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Effect of phase change materials on heat dissipation of a multiple heat source system

  • Kai Yu , Yao Wang , Yanxin Li , Jakov Baleta , Jin Wang EMAIL logo and Bengt Sundén
Published/Copyright: December 31, 2019

Abstract

This paper experimentally investigates heat dissipation of a heat pipe with phase change materials (PCMs) cooling in a multiple heat source system. Two heat sources are fixed at one end of the heat pipe. Considering that a heat sink cannot dissipate all the heat generated by two heat sources, various PCMs are used due to a large latent heat. Different materials in a container are wrapped outside of the middle heat pipe to take away the heat from the evaporation section. The experimental tests obtain temperature data of heat source, evaporation section, and energy storage characteristics of PCMs are also determined under constant and dynamic values of the heat source powers. It is found that under this multiple heat source system structure, the phase change material RT35 maintains temperature variations of the evaporation section at a lower temperature and shortens the required time to reach the equilibrium temperature under a heating power of 20 W.

1 Introduction

Low heat dissipation efficiency and long reaction time can be easily found in the conventional cooling method for a multiple heat source system. Considerable amounts of heat and many fluctuations are generated in multiple heat source systems, such as multi-core CPUs and highly integrated electronic equipment. Generally, an increase of dissipate heat under a transient high-power operation of a heat source is fulfilled by increasing the power of the cooling fan. Most heat is dissipated by using forced air convection with and without a heat pipe in a periodic or a transient manner. As a latent heat storage material, PCMs (phase change materials) have been widely used in many fields, such as solar thermal energy storage, solar water heating systems, photovoltaic panels, battery thermal management, and electronic devices [1]. An increase in power consumption of electronic devices will result in a temperature rise above a critical value. The latent heat of PCMs can effectively store the instantaneous heat and periodic heat generated by electronic devices, which can prevent the electronic devices from accumulating a large amount of heat in a short time [2]. Al-Jethelah et al. [3] numerically studied melting process of PCMs in a latent heat storage system. Nusselt number and melt fraction of PCMs were analyzed to obtain effects of ambient temperature on convective heat transfer coefficient and melting rate. Ebadi et al. [4] analyzed performance of the RT35 in a vertical cylindrical thermal energy storage system experimentally and numerically. The results showed that as the melting process progressed, the dominant heat transfer method of RT-35 changed from heat conduction to convective heat transfer. Zhao and Tan [5] presented an evaluation of a prototype thermoelectric system integrated with PCMs for space cooling. Emamet al. [6] investigated the passive thermal management of electronic devices and concentrator photovoltaic (CPV) systems with using phase change material, and they found that formation of air cavities inside solid PCMs showed little impact on their cooling performance. Kalbasi et al. [7] presented a correlation to estimate the optimum number of fins and optimum volume fraction of PCMs in a heat sink. Mashaei et al. [8] pointed out that the heat dissipation in systems with multiple heat sources is not different from that for a single heat source.

Heat pipes integrated with heat sinks have been extensively investigated by using various PCMs [9]. The PCMs show an important role in absorbing dissipated heat of thermal management systems. In 2003, Tan and Tso [10] conducted an experimental study to cool a mobile electronic device using a thermal energy storage unit filled with phase change materials. They found that the temperature distribution was significantly affected by the orientation of the heat storage unit. Wang and Yang [11] numerically investigated variations of operation temperature and melting time by using a PCM based multi-fin heat sink. Results showed that prediction accuracy of transient surface temperature was within 10.2%. In addition, researchers have tried a variety of ways to improve thermal conductivity of PCMs. Wang et al. [12] embedded phase change material paraffin into copper foam metal, and results showed that 40% reduction of heat storage time of paraffin wax was obtained by using copper foam. Ebrahimi et al. [13] investigated phase change materials in a shell-tube heat exchanger enhanced with heat pipe, and they found that the melting time decreased by 91% compared with no heat pipe case. Abujas et al. [14] numerically studied effects of finned pipes and conductive foams on the charge time and the energy distribution. It was found that aluminum fins had a significant reduction on the charge time of the system. In addition, researchers used nanoparticles to increase heat transfer properties of solid and liquid materials. Wang et al. [15] experimentally analyzed an effect of different magnetic fields on heat transfer performance of the ferrofluid. It was found that the configuration of adjacent magnetic cannulas could provide a continuous enhancement of convective heat transfer. Chen et al. [16] investigated the effect of Fe3O4-EGW (a mixture of ethylene glycol and DI-water) nanofluids on heat transfer characteristics in an electric heater. The results show that when 0.5%Fe3O4-EGW nanofluid was used, the equilibrium temperature of the middle fin of the electric heater obtained 14.68% enhancement by adding an external magnetic field of 100 mT.

However, most researchers focused on thermal performances of heat sinks and heat pipes under multiple heat sources. Han et al. [17] studied a novel flat heat pipe with multiple heat sources, and results showed that both thermal resistance and the maximum heat transport capacity increased with the increase of the number of heat sources. Zhang et al. [18] proposed a novel ultra-thin aluminum flat heat pipe to improve thermal performance of two phase device. Results showed that the wicked heat pipes provided an enhancement of thermal performance under inclination angles of 30 and 60. Chougule and Sahu [19] reported thermal performance of a nanofluid inside a heat pipe with PCMs for electronic cooling. They found that the heat pipe with paraffin reduced the fan power consumption up to 66%, compared with a heat pipe with water as energy storage material. Shabgard and Faghri [20] presented a model of cylindrical heat pipes with multiple heat sources. They focused on the analysis of the constant heat flow and convection cooling during the condensation process, and results from a developed simple method showed good agreement with the full simulation results. Tang et al. [21] proposed a cooling method for a multiple heat source heat pipe. Compared with other cooling methods, this multiple heat source and double-end cooling (MSDC) improved the thermal performance of heat pipes.

Based on tests of the charge, discharge and simultaneous charge/discharge performances, Weng et al. [22] investigated the thermal performance of a heat pipe with phase change materials. They found that a cooling module with tricosane as PCM saved 46% fan power consumption, compared with the traditional heat pipe. Zhuang et al. [23] proposed a novel heat pipe wrapped with PCMs, and they found that the novel composite heat pipe (CHP) filled with 75% PCMs showed a stable temperature reduction of 9.31%, compared to that without PCMs. Behi et al. [24] both experimentally and numerically investigated heat dissipation and cooling process of a horizontal PCM-assisted heat pipe. They found that the PCM-assisted heat pipe provided up to 86.7% cooling load under a power range of 50–80 W.

This paper aims to investigate heat dissipation performance of a multiple heat source system under constant and dynamic powers of the heat sources. Various PCMs are used to remove thermal energy from a heat pipe. Thermal performance of the heat pipe with PCMs (deionized water, paraffins RT30, RT35 and RT45) during the charge and discharge processes are tested under different powers of the heat sources. Temperature values on the evaporation section of the heat pipe are discussed to find the optimum PCM for the system heat dissipation.

2 Experimental investigations

2.1 Experimental setup and details

This experimental research aims to investigate cooling performance of PCMs outside a heat pipe with multiple heat sources. Thermocouples are used to measure temperature variations of the heat sources, heat pipe and PCMs. The experimental system consists of a flat heat pipe, two resistors, a container, a fan, heat sinks, two DC power supplies, a computer, and a data acquisition system (Agilent Co.) as shown in Figure 1. The experimental section includes three parts, i.e., a heating part (100 mm), an energy storage part (100 mm) and a condensing part (100 mm). All the three parts are installed on a flat heat pipe. The flat heat pipe is a copper-water capillary wick structure with a length of 310 mm and a width of 11 mm. As shown in Figure 2, several PCMs and DI-water are used as materials for thermal energy storage during the tests. The paraffin was purchased from Nanyang Hannuo Petrochemical Co. Ltd. China. The thermophysical properties of PCMs and DI-water are shown in Table 1.

Figure 1 Schematic and photos of experimental setup (unit: mm)
Figure 1

Schematic and photos of experimental setup (unit: mm)

Figure 2 Experimental material samples
Figure 2

Experimental material samples

Table 1

Thermophysical properties of PCMs

Parameters Melting point (C) Specific heat Latent heat (kJ kg−1) Thermal conductivity
(kJ kg−1∘C−1) (W m−1 K−1)
DI-water 0 4.2 - 0.6
RT30 30±2.5 2.0 163 0.2
RT35 35±2.5 2.0 172 0.2
RT45 45±2.5 1.8 165 0.2

A heating system with multiple heat sources is installed on the evaporator section of the heat pipe. The heating system consists of two heating modules which generate various heat fluxes by resistors with a direct current. As shown in Figure 1, each heating module has a length of 50 mm and a width of 14 mm. Each heating module contains two heating-resistor blocks connected to two DC power supplies. The input power of the heating system is controlled by adjusting the voltage of the DC power supplies. In order to simulate the real system, the testing section is heated continually until the temperature of the heat source reaches the equilibrium state. To judge the equilibrium state, a criteria is given as: when temperature values of heat sources change less than 1C within 1 min, it is regarded as equilibrium state.

The container for the energy storage is a tank full of the PCMs. This container with dimensions of 106 mm ×31 mm×23 mm was made from polylactide acid by a 3D printer, and it was covered by insulation materials to reduce the heat dissipation. The gap between the heat pipe and the PCM container is filled with thermal silica gel to avoid the leakage of the PCMs. The condensation section consists a fan and a heat sink attached to the other end of the heat pipe. The heat sink made of aluminum has a total cooling area of 0.128 m2.

Temperature distributions along the heat pipe and on each part of testing sections are measured by T-type thermocouples. Locations of the thermocouples are shown in Figure 1. In order to heat from the same initial condition, the ambient temperature is measured during each test. In order to record temperature values at different testing positions of the heat pipe and PCMs, thermocouples are arranged in the evaporative section, the adiabatic section and the condensing section of the heat pipe. Another five thermocouples are located along the heat pipe.

2.2 Uncertainty analysis

The uncertainties of the experimental results are estimated based on an error analysis of the present measurements. T-type thermocouples are calibrated with an accuracy of ±0.2C, while the data acquisition unit has an accuracy of 0.05C. Moreover, the input power is supplied by a DC power supply with 0.1% voltage accuracy and 0.5% current accuracy.

3 Results and discussion

In order to investigate the effect of the PCMs on the heat dissipation performance, constant systems with multiple heat sources are used by a variety of power combinations.

3.1 Constant multiple heat sources

In this part, four conditions with constant heat sources are analyzed by using different PCMs. The heat sources 1 and 2 are set to powers of 5 W and 10W, respectively. Investigations of temperature values on heat sources, evaporation section, adiabatic section, and energy storage part are conducted under both charge and discharge processes of the different heat sources.

Figure 3 shows transient temperature responses during different heat inputs for various PCMs. It is found from Figure 3(a), that temperature value of heat source 1 reaches to 96.9C for the material RT35 under a heat source of 10 W-10 W. Compared to the case without PCMs (W/O PCM), the temperature of the heat source 1 is reduced by 34.4% (50.9C) from 147.8C. Compared with other PCMs, the RT30 also shows a slight advantage for heat dissipation. Moreover, the temperature value of the heat source 1 for the RT30 is 112.6C, which is 23.8% (35.2C) lower than that for no PCM material. Although the RT45 can reduce the temperature by 11.4C compared with no PCMs, the RT45 shows a worse heat dissipation compared to the DI-water.As shown in Figures 3(b)-3(d), the maximum temperature differences between the cases with and without PCM are 4.1C, 3.5C and 2.3C for heating powers of 10 W-5 W, 5 W-10 W, and 5 W-5 W, respectively.

Figure 3 Temperature variations of heat source 1 under different heating conditions (Heat source 1 power–heat source 2 power)
Figure 3

Temperature variations of heat source 1 under different heating conditions (Heat source 1 power–heat source 2 power)

In addition, the equilibrium temperature of the heat source is quickly reached by using the RT35, and the heating stabilization time is 1310 s, as shown in Table 2. The heating stabilization times required for no material, DI-water, RT30 and RT45 are 1570 s, 2040 s, 1640 s and 1790 s, respectively. When the power of the heat source 2 decreases as shown in Figure 3(b), the temperature values for the RT30, RT35 and RT45 show a similar increasing trend. Compared with the data for the cases with no PCMs, DI-water, RT30, RT35 and RT45 in Figure 3(a), the maximum temperature values of the heat source 1 decrease by 71.8C, 50.6C, 40.4C, 24.3C and 62.1C, respectively. It is concluded that when the power is relatively high (10 W-10 W), the RT35 shows a better cooling performance due to a high energy storage in the PCM box. However, the results indicate that due to its sensible heat absorption, the DI-water under a low heating power provides a lower heating equilibrium temperature than the PCMs.

Table 2

The heating time and cooling time under different heating conditions

Materials 10 W-10 W 10 W-5 W 5 W-10 W 5 W-5 W

Heating Cooling Heating Cooling Heating Cooling Heating Cooling
time (s) time (s) time (s) time (s) time (s) time (s) time (s) time (s)
W/O PCM 1570 1140 770 920 800 1100 680 1020
DI-water 2040 2330 940 2080 950 2280 800 2040
RT30 1640 3940 690 1970 590 1780 610 1540
RT35 1310 4080 780 2070 720 1850 620 1800
RT45 1790 2540 720 1780 680 1290 630 1520

Figure 4 presents transient temperature variations of the evaporation section under different heating conditions. Compared with no PCMs, DI-water, RT30 and RT45 as shown in Figure 4(a), the maximum temperature values of the evaporation section for the RT35 are reduced by 39.4%, 17.3%, 8.1% and 29.7%, respectively. Based on a comparison of the results in Figure 4(a) - 4(d), it is found that the RT35 has a higher capacity of energy storage under a high heating power compared with the other materials. When the heat source power changes from 5 W-5Wto 10W-10W, the temperature of the evaporation section for the RT35 increases by 47.6% (from 38.9C to 57.4C). For the DI-water and the RT30, the temperature of the evaporation section increases by 81.5% and 61.9%, respectively. However, three PCMs (RT30, RT35, and RT45) under a low heating power show worse cooling performance than the DI-water. It is also concluded that PCMs can provide good cooling protection in a multiple heat source system, which avoids damage of the equipment caused by transient high power operation in a short time.

Figure 4 Temperature variations of the evaporation section under different heating conditions (Heat source 1 power–heat source 2 power)
Figure 4

Temperature variations of the evaporation section under different heating conditions (Heat source 1 power–heat source 2 power)

In charge and discharge processes of heat sources, the temperature variations of materials in the energy storage tank are illustrated by changing the heating conditions as shown in Figure 5. In Figure 5(a), the maximum temperature of the DI-water in the storage tank reaches 44.9C, and the corresponding equilibrium time is up to 2050 s. When the heat source temperature reaches equilibrium, the temperature values for the RT30 and RT35 are 37.8C and 35.0C, respectively. As shown in Figure 5(b), the temperature of the DI-water rises to 37.9C after 960 s when the heat source temperature reaches equilibrium, whereas the temperature values of the RT30 and RT35 increase to 29.6C and 32.8C, respectively. For the heat source in Figure 5(c), the RT30 and RT35 have equilibrium temperature values of 29.1C and 32.5C, respectively.

Figure 5 Temperature variations of materials in an energy storage tank under different heating conditions (heat source 1 power–heat source 2 power)
Figure 5

Temperature variations of materials in an energy storage tank under different heating conditions (heat source 1 power–heat source 2 power)

As can be seen from Figure 5(b) and 5(c), the temperatures of the DI-water, RT30 and RT35 in the container are close for the same conditions of the total heat source. With increasing the power as shown in Figures 5(a)-5(b), the temperature values of the DI-water, the RT30 and the RT35 increase by 7.0C, 5.4C and 5.0C, respectively. Decreasing the heating power as shown in Figure 5(d), the equilibrium temperature of the heat source attains lower values (33.5C, 28.2C, and 30.2C for DI-water, RT30, and RT35, respectively).

It can be seen from Figure 5(a) that the PCMs in the storage tank are in equilibrium for the DI-water. However, the heating temperature for the DI-water is relatively high, and the heat from the source 1 cannot be effectively dissipated. Although temperature curves for the three PCMs (RT30, RT35, and RT45) have upward trends (that means the PCMs have not reached the equilibrium temperature), the rising temperature values are lower than for the DI-water and no material. This result indicates that PCMs plays an important role in heat dissipation and absorption of heat generation from a multiple heat source system with a high power.

3.2 Dynamic multiple heat sources

In order to analyze heat dissipation performance of various PCMs, Figure 6 shows the transient temperature response of the heat source 1 to dynamic systems with multiple heat sources. One of the two heat sources is kept a fixed power value (5Wor 10W), and the other heat source varies in dynamic power values (5-10-15-10-15-10-15-10-5 W or 5-10-5-10-5-10-5 W). For dynamic characteristics of the heat pipe with various PCMs, dynamic power changes with an interval of 5 min are considered, as shown in Table 3. It is observed that before a heating time of 750 s, a lower temperature of the heat source 1 is obtained by using the DI-water compared with the PCMs. After a heating time of 1000 s, the material RT35 shows a significant cooling performance on the heat source 1 as shown in Figure 6(a). Compared with the condition without PCM material during periodic heating, the maximum temperature for the RT35 in the three heating processes is reduced by 12.9%, 18.9% and 19.5%, respectively. For periodic heating with low powers as shown in Figure 6(b), the RT35 shows a larger enhancement of the heat dissipation for the heat source 1 than the other PCMs. Compared with no PCMs, the maximum temperature values in the three heating processes are reduced by 11.6%, 11.6% and 11.0%, respectively.

Figure 6 Temperature variations of heat source 1 under dynamic heating powers (heat source 1 power–heat source 2 power)
Figure 6

Temperature variations of heat source 1 under dynamic heating powers (heat source 1 power–heat source 2 power)

Table 3

The periodical heating processes for dynamic multiple heat sources

Time (min) Heating condition 1 Heating condition 2 Heating condition 3 Heating condition 4

Heat Heat Heat Heat Heat Heat Heat Heat
source 1 source 2 source 1 source 2 source 1 source 2 source 1 source 2
(W) (W) (W) (W) (W) (W) (W) (W)
0-5 5 5 5 5 5 10 10 5
5-10 10 5 5 10 10 10 10 10
10-15 15 5 5 15 5 10 10 5
15-20 10 5 5 10 10 10 10 10
20-25 15 5 5 15 5 10 10 5
25-30 10 5 5 10 10 10 10 10
30-35 15 5 5 15 5 10 10 5
35-40 10 5 5 10 - - - -
40-45 5 5 5 5 - - - -

During the three heating processes, the maximum temperature of the heat source 1 for the DI-water gradually increased from 118.3C (in the first heating) to 133.2C (in the third heating). For the RT30, the maximum temperature increases from 124.9C (in the first heating) to 129.7C (in the third heating). For the RT35 condition, the maximum temperature of the heat source 1 increases from 116.7C (in the first heating) to 123.5C (in the third heating). It is also concluded that the RT35 has more energy storage after a periodic heating, which results in good cooling performance from the RT35 for a dynamic heating power. Compared with the DI-water in the three heating processes, the maximum temperature of heat source 1 for RT35 is reduced by 1.1%, 9.5%, and 13.4%, respectively.

Figure 7 illustrates temperature variations of the evaporation section with time under different heating conditions. It is found that the temperature trends are consistent in Figure 6-7. Temperature values of the evaporation section for the DI-water are lower than for other PCMs in the range of 0-1000 s, whereas temperature values of the evaporation section for RT35 is lowest after 1200 s. According to these results, this study proves that the RT35 effectively provides a lower temperature rise and also more uniform temperature evolutions when a dynamic heating power is given to the evaporation section of the heat pipe. After two periodic heating processes, the temperature of the evaporation section for the RT35 maintains a relatively low value.

Figure 7 Temperature variations of the evaporation section under different heating powers (heat source 1 power–heat source 2 power)
Figure 7

Temperature variations of the evaporation section under different heating powers (heat source 1 power–heat source 2 power)

Temperature variations of materials in the energy storage tank are analyzed under different heating conditions as shown in Figure 8. It is observed that the maximum temperature values of RT30 and RT35 are steadily rising until they approach the phase transition values of the PCMs. This is because the PCMs can absorb most of the heat flux continuously before the phase transition point due to its sensible heat, and then the latent heat of PCMs works when the temperature reaches the phase transition point. However, the DI-water absorbs all the heat flux by sensible heat because of no phase transition (above 0C).

Figure 8 Temperature variations of materials in an energy storage tank under different heating conditions (heat source 1 power–heat source 2 power)
Figure 8

Temperature variations of materials in an energy storage tank under different heating conditions (heat source 1 power–heat source 2 power)

4 Conclusions

In this paper, effects of PCMs on transient temperature of heat source, evaporation section, and energy storage characteristics of PCMs were investigated by using a multiple heat source system. Both constant and dynamic systems with two heat sources are studied under various heat source powers. Experimental tests and analysis of results are conducted by changing energy storage materials in a tank, including DI-water, RT30, RT35 and RT45.

Compared with no PCMs, DI-water, RT30 and RT45 for the constant power of heat sources, the maximum temperature values of the evaporation section for the RT35 show reductions of 39.4%, 17.3%, 8.1% and 29.7%, respectively. Based on temperature testing on the evaporation section, it is proved that the RT35 can take away more heat from the evaporation section of the heat pipe and shorten the time required for reaching the heating balance.

Compared with no cooling material under a dynamic power of heat sources, the maximum temperature values for the RT35 in the three heating processes decrease by 12.9%, 18.9% and 19.5%, respectively. It is found that the RT35 under a high power of 20 W(10W-10W) can provide a better cooling performance than other PCMs and DI-water, although the DI-water shows a lower heating equilibrium temperature than other PCMs under low heating power (P ≤ 15 W).

Acknowledgement

This work is supported by the National Natural Science Foundation of China [Grant numbers 51576059 and 51806057] and Project of Innovation Ability Training for Postgraduate Students of Education Department of Hebei Province [Grant number CXZ-ZSS2019012].

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Received: 2019-09-27
Accepted: 2019-10-24
Published Online: 2019-12-31

© 2019 Kai Y. et al., published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.

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  29. Time fractional modified KdV-type equations: Lie symmetries, exact solutions and conservation laws
  30. Exact solutions of equal-width equation and its conservation laws
  31. MHD and Slip Effect on Two-immiscible Third Grade Fluid on Thin Film Flow over a Vertical Moving Belt
  32. Vibration Analysis of a Three-Layered FGM Cylindrical Shell Including the Effect Of Ring Support
  33. Hybrid censoring samples in assessment the lifetime performance index of Chen distributed products
  34. Study on the law of coal resistivity variation in the process of gas adsorption/desorption
  35. Mapping of Lineament Structures from Aeromagnetic and Landsat Data Over Ankpa Area of Lower Benue Trough, Nigeria
  36. Beta Generalized Exponentiated Frechet Distribution with Applications
  37. INS/gravity gradient aided navigation based on gravitation field particle filter
  38. Electrodynamics in Euclidean Space Time Geometries
  39. Dynamics and Wear Analysis of Hydraulic Turbines in Solid-liquid Two-phase Flow
  40. On Numerical Solution Of The Time Fractional Advection-Diffusion Equation Involving Atangana-Baleanu-Caputo Derivative
  41. New Complex Solutions to the Nonlinear Electrical Transmission Line Model
  42. The effects of quantum spectrum of 4 + n-dimensional water around a DNA on pure water in four dimensional universe
  43. Quantum Phase Estimation Algorithm for Finding Polynomial Roots
  44. Vibration Equation of Fractional Order Describing Viscoelasticity and Viscous Inertia
  45. The Errors Recognition and Compensation for the Numerical Control Machine Tools Based on Laser Testing Technology
  46. Evaluation and Decision Making of Organization Quality Specific Immunity Based on MGDM-IPLAO Method
  47. Key Frame Extraction of Multi-Resolution Remote Sensing Images Under Quality Constraint
  48. Influences of Contact Force towards Dressing Contiguous Sense of Linen Clothing
  49. Modeling and optimization of urban rail transit scheduling with adaptive fruit fly optimization algorithm
  50. The pseudo-limit problem existing in electromagnetic radiation transmission and its mathematical physics principle analysis
  51. Chaos synchronization of fractional–order discrete–time systems with different dimensions using two scaling matrices
  52. Stress Characteristics and Overload Failure Analysis of Cemented Sand and Gravel Dam in Naheng Reservoir
  53. A Big Data Analysis Method Based on Modified Collaborative Filtering Recommendation Algorithms
  54. Semi-supervised Classification Based Mixed Sampling for Imbalanced Data
  55. The Influence of Trading Volume, Market Trend, and Monetary Policy on Characteristics of the Chinese Stock Exchange: An Econophysics Perspective
  56. Estimation of sand water content using GPR combined time-frequency analysis in the Ordos Basin, China
  57. Special Issue Applications of Nonlinear Dynamics
  58. Discrete approximate iterative method for fuzzy investment portfolio based on transaction cost threshold constraint
  59. Multi-objective performance optimization of ORC cycle based on improved ant colony algorithm
  60. Information retrieval algorithm of industrial cluster based on vector space
  61. Parametric model updating with frequency and MAC combined objective function of port crane structure based on operational modal analysis
  62. Evacuation simulation of different flow ratios in low-density state
  63. A pointer location algorithm for computer visionbased automatic reading recognition of pointer gauges
  64. A cloud computing separation model based on information flow
  65. Optimizing model and algorithm for railway freight loading problem
  66. Denoising data acquisition algorithm for array pixelated CdZnTe nuclear detector
  67. Radiation effects of nuclear physics rays on hepatoma cells
  68. Special issue: XXVth Symposium on Electromagnetic Phenomena in Nonlinear Circuits (EPNC2018)
  69. A study on numerical integration methods for rendering atmospheric scattering phenomenon
  70. Wave propagation time optimization for geodesic distances calculation using the Heat Method
  71. Analysis of electricity generation efficiency in photovoltaic building systems made of HIT-IBC cells for multi-family residential buildings
  72. A structural quality evaluation model for three-dimensional simulations
  73. WiFi Electromagnetic Field Modelling for Indoor Localization
  74. Modeling Human Pupil Dilation to Decouple the Pupillary Light Reflex
  75. Principal Component Analysis based on data characteristics for dimensionality reduction of ECG recordings in arrhythmia classification
  76. Blinking Extraction in Eye gaze System for Stereoscopy Movies
  77. Optimization of screen-space directional occlusion algorithms
  78. Heuristic based real-time hybrid rendering with the use of rasterization and ray tracing method
  79. Review of muscle modelling methods from the point of view of motion biomechanics with particular emphasis on the shoulder
  80. The use of segmented-shifted grain-oriented sheets in magnetic circuits of small AC motors
  81. High Temperature Permanent Magnet Synchronous Machine Analysis of Thermal Field
  82. Inverse approach for concentrated winding surface permanent magnet synchronous machines noiseless design
  83. An enameled wire with a semi-conductive layer: A solution for a better distibution of the voltage stresses in motor windings
  84. High temperature machines: topologies and preliminary design
  85. Aging monitoring of electrical machines using winding high frequency equivalent circuits
  86. Design of inorganic coils for high temperature electrical machines
  87. A New Concept for Deeper Integration of Converters and Drives in Electrical Machines: Simulation and Experimental Investigations
  88. Special Issue on Energetic Materials and Processes
  89. Investigations into the mechanisms of electrohydrodynamic instability in free surface electrospinning
  90. Effect of Pressure Distribution on the Energy Dissipation of Lap Joints under Equal Pre-tension Force
  91. Research on microstructure and forming mechanism of TiC/1Cr12Ni3Mo2V composite based on laser solid forming
  92. Crystallization of Nano-TiO2 Films based on Glass Fiber Fabric Substrate and Its Impact on Catalytic Performance
  93. Effect of Adding Rare Earth Elements Er and Gd on the Corrosion Residual Strength of Magnesium Alloy
  94. Closed-die Forging Technology and Numerical Simulation of Aluminum Alloy Connecting Rod
  95. Numerical Simulation and Experimental Research on Material Parameters Solution and Shape Control of Sandwich Panels with Aluminum Honeycomb
  96. Research and Analysis of the Effect of Heat Treatment on Damping Properties of Ductile Iron
  97. Effect of austenitising heat treatment on microstructure and properties of a nitrogen bearing martensitic stainless steel
  98. Special Issue on Fundamental Physics of Thermal Transports and Energy Conversions
  99. Numerical simulation of welding distortions in large structures with a simplified engineering approach
  100. Investigation on the effect of electrode tip on formation of metal droplets and temperature profile in a vibrating electrode electroslag remelting process
  101. Effect of North Wall Materials on the Thermal Environment in Chinese Solar Greenhouse (Part A: Experimental Researches)
  102. Three-dimensional optimal design of a cooled turbine considering the coolant-requirement change
  103. Theoretical analysis of particle size re-distribution due to Ostwald ripening in the fuel cell catalyst layer
  104. Effect of phase change materials on heat dissipation of a multiple heat source system
  105. Wetting properties and performance of modified composite collectors in a membrane-based wet electrostatic precipitator
  106. Implementation of the Semi Empirical Kinetic Soot Model Within Chemistry Tabulation Framework for Efficient Emissions Predictions in Diesel Engines
  107. Comparison and analyses of two thermal performance evaluation models for a public building
  108. A Novel Evaluation Method For Particle Deposition Measurement
  109. Effect of the two-phase hybrid mode of effervescent atomizer on the atomization characteristics
  110. Erratum
  111. Integrability analysis of the partial differential equation describing the classical bond-pricing model of mathematical finance
  112. Erratum to: Energy converting layers for thin-film flexible photovoltaic structures
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