Effect of Percolation on Equivalent Thermal Conductivity of Insulating Layer in Insulated Metal Substrates

2003 ◽  
Author(s):  
Kenji Monden
Keyword(s):  
Thermal Conductivity ◽  
Effective Thermal Conductivity ◽  
Volume Fraction ◽  
High Thermal Conductivity ◽  
Inorganic Filler ◽  
Interfacial Region ◽  
Equivalent Thermal Conductivity ◽  
Metal Base ◽  
Predictive Values ◽  
Insulating Layer

An insulated metal substrate (IMS) is a circuit board comprising an insulating layer on a metal base plate. The insulating layer is made from epoxy resin incorporating dense inorganic fillers with high thermal conductivity. Because the substrates have high thermal conductivity, they are used in applications where electric parts generate intense heat, such as inverters, amplifiers, motor drivers and so on. It is expected that the insulating layer has higher thermal conductivity as the use of an IMS is expanded. Therefore, the influence of percolation on the equivalent thermal conductivity of an insulating layer is considered. The effect of the volume fraction of inorganic filler on the equivalent thermal conductivity of insulating layer in IMS is experimentally investigated. The equivalent thermal conductivity of insulating layer as a function of volume fraction of filler is estimated by FEM and Monte Carlo technique together. The acquired value of percolation threshold volume fraction is the same grade as the previous reported value. Based on these experimental and numerical results, an effective thermal conductivity of a filler which contains surrounding interfacial region is evaluated. The effective thermal conductivity of an irregular filler is presumed smaller than that of a spherical filler. It is noted that the control of filler size and shape is important for the formation of high thermal conductivity of an insulating layer. In addition, an improved equation for the equivalent thermal conductivity of insulating layer in IMS is proposed. The predictive values from the equation for insulating layer in an improved IMS agree with experimental results.

Equivalent Thermal Conductivity of Insulating Layer in Insulated Metal Substrates

2006 ◽  
Vol 45 ◽  
pp. 2664-2669 ◽  
Author(s):  
Kenji Monden
Keyword(s):  
Thermal Conductivity ◽  
Volume Fraction ◽  
Base Plate ◽  
Circuit Board ◽  
Equivalent Thermal Conductivity ◽  
Metal Base ◽  
Predictive Values ◽  
Insulating Layer ◽  
Ceramic Fillers ◽  
Intense Heat

An insulated metal substrate (IMS) is a circuit board comprising an insulating layer on a metal base plate. The insulating layer is made from epoxy resin incorporating dense ceramic fillers. The substrates are used in applications where electric parts generate intense heat. It is expected that the insulating layer has higher thermal conductivity as the use of an IMS is expanded. Therefore, the influence of percolation on the equivalent thermal conductivity (ETC) of an insulating layer is considered. The Effect of the volume fraction of ceramic filler on the ETC of insulating layer in IMS is investigated. The ETC as a function of volume fraction of filler is estimated. Based on these experimental and numerical results, an ETC of a filler is evaluated. The ETC of an irregular filler is presumed smaller than that of a spherical filler. It is thought that the control of filler size and shape is important for the formation of high thermal conductivity of an insulating layer. In addition, an improved equation for the ETC of IMS is proposed. The predictive values from the equation for an improved IMS agree with experimental results.

Reliability Improvement of Solder Joints Between Ceramic Chip Resistors and Insulated Metal Substrates With Thick Copper Pads

2005 ◽  
Author(s):  
Kenji Monden
Keyword(s):  
Thermal Conductivity ◽  
Finite Element ◽  
Epoxy Resin ◽  
Base Plate ◽  
Temperature Cycling ◽  
High Thermal Conductivity ◽  
Metal Base ◽  
Insulating Layer ◽  
Cycling Test ◽  
Temperature Cycling Test

An insulated metal substrate (IMS) is a circuit board comprised of an insulating layer on a metal base plate. The insulating layer is made from epoxy resin incorporating dense inorganic fillers with high thermal conductivity. Because the substrates have high thermal conductivity, they have been used in electrical products that generate intense heat, such as inverters, amplifiers, motor drivers and so on. For using a high power semiconductor, thick copper pads are used on IMSs. In many times, aluminum plates are used for metal base plates in IMSs. The substrates are repeated heating and cooling in ordinary usage. So cracks of solder joints between ceramic chip resistors and IMSs often occur because of coefficient of thermal expansion (CTE) mismatch between ceramic and aluminum. Moreover, SnAgCu solder used to replace eutectic Sn/Pb solder as the joint has become major trend from a viewpoint of earth environmental protection. Finite element analysis was used for development of a high reliable IMS to meet these demand for the IMSs. The accelerated temperature cycling test on IMS was simulated by finite element method. The influence of the CTE of metal base plate and the influence of the modulus of insulating layer were studied. The reliability of solder was predicted to increase with CTE reduction of metal base plate. The modulus of insulating layer must be reduced sharply for a high reliable IMS. However, the insulating layer is difficult to be realized by using the epoxy resin. So the effect by fixing the chip resistor on a IMS using resin was calculated. When the space between the bottom of a chip resistor and the copper pads were filled up with resin such as underfill resin in ball grid array (BGA) mounting, it was predicted that the stress of solder decreased. The effect was confirmed by experiment. Solder joint fracture life of accelerated temperature cycling test on IMS was improved more than three times longer by using the underfill resin.

scholarly journals Effective Thermal Conductivity of Open Cell Polyurethane Foam Based on the Fractal Theory

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Kan Ankang ◽  
Han Houde
Keyword(s):  
Thermal Conductivity ◽  
Fractal Dimension ◽  
Effective Thermal Conductivity ◽  
Polyurethane Foam ◽  
Solid Phase ◽  
Fractal Theory ◽  
Heat Radiation ◽  
Total Thermal Conductivity ◽  
Equivalent Thermal Conductivity ◽  
Open Cell

Based on the fractal theory, the geometric structure inside an open cell polyurethane foam, which is widely used as adiabatic material, is illustrated. A simplified cell fractal model is created. In the model, the method of calculating the equivalent thermal conductivity of the porous foam is described and the fractal dimension is calculated. The mathematical formulas for the fractal equivalent thermal conductivity combined with gas and solid phase, for heat radiation equivalent thermal conductivity and for the total thermal conductivity, are deduced. However, the total effective heat flux is the summation of the heat conduction by the solid phase and the gas in pores, the radiation, and the convection between gas and solid phase. Fractal mathematical equation of effective thermal conductivity is derived with fractal dimension and vacancy porosity in the cell body. The calculated results have good agreement with the experimental data, and the difference is less than 5%. The main influencing factors are summarized. The research work is useful for the enhancement of adiabatic performance of foam materials and development of new materials.

Figure of Merit-Based Optimization Approach of Phase Change Material-based Composites for Portable Electronics Using Simplified Model

2021 ◽  
Author(s):  
Ayushman Singh ◽  
Srikanth Rangarajan ◽  
Leila Choobineh ◽  
Bahgat Sammakia
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Phase Change ◽  
Effective Thermal Conductivity ◽  
Phase Change Material ◽  
Figure Of Merit ◽  
Volume Fraction ◽  
Simplified Model ◽  
Transient Temperature ◽  
Change Material

Abstract This work presents an approach to optimally designing a composite with thermal conductivity enhancers (TCEs) infiltrated with phase change material (PCM) based on figure of merit (FOM) for thermal management of portable electronic devices. The FOM defines the balance between effective thermal conductivity and energy storage capacity. In present study, TCEs are in the form of a honeycomb structure. TCEs are often used in conjunction with PCM to enhance the conductivity of the composite medium. Under constrained composite volume, the higher volume fraction of TCEs improves the effective thermal conductivity of the composite, while it reduces the amount of latent heat storage simultaneously. The present work arrives at the optimal design of composite for electronic cooling by maximizing the FOM to resolve the stated trade-off. In this study, the total volume of the composite and the interfacial heat transfer area between the PCM and TCE are constrained for all design points. A benchmarked two-dimensional direct CFD model was employed to investigate the thermal performance of the PCM and TCE composite. Furthermore, assuming conduction-dominated heat transfer in the composite, a simplified effective numerical model that solves the single energy equation with the effective properties of the PCM and TCE has been developed. The effective thermal conductivity of the composite is obtained by minimizing the error between the transient temperature gradient of direct and simplified model by iteratively varying the effective thermal conductivity. The FOM is maximized to find the optimal volume fraction for the present design.

Quantification of effective thermal conductivity in the annealing process of Cu2ZnSn(S,Se)4 solar cells with 9.7% efficiency fabricated by magnetron sputtering

2018 ◽  
Vol 2 (5) ◽  
pp. 999-1006 ◽  
Author(s):  
Woo-Lim Jeong ◽  
Jung-Hong Min ◽  
Hae-Sun Kim ◽  
Ji-Hun Kim ◽  
Jin-Hyeok Kim ◽  
...  
Keyword(s):  
Thermal Conductivity ◽  
Solar Cells ◽  
Solar Cell ◽  
Magnetron Sputtering ◽  
Effective Thermal Conductivity ◽  
Fill Factor ◽  
Annealing Process ◽  
High Thermal Conductivity ◽  
Shunt Resistance

A CZTSSe solar cell fabricated using a graphite box designed with high thermal conductivity exhibited a high shunt resistance and a fill factor.

THE EFFECT OF VERTICAL AIR GAPS TO THERMAL TRANSMITTANCE OF HORIZONTAL THERMAL INSULATING LAYER

2009 ◽  
Vol 15 (3) ◽  
pp. 309-315 ◽  
Author(s):  
Jolanta Šadauskienė ◽  
Andrius Buska ◽  
Arūnas Burlingis ◽  
Raimondas Bliūdžius ◽  
Albinas Gailius
Keyword(s):  
Thermal Conductivity ◽  
Effective Thermal Conductivity ◽  
Thermal Insulation ◽  
Standard Method ◽  
Mineral Wool ◽  
Insulating Layer ◽  
Air Gaps ◽  
Thermal Transmittance ◽  
Thermal Insulating ◽  
The Impact

In order to reduce the amounts of work at the construction site, single‐ply dual density thermal insulating roofing boards are used with increasing frequency for thermal insulation of flat roofs. In this case, the joints between boards are not overlapped by the other ply over it; therefore gaps of varying width form between the sides of the boards through the entire thickness of the insulating layer, whose effect on the effective thermal conductivity of the thermal insulating layer must be evaluated. The aim of this project was to assess the reliability of standard method, used to determine the impact of such air gaps on the effective thermal conductivity of the thermal insulating layer by comparing the results of calculations and the results of measurements of thermal conductivity, also to determine the correction factors for thermal transmittance of horizontal thermal insulation layers due to the forming vertical air gaps between the single‐ply mineral wool boards. After measurements of thermal resistances of 50 mm thick thermal insulation board with the air gaps which width varied from 3 mm to 20 mm, it was determined that the thermal conductivity value of the air gaps increases with the increment of the width of air gaps. After completion the experimental measurements of thermal conductivity it was determined that the height of closed and unventilated or partly ventilated air gaps has no effect on the properties of effective thermal conductivity of the thermal insulation layer when the air gap width is up to 5 mm. When wider unventilated or partly ventilated air gaps occur, the effective thermal conductivity coefficient increases proportionally as the height of the air gaps increases. Calculated according to the standard method the affix to the thermal transmittance is overly general and not always appropriate. In some cases it is 6 times higher or 4 times lower than the measured one. In this paper a method to evaluate the effects of air gaps by the use of correction factor to the thermal transmittance of the horizontal thermal insulating layer is proposed. Santrauka Nornt sumažinti darbų apimtis statybos vietoje, stogams šiltinti vis dažniau naudojamos vienu sluoksniu klojamos dvitankės termoizoliacinės plokštės. Šiuo atveju plokščių sandūros neperdengiamos, todėl tarp plokščių kraštinių susidaro įvairaus pločio plyšių, kurių įtaka termoizoliacinio sluoksnio šilumai perduoti turi būti įvertinta. Šio darbo tikslas yra įvertinti standartinio metodo, taikomo tokių plyšių poveikiui sluoksnio šilumos laidumui, patikimumui nustatyti lyginant skaičiavimo ir šilumos laidumo matavimų rezultatus, nustatyti horizontaliojo termoizoliacinio sluoksnio šilumos perdavimo koeficiento pataisas dėl vertikaliųjų oro plyšių susidarymo. Apskaičiavus 50 mm storio termoizoliacinio sluoksnio oro plyšių šilumines varžas, kai plyšių plotis yra nuo 3–20 mm, nustatyta, kad oro plyšių šilumos laidumo koeficiento vertė didėja didėjant oro plyšio pločiui. Atlikus eksperimentinius šilumos laidumo matavimus, nustatyta, kad susidarančių uždarų ir nevėdinamų arba iš dalies vėdinamų oro plyšių aukštis neturi įtakos termoizoliacinio sluoksnio šilumos laidumo savybėms, kai oro plyšys yra iki 5 mm pločio. Esant platesniems uždariems ir nevėdinamiems oro plyšiams, šilumos laidumo koeficientas proporcingai didėja didėjant oro plyšių aukščiui. Pagal standartinį metodą skaičiuotas šilumos perdavimo koeficiento priedas yra per daug apibendrinantis ir ne visada tinkamas. Kai kuriais atvejais jis yra 6 kartus didesnis arba 4 kartus mažesnis už išmatuotąjį. Šiame darbe pasiūlytas horizontaliojo termoizoliacinio sluoksnio šilumos perdavimo koeficiento priedo, naudojamo plyšių įtakai įvertinti, skaičiavimo metodas.

Thermal Conductivity of Metal-Oxide Nanofluids: Particle Size Dependence and Effect of Laser Irradiation

2006 ◽  
Vol 129 (3) ◽  
pp. 298-307 ◽  
Author(s):  
Sang Hyun Kim ◽  
Sun Rock Choi ◽  
Dongsik Kim
Keyword(s):  
Thermal Conductivity ◽  
Particle Size ◽  
Effective Thermal Conductivity ◽  
Laser Irradiation ◽  
Volume Fraction ◽  
Suspended Particle ◽  
Titanium Dioxide Nanoparticles ◽  
Size Change ◽  
Conductivity Enhancement ◽  
Wide Range

The thermal conductivity of water- and ethylene glycol-based nanofluids containing alumina, zinc-oxide, and titanium-dioxide nanoparticles is measured using the transient hot-wire method. Measurements are performed by varying the particle size and volume fraction, providing a set of consistent experimental data over a wide range of colloidal conditions. Emphasis is placed on the effect of the suspended particle size on the effective thermal conductivity. Also, the effect of laser-pulse irradiation, i.e., the particle size change by laser ablation, is examined for ZnO nanofluids. The results show that the thermal-conductivity enhancement ratio relative to the base fluid increases linearly with decreasing the particle size but no existing empirical or theoretical correlation can explain the behavior. It is also demonstrated that high-power laser irradiation can lead to substantial enhancement in the effective thermal conductivity although only a small fraction of the particles are fragmented.

An Analytical Modeling for Effective Thermal Conductivity of Multi-Phase Transversely Isotropic Fiberous Composites Using Generalized Self-Consistent Method

2012 ◽  
Vol 249-250 ◽  
pp. 904-909 ◽  
Author(s):  
Syed Aadil Hassan ◽  
Hassaan Ahmed ◽  
Asif Israr
Keyword(s):  
Thermal Conductivity ◽  
Effective Thermal Conductivity ◽  
Composite System ◽  
Volume Fraction ◽  
Transversely Isotropic ◽  
Balance Principle ◽  
Isotropic Composite ◽  
Self Consistent ◽  
Consistent Method ◽  
Multi Phase

In this paper a theoretical relationship for the effective thermal conductivity of a multiphase transversely isotropic composite system is obtained. The Generalized Self-Consistent Method and simple energy balance principle is employed to derive a more appropriate model. In the derivation, it is assumed that the orientation of fiber within the transversely isotropic composite system is unidirectional and surrounded by two different phases of porous and matrix phase. A combined effect of these three different phases on the effective thermal conductivity of the composite system in transverse direction is studied. The effect of the interfacial contact conductance between the fibers and porous medium is also considered. Results of effective thermal conductivity are plotted against volume fraction and conductance which shows extremely good agreement.

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