated in three commonly used orientations under both natural convection and forced air cooling conditions. In addition, thermal performance in a temperature humidity chamber was also evaluated. Several main conclusions obtained from the study are summarized as follows:

• (1)

• Under natural convection, the proposed miniature loop heat pipe could efficiently transfer a maximum heat load of 15 W with a junction temperature below 96.6 °C for all test orientations.

• (2)

• Under forced air cooling, the miniature loop heat pipe had the lower junction temperatures at the fan voltage of 5 V with a heat load not exceeding 25 W. However, when the heat load was over 25 W, the miniature loop heat pipe showed a higher thermal performance at a fan voltage of 2 V. A minimum total thermal resistance of 2.17 °C/W was achieved at 30 W for $\phi =-90Â°$ at a fan voltage of 2 V.

• (3)

• In a temperature humidity chamber at 35 °C, the miniature loop heat pipe could dissipate 25 W with the junction temperature of 84.7 °C in the horizontal orientation at 5 V, which is within the maximum permissible junction temperature for the microprocessors; meanwhile, the junction temperature was 92.5 °C at 2 V for the miniature loop heat pipe.

• (4)

• Due to its ultrathin thickness and high heat transfer performance, the proposed miniature loop heat pipe cooling module is an energy-efficient solution for high-end ultra-slim laptop computers. By using the proposed miniature loop heat pipe module, the energy consumption could be reduced by 80% or so, with a total energy savings of more than 600 million kW·h per year globally.

• (5)

• With the aid of the proposed miniature loop heat pipe cooling module, the reliability, stability and energy efficiency would be improved substantially owing to the lower CPU temperature.

In general, considering its extremely low power consumption, very low noise level and high long term stability, the proposed miniature loop heat pipe module is an ideal solution for the future high-end ultra-slim laptop computers.

## Conflict of interest

All the works were conducted in Li’s lab. The views, opinions, and/or findings contained in this article/presentation are those of the authors only.

## Acknowledgements

This work is supported by National Natural Science Foundation of China (Project No. 51476161).

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