# Entropy Generation Methodology for Defect Analysis of Electronic and Mechanical Components—A Review

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## Abstract

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## 1. Introduction

## 2. Entropy Methodologies for Damage Characterization of Electronic Components

#### 2.1. Entropy Methodologies for Electronic Devices

#### 2.2. Entropy Methodologies for Microstructures

#### 2.3. Entropy Methodologies for Composite Boards

#### 2.4. Entropy Methodologies for Electronic Systems

_{sa}is the sink-to-ambient resistance, T

_{a}is the ambient temperature, P is the pressure. Herein, the intermediate derivation process based on entropy generation analysis is expressed as

## 3. Entropy Methodologies for Defect Diagnosis of Mechanical Components

#### 3.1. Research Progress on Defect Diagnosis

#### 3.2. Methodologies for Defect Diagnosis

_{N}) has been provided as [70]

## 4. Conclusions

- (1)
- The reliability prediction and defect diagnosis for electronic systems are focused on the influence of temperature gradient. In addition, the investigation on the relationship between power and entropy generation and the assessment of electronic system reliability is still in its early stages.
- (2)
- The prediction of fatigue in mechanical components focuses on the influence of structural deformation by ignoring the influence of temperature gradient. Mechanical materials are mostly metal materials with good thermal conductivity during the entire fatigue failure; thus, their temperature change is minimal. Further investigations into the defect characteristics of mechanical components with internal and/or surface entropy losses should be carried out in the future.
- (3)
- Unlike that of electronic and mechanical materials, the entropy generation of heat transfer systems focuses on temperature gradients and many fluid parameters, such as friction coefficient, Nusselt number, and Boit number. Moreover, the cooling system parameters and structural parameters of a heat exchange system are optimized on the basis of the second law of thermodynamics to improve system reliability.
- (4)
- Care should be taken on the boundary conditions; radiative heat transfer is neglected in the vast majority of studies on entropy generation. This oversight is an important drawback because radiation dramatically affects most high power devices and plays an important role in high-density circuit design. Thus, the consideration of thermodynamic irreversibility due to radiative phenomena is necessary for future works, especially those on high density electronic and mechanical components.
- (5)
- Further irreversible aging monitoring of electronic devices is expected to become a growing trend in the future for entropy generation methodologies. Power devices, sensors, and third-generation semiconductors should be considered in irreversible burn-in evaluation to improve their reliability.
- (6)
- The research on the fatigue testing of metal materials should be expanded to ensure variety. Metal materials, such as stainless steel and Al, have been studied in a number of investigations, but few studies have focused on the fatigue analysis of other types of metal materials (e.g., Cu) based on entropy generation. In addition, the research on fatigue testing should progress to nonmetal materials with the second law of thermodynamics. Nonmetal materials for epoxy, such as Si, are widely used in electronic components, but related irreversible thermodynamic research theories and applications are limited.

## Author Contributions

## Funding

## Conflicts of Interest

## Nomenclature

$S$ | Entropy generation, J kg^{−1} K^{−1} |

$Q$ | Heat, J |

$T$ | Temperature, K |

${E}_{\mathrm{in}}$ | Input energy, J |

$\dot{w}$ | Heat dissipated at a certain temperature, J/s |

$W$ | Light output energy, J |

${E}_{irr}$ | Irreversible energy, J |

$P$ | Power |

$t$ | Time, s |

$U$ | Voltage drop, V |

$I$ | Electric current, A |

$\lambda $ | Wavelength, nm |

$R$ | Resistance |

${S}_{e}$ | External entropy generation |

${S}_{i}$ | Internal entropy generation |

${Q}_{e}$ | Heat dissipated into the environment, J |

${K}_{\mathrm{lim}}$ | Limit constant |

${C}_{p}$ | Capacitance of pyroelectric material |

$\eta $ | Absorption coefficient of radiation |

$A$ | Electrode area, m^{2} |

${T}_{f}$ | Final temperature, K |

${T}_{i}$ | Initial temperatures, K |

$\psi $ | Exergy |

$G$ | Specific enthalpy, J/kg |

$R$ | Thermal resistance |

$\mathrm{a}$ | Ambient |

$\mathrm{c}$ | Case |

$\mathrm{CS}$ | Case-to-sink |

$\mathrm{FoM}$ | Related to the figure of merit |

$in$ | Input |

$j$ | Junction |

${\eta}_{\coprod}$ | Second law coefficient |

${Z}_{power}$ | Uniformity coefficient |

$T\left(\mathrm{X}\right)$ | Temperature-dependent distance, K |

${N}_{f}$ | Total number of cycles to failure |

$F$ | Driving force, N |

P | Pressure |

$T\left(t\right)$ | Temperature-dependent time, K |

${J}_{p}$ | Heat flux through the boundary |

$W\left(t\right)$ | Work by deformation |

$V$ | Solder volume |

$kT$ | Thermal energy |

$D$ | Diffusivity |

$N$ | Avogadro’s number |

$M$ | Mass rate |

$\overrightarrow{q}$ | Heat flux |

$gradT$ | Temperature gradient |

${t}_{f}$ | Failure time |

$C$ | Heat capacity |

$h$ | Convective heat transfer coefficient |

${D}_{N}$ | Damage parameter |

${Q}_{cyc}$ | Unit cycle energy, J |

$k$ | Wear coefficient |

${H}_{ar}$ | Hardness pressure |

$L$ | Normal load |

$B$ | (dw/ds) for a particular process |

jc | Junction-to-case |

ja | Junction-to-ambient |

$p$ | Related to processor |

$out$ | Outlet |

$S$ | Sink |

$sa$ | Sink-to-ambient |

## References

- Zhang, Y. Principle of maximum entropy for reliability analysis in the design of machine components. Front. Mech. Eng.
**2019**, 14, 21–32. [Google Scholar] [CrossRef] - Lai, W.; Liu, X.; Chen, W.; Lei, X.; Cao, X. Thermal Characteristics Analysis of Die Attach Layer Based on Time-Constant Spectrum for High-Power LED. IEEE Trans. Electron Devices
**2015**, 62, 3715–3721. [Google Scholar] [CrossRef] - Hamidnia, M.; Luo, Y.; Wang, X.D. Application of micro/nano technology for thermal management of high power LED packaging—A review. Appl. Therm. Eng.
**2018**, 145, 637–651. [Google Scholar] [CrossRef] - Qian, C.; Gheitaghy, A.M.; Fan, J.; Tang, H.; Sun, B.; Ye, H.; Zhang, G. Thermal Management on IGBT Power Electronic Devices and Modules. IEEE Access
**2018**, 6, 12868–12884. [Google Scholar] [CrossRef] - Bai, Y.; Gu, L.; Qi, X. Comparative Study of Energy Performance between Chip and Inlet Temperature-Aware Workload Allocation in Air-Cooled Data Center. Energies
**2018**, 11, 669. [Google Scholar] - Zheng, B.; Lin, J.; Chen, W. Simulation of heat conduction problems in layered materials using the meshless singular boundary method. Eng. Anal. Bound. Elem.
**2019**, 100, 88–94. [Google Scholar] [CrossRef] - Gidwani, A.; James, S.; Jagtap, S.; Karthikeyan, R.; Vincent, S. Effect of Entropy Generation on Wear Mechanics and System Reliability. IOP Conf. Ser. Mater. Sci. Eng.
**2018**, 346, 12076. [Google Scholar] [CrossRef] - Shih, C.J.; Liu, G.C. Optimal Design Methodology of Plate-Fin Heat Sinks for Electronic Cooling Using Entropy Generation Strategy. IEEE Trans. Compon. Packag. Technol.
**2004**, 27, 551–559. [Google Scholar] [CrossRef] - Lai, Y.; Gusak, A.; Tu, K.; Ouyang, F. Effect of entropy production on microstructure change in eutectic SnPb flip chip solder joints by thermomigration. Appl. Phys. Lett.
**2006**, 89, 221906. [Google Scholar] [CrossRef] - Cui, P.; Cai, M.; Yang, D. Effect of defected behavior on interfacial heat transferring performance for HP-LED packaging based on entropy generation analysis. In Proceedings of the 19th International Conference on Electronic Packaging Technology (ICEPT), Shanghai, China, 8–11 August 2018. [Google Scholar]
- Cuadras, A.; Crisóstomo, J.; Ovejas, V.J.; Quilez, M. Irreversible entropy model for damage diagnosis in resistors. J. Appl. Phys.
**2015**, 118, 165103. [Google Scholar] [CrossRef] [Green Version] - Cuadras, A.; Romero, R.; Ovejas, V.J. Entropy characterisation of overstressed capacitors for lifetime prediction. J. Power Sources
**2016**, 336, 272–278. [Google Scholar] [CrossRef] [Green Version] - Cuadras, A.; Yao, J.; Quilez, M. Determination of LEDs degradation with entropy generation rate. J. Appl. Phys.
**2017**, 122, 145702. [Google Scholar] [CrossRef] - Wang, T.; Samal, S.K.; Lim, S.K.; Shi, Y. Entropy Production-Based Full-Chip Fatigue Analysis: From Theory to Mobile Applications. IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst.
**2019**, 38, 84–95. [Google Scholar] [CrossRef] - Wang, T.; Samal, S.K.; Lim, S.K.; Shi, Y. A Novel Entropy Production Based Full-Chip TSV Fatigue Analysis. In Proceedings of the 2015 IEEE/ACM International Conference on Computer-Aided Design (ICCAD), Austin, TX, USA, 2–6 November 2015; Volume 2015, pp. 744–751. [Google Scholar]
- Naderi, M.; Amiri, M.; Khonsari, M.M. On the thermodynamic entropy of fatigue fracture. Proc. R. Soc. A
**2010**, 466, 423–438. [Google Scholar] [CrossRef] [Green Version] - Naderi, M.; Khonsari, M.M. An experimental approach to low-cycle fatigue damage based on thermodynamic entropy. Int. J. Solids Struct.
**2010**, 47, 875–880. [Google Scholar] [CrossRef] [Green Version] - Amiri, M.; Naderi, M.; Khonsari, M.M. An Experimental Approach to Evaluate the Critical Damage. Int. J. Damage Mech.
**2011**, 20, 89–112. [Google Scholar] [CrossRef] - Ontiveros, V.; Amiri, M.; Kahirdeh, A.; Modarres, M. Thermodynamic entropy generation in the course of the fatigue crack initiation. Fatigue Fract. Eng. Mater. Struct.
**2017**, 40, 423–434. [Google Scholar] [CrossRef] - Oztop, H.F.; Al-Salem, K. A review on entropy generation in natural and mixed convection heat transfer for energy systems. Renew. Sustain. Energy Rev.
**2012**, 16, 911–920. [Google Scholar] [CrossRef] - Aziz, A.; Makinde, O.D. Heat transfer and entropy generation in a two-dimensional orthotropic convection pin fin. Int. J. Exergy
**2010**, 7, 579. [Google Scholar] [CrossRef] - Yang, W.; Furukawa, T.; Torii, S. Optimal package design of stacks of convection-cooled printed circuit boards using entropy generation minimization method. Int. J. Heat Mass Transf.
**2008**, 51, 4038–4046. [Google Scholar] [CrossRef] - Wang, Z.; Li, Y. A combined method for surface selection and layer pattern optimization of a multistream plate-fin heat exchanger. Appl. Energy
**2016**, 165, 815–827. [Google Scholar] [CrossRef] - Mehrgoo, M.; Amidpour, M. Constructal design and optimization of a dual pressure heat recovery steam generator. Energy
**2017**, 124, 87–99. [Google Scholar] [CrossRef] - Furukawa, T.; Yang, W.J. Reliability of Heat Sink Optimization Using Entropy Generation Minimization. In Proceedings of the 8th AIAA/ASME Joint Thermophysics and Heat Transfer Conference, St. Louis, MO, USA, 24–26 June 2002; Volume 2002. [Google Scholar] [CrossRef] [Green Version]
- Torabi, M.; Zhang, K.; Yang, G.; Wang, J.; Wu, P. Temperature distribution, local and total entropy generation analyses in asymmetric cooling composite geometries with multiple nonlinearities: Effect of imperfect thermal contact. Energy
**2014**, 78, 218–234. [Google Scholar] [CrossRef] - Aziz, A.; Khan, W.A. Entropy generation in an asymmetrically cooled slab with temperature-dependent internal heat generation. Heat Transf. Asian Res.
**2012**, 41, 260–271. [Google Scholar] [CrossRef] - Aziz, A.; Khan, W.A. Classical and minimum entropy generation analyses for steady state conduction with temperature dependent thermal conductivity and asymmetric thermal boundary conditions: Regular and functionally graded materials. Energy
**2011**, 36, 6195–6207. [Google Scholar] [CrossRef] - Shah, A.J.; Carey, V.P.; Bash, C.E.; Patel, C.D. An Exergy-Based Figure-of-Merit for Electronic Packages. J. Electron. Packag.
**2006**, 128, 360–369. [Google Scholar] [CrossRef] - Hsiao, C.; Liang, B. The Generated Entropy Monitored by Pyroelectric Sensors. Sensors
**2018**, 18, 3320. [Google Scholar] [CrossRef] [Green Version] - Borjigin, S.; Ma, T.; Zeng, M.; Wang, Q. A Numerical Study of Small-Scale Longitudinal Heat Conduction in Plate Heat Exchangers. Energies
**2018**, 11, 1727. [Google Scholar] [CrossRef] [Green Version] - De Vita, A.; Maheshwari, A.; Destro, M.; Santarelli, M.; Carello, M. Transient thermal analysis of a lithium-ion battery pack comparing different cooling solutions for automotive applications. Appl. Energy
**2017**, 206, 101–112. [Google Scholar] [CrossRef] - Huggins, R.A. Thermodynamics of materials. Mater. Res. Bull.
**1980**, 15, 8. [Google Scholar] - Zhang, B.; Yang, D. Delamination modeling in LED package by cohesive zone method. In Proceedings of the 14th International Conference on Electronic Packaging Technology, Dalian, China, 11–14 August 2013. [Google Scholar]
- Pascoe, J.A.; Alderliesten, R.C.; Benedictus, R. Methods for the prediction of fatigue delamination growth in composites and adhesive bonds—A critical review. Eng. Fract. Mech.
**2013**, 112–113, 72–96. [Google Scholar] [CrossRef] - Ryan, J.T.; Yu, L.; Han, J.; Kopanski, J.J.; Cheung, K.P.; Zhang, F.; Wang, C.; Campbell, J.P.; Suehle, J.S.; Tilak, V. A new interface defect spectroscopy method. In Proceedings of the 2011 International Reliability Physics Symposium, Monterey, CA, USA , 10–14 April 2011; Volume 2011, p. 5784477. [Google Scholar]
- Suhl, D. Thermally induced IC package cracking. IEEE Trans. Comp. Hybrids Manufact. Technol.
**1990**, 13, 940–945. [Google Scholar] [CrossRef] - Fu, J.; Zhao, L.; Cao, H.; Sun, X.; Sun, B.; Wang, J.; Li, J. Degradation and corresponding failure mechanism for GaN-based LEDs. AIP Adv.
**2016**, 6, 55219. [Google Scholar] [CrossRef] - Hu, J.; Yang, L.; Whan Shin, M. Mechanism and thermal effect of delamination in light-emitting diode packages. Microelectron. J.
**2007**, 38, 157–163. [Google Scholar] [CrossRef] [Green Version] - Wang, C.; Chen, T.; Fu, H.; Chang, T.; Chou, P.; Chu, M. Analysis of thermal characteristics and mechanism of degradation of flip-chip high power LEDs. Microelectron. Reliab.
**2012**, 52, 698–703. [Google Scholar] [CrossRef] - Liu, Y.; Leung, S.Y.Y.; Zhao, J.; Wong, C.K.Y.; Yuan, C.A.; Zhang, G.; Sun, F.; Luo, L. Thermal and mechanical effects of voids within flip chip soldering in LED packages. Microelectron. Reliab.
**2014**, 54, 2028–2033. [Google Scholar] [CrossRef] - Fleischer, A.S.; Chang, L.; Johnson, B.C. The effect of die attach voiding on the thermal resistance of chip level packages. Microelectron. Reliab.
**2006**, 46, 794–804. [Google Scholar] [CrossRef] - Jiang, C.; Fan, J.; Qian, C.; Zhang, H.; Fan, X.; Guo, W.; Zhang, G. Effects of Voids on Mechanical and Thermal Properties of the Die Attach Solder Layer Used in High-Power LED Chip-Scale Packages. IEEE Trans. Compon. Packag. Manufact. Technol.
**2018**, 8, 1254–1262. [Google Scholar] [CrossRef] - Ferreira Costa, L.; Liserre, M. Failure Analysis of the dc-dc Converter: A Comprehensive Survey of Faults and Solutions for Improving Reliability. IEEE Power Electron. Mag.
**2018**, 5, 42–51. [Google Scholar] [CrossRef] - Mo, Y.; Yang, D.; Cai, M.; Liu, D.; Nie, Y. Thermal transfer influence of delamination in the die attach layer of chip-on-board LED package base on entropy generation analysis. In Proceedings of the 2016 17th International Conference on Electronic Packaging Technology (ICEPT), Wuhan, China , 16–19 August 2016; Volume 2016, pp. 646–651. [Google Scholar]
- Živić, M.; Galović, A.; Ferdelji, N. Local entropy generation during steady heat conduction through a plane wall. Tehnički Vjesnik: Znanstveno-Stručni Časopis Tehničkih Fakulteta Sveučilišta u Osijeku
**2010**, 17, 337–341. [Google Scholar] - Bejan, A. Entropy Generation Minimization, Exergy Analysis, and the Constructal Law. Arab. J. Sci. Eng.
**2013**, 38, 329–340. [Google Scholar] [CrossRef] - Torabi, M.; Aziz, A. Entropy generation in a hollow cylinder with temperature dependent thermal conductivity and internal heat generation with convective—Radiative surface cooling. Int. Commun. Heat Mass
**2012**, 39, 1487–1495. [Google Scholar] [CrossRef] - KOLENDA, Z. On the minimum entropy production in steady state heat conduction processes. Energy
**2004**, 29, 2441–2460. [Google Scholar] [CrossRef] - Torabi, M.; Zhang, K.; Karimi, N.; Peterson, G.P. Entropy generation in thermal systems with solid structures—A concise review. Int. J. Heat Mass Transf.
**2016**, 97, 917–931. [Google Scholar] [CrossRef] [Green Version] - Shah, A.; Carey, V.; Bash, C.; Patel, C. Impact of chip power dissipation on thermodynamic performance. IEEE
**2005**, 99–108. [Google Scholar] [CrossRef] - Pavelka, M.; Klika, V.; Vagner, P.; Marsik, F. Generalization of exergy analysis. Appl. Energy
**2015**, 137, 158–172. [Google Scholar] [CrossRef] - Zimparov, V.; Vulchanov, N.L. Performance evaluation criteria for enhanced heat transfer surfaces. Int. J. Heat Mass Transf.
**1994**, 37, 1807–1816. [Google Scholar] [CrossRef] - Tian, X.; Lai, X.; Zhu, P.; Wang, L. Beyond the classical theory of heat conduction: A perspective view of future from entropy. Proc. R. Soc. A Math. Phys. Eng. Sci.
**2016**, 472, 20160362. [Google Scholar] [CrossRef] [PubMed] - Mohammadi, B.; Mahmoudi, A. Developing a new model to predict the fatigue life of cross-ply laminates using coupled CDM-Entropy generation approach. Theoret. Appl. Fract. Mech.
**2018**, 95, 18–27. [Google Scholar] [CrossRef] - Wöhler, A. Wöhler’s experiments on the strength of metals. Engineering
**1867**, 4, 160–161. [Google Scholar] - Jiang, Y.; Chen, M. Researches on the Fatigue Crack Propagation of Pipeline Steel. Energy Procedia
**2012**, 14, 524–528. [Google Scholar] [CrossRef] [Green Version] - Meneghetti, G. Analysis of the fatigue strength of a stainless steel based on the energy dissipation. Int. J. Fatigue
**2007**, 29, 81–94. [Google Scholar] [CrossRef] - Meneghetti, G.; Ricotta, M.; Atzori, B. A synthesis of the push-pull fatigue behaviour of plain and notched stainless steel specimens by using the specific heat loss. Fatigue Fract. Eng. Mater. Struct.
**2013**, 36, 1306–1322. [Google Scholar] [CrossRef] - Italyantsev, Y.F. Thermodynamic state of deformed solids. Report 2. Entropy failure criteria and their application for simple tensile loading problems. Strength Mater.
**1984**, 16, 242–247. [Google Scholar] [CrossRef] - Tchankov, D.S.; Vesselinov, K.V. Fatigue life prediction under random loading using total hysteresis energy. Int. J. Press. Vessels Pip.
**1998**, 75, 955–960. [Google Scholar] [CrossRef] - Eger, T.; Bol, T.; Thévenin, D.; Schroth, R.; Janiga, G. Preliminary Numerical Investigations of Entropy Generation in Electric Machines Based on a Canonical Configuration. Entropy
**2015**, 17, 8187–8206. [Google Scholar] [CrossRef] [Green Version] - Pan, M.; Pan, H.; Xu, X.; Liu, H. Fault diagnosis of automatic mechanism of Gatling gun based on information entropy of second-generation wavelet. In Proceedings of the 14th International Conference on Ubiquitous Robots and Ambient Intelligence (URAI), Jeju, Korea, 28 June–1 July 2017. [Google Scholar]
- Jang, J.Y.; Khonsari, M.M. On the evaluation of fracture fatigue entropy. Theor. Appl. Fract. Mech.
**2018**, 96, 351–361. [Google Scholar] [CrossRef] - Slattery, J.C.; Cizmas, P.G.A. Macro-scale fracture analysis of isothermal composites: Theory and seven applications. Eng. Fract. Mech.
**2016**, 163, 366–380. [Google Scholar] [CrossRef] - Radkowski, S.; Jasiński, M.; Gumiński, R.; Gałęzia, A. Using of Entropy Method in Failure Diagnostics. In Advances in Condition Monitory of Machinery; Springer: Berlin, Germany, 2018. [Google Scholar]
- Yi, C.; Lv, Y.; Ge, M.; Xiao, H.; Yu, X. Tensor Singular Spectrum Decomposition Algorithm Based on Permutation Entropy for Rolling Bearing Fault Diagnosis. Entropy
**2017**, 19, 139. [Google Scholar] [CrossRef] [Green Version] - Liu, L.; Zhi, Z.; Zhang, H.; Guo, Q.; Peng, Y.; Liu, D. Related Entropy Theories Application in Condition Monitoring of Rotating Machineries. Entropy
**2019**, 21, 1061. [Google Scholar] [CrossRef] [Green Version] - Wu, M.; Dai, W.; Lu, Z.; Zhao, Y.; Wang, M. The Method for Risk Evaluation in Assembly Process based on the Discrete-Time SIRS Epidemic Model and Information Entropy. Entropy
**2019**, 21, 1029. [Google Scholar] [CrossRef] [Green Version] - Duyi, Y.; Zhenlin, W. A new approach to low-cycle fatigue damage based on exhaustion of static toughness and dissipation of cyclic plastic strain energy during fatigue. Int. J. Fatigue
**2001**, 23, 679–687. [Google Scholar] [CrossRef]

**Figure 1.**Application of entropy generation in the reliability field. (Capacitor [12], resistor [11], light emitting diode (LED) [13], pyroelectric sensor [30], through silicon via [15], solder ball [9], 304 stainless steel [18], aluminum block [7], sink [25], fin [31], circuit board [22], and heat exchanger).

**Figure 2.**Entropy generation analysis for damage characterization of electronic systems (microscopic defect from [14]).

**Figure 5.**FFE (fracture fatigue entropy) of AISI 1018 carbon steel [64].

Authors | Application Object | Highlights |
---|---|---|

Zimparov et al. [53] | Spiral bellows | - An equation of the performance evaluation criteria was developed to evaluate heat transfer enhancement techniques for entropy analysis. |

Lai et al. [9] | SnPb solder joint | - The influence of entropy generation on the thermal transfer of a solder joint microstructure was presented. |

Yang et al. [22] | Printed circuit board stack package | - The thermal optimization of stacked printed circuit boards was realized. - Entropy production is affected by the flow and temperature fields. |

Zhang et al. [34] Cui et al. [10] | Die attach | - The cohesive zone method can predict interfacial stratification. - Entropy generation increases with increasing crack length. |

Wang et al. [14] | Through-silicon via (TSV) mobile applications | - Fatigue analysis and prediction of TSV without any fitting data were studied. - Entropy generation was applied to the fatigue lifetime of mobile chips and full-chip TSV. |

Shah et al. [51] Shah et al. [29] | Intel chip Electronic package | - Power distribution based on exergy analysis for future processor chips was analyzed. - An uneven coefficient was proposed to evaluate thermal performance. |

Tian et al. [54] | A review of thermodynamic evolution | - The second law of thermodynamics was applied to a 1D structure, and recommendations for future applications were reviewed. |

Aziz et al. [27] | Entropy generation in an asymmetrically cooled slab | - The total entropy generation rate depends on five dimensionless parameters. - Appropriate cooling parameters can result in the minimization of the total entropy. |

Aziz et al. [28] | Classical and minimum entropy generation analyses | - Three different heat transfer coefficients with entropy were analyzed. - Regular and functionally graded materials were considered. |

Torabi et al. [26] | Asymmetric cooling composite geometries | - Temperature distribution and local and total entropy generation were analyzed. - Three composite media, including composite walls, cylinders, and spheres, were studied. |

Torabi et al. [50] | A thermal system with a solid structure | - The main solutions include accurate numerical methods, rough numerical methods, and software simulations. |

Mohammadi et al. [55] | Cross laminate | - Thermodynamic entropy can predict the fatigue life of cross-layered plates. |

Cuadras et al. [11] | Carbon film resistors | - Entropy is a more important indicator than resistance degradation in resistor research. |

Cuadras et al. [12] Hsiao et al. [30] | Capacitor | - Entropy generation was affected by capacitance, geometry, and voltage. - A sensor for detecting entropy generation in a capacitor was presented. |

Cuadras et al. [13] | Light emitting diodes (LEDs) | - The degradation entropy generation rate is independent of light parameters. - A threshold of entropy generation of end-of-life LEDs was proposed. |

Lai et al. [9] | Pb37Sn63 solder joint | - A new damage indicator combines traditional damage parameters with entropy generation. |

Authors | Application Object | Highlights |
---|---|---|

Italyantsev et al. [60] | Mechanical parts | - The reliability of working mechanical parts can be predicted. |

Tchankov et al. [61] | 35 steel | - The fatigue life was predicted by calculating the hysteresis energy. - The method avoids the cyclic counting procedure and is not limited to high or low cycle fatigue. |

Naderi et al. [16] | 6061-T6 aluminum and 304 stainless steel (SS) | - The fatigue life of components was determined. - Irreversible entropy was verified as a degradation attribute. |

Naderi et al. [17] | Al-6061 and SS 304 | - The fatigue damage evolution with cyclic energy dissipation was determined. - The fatigue failure of components under torsion, bending, and tension-compression can be tested. |

Amiri et al. [18] | Aluminum | - Low cycle bending fatigue on irreversible heat dissipation was studied. - Heat transferred from the surface area of the specimen to the surroundings was emphasized. |

Eger et al. [62] | Electric machines | - Complex flow processes were analyzed with entropy in real alternator systems. - Heat exchange processes, including concerning fluid and heat transport, were optimized. |

Ontiveros et al. [19] | Al 6061-T6 and SS 304 L | - The entropy accumulation of failure life is a constant value. |

Slattery et al. [65] | Composite wall | - Evaluation of fresh crack surfaces based on macroscopic entropy was considered. - Macroscopic energy balance and macroscopic entropy inequality were considered. |

Pan et al. [63] | Automatic mechanism of guns | - Entropy value was used as input to realize fault diagnosis. - The fault recognition rate can be improved with entropy. |

Zhang et al. [1] | Connecting rod, vehicle axle | - The reliability prediction of structures can be realized. |

Jang et al. [68] | Metal fatigue | - FFE was treated as a property of metal materials. - FFE was not affected by loading condition, frequency, and geometry. |

Gidwani et al. [7] | Wear mechanics and system reliability | - The reliability-entropy hypothesis was applied to predict mechanical system reliability. - The degradation entropy generation theorem was considered. |

Radkowski et al. [66] | Gear crack | - The entropy method was used for failure diagnosis. - Single-frequency entropy can read the signals of frequency differences. |

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## Share and Cite

**MDPI and ACS Style**

Cai, M.; Cui, P.; Qin, Y.; Geng, D.; Wei, Q.; Wang, X.; Yang, D.; Zhang, G.
Entropy Generation Methodology for Defect Analysis of Electronic and Mechanical Components—A Review. *Entropy* **2020**, *22*, 254.
https://doi.org/10.3390/e22020254

**AMA Style**

Cai M, Cui P, Qin Y, Geng D, Wei Q, Wang X, Yang D, Zhang G.
Entropy Generation Methodology for Defect Analysis of Electronic and Mechanical Components—A Review. *Entropy*. 2020; 22(2):254.
https://doi.org/10.3390/e22020254

**Chicago/Turabian Style**

Cai, Miao, Peng Cui, Yikang Qin, Daoshuang Geng, Qiqin Wei, Xiyou Wang, Daoguo Yang, and Guoqi Zhang.
2020. "Entropy Generation Methodology for Defect Analysis of Electronic and Mechanical Components—A Review" *Entropy* 22, no. 2: 254.
https://doi.org/10.3390/e22020254