Experimental Characterization Methods for Thermal Contact Resistance a Review
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Research-Article
Experimental Characterization and Modeling of Thermal Contact Resistance of Electric Machine Stator-to-Cooling Jacket Interface Under Interference Fit Loading
J. Thermal Sci. Eng. Appl. Aug 2018, ten(4): 041016 (7 pages)
Published Online: May viii, 2018
Cooling of electric machines is a key to increasing power density and improving reliability. This newspaper focuses on the blueprint of a machine using a cooling jacket wrapped around the stator. The thermal contact resistance (TCR) between the electrical car stator and cooling jacket is a significant factor in overall performance and is not well characterized. This interface is typically an interference fit subject to compressive force per unit area exceeding 5 MPa. An experimental investigation of this interface was carried out using a thermal transmittance setup using pressures betwixt five and 10 MPa. The results were compared to currently available models for contact resistance, and one model was adapted for prediction of TCR in future motor designs.
Introduction
Cooling of electrical machines is an important factor in increasing power density. Components within an electric machine such as the magnets and wire insulation experience reduced performance or reliability when exposed to temperatures beyond their thermal specifications [1]. Therefore, heat must be removed from these components to limit the temperature to which they are exposed. Typically, estrus must flow through several components and material interfaces or contacts before the estrus tin can be extracted from the motor through convective cooling. For this reason, the convective cooling arroyo for the machine can impact the path of heat transfer through the electric auto, resulting in certain materials or interfaces having a larger touch on on the overall thermal management of the electrical motorcar. Examples of some thermal management approaches that have been practical to electric machines are summarized in Ref. [two].
The option of convective cooling technology depends on the electric motorcar's performance requirements, intended application, and available coolants. The enquiry described in this paper focused on a new electrical car design cooled with a high-performance cooling jacket integrated into the machine example using h2o–ethylene glycol, as shown in Fig. 1.
Fig. i
Electric car cross section highlighting stator-to-case contact
Fig. 1
Electrical machine cross section highlighting stator-to-example contact
Close modal
Because the car of involvement used a loftier-performance cooling jacket for heat removal, the heat flow path through the machine was predominantly radial. A parameter sensitivity report was performed on a preliminary pattern of the electrical machine using a thermal finite chemical element assay model to determine which thermal resistances were nigh significant. To perform the study, the thermal properties of each textile or interface were decreased past twenty%, and the alter in maximum temperature was reported. The thermal sensitivity assay indicated that the ascendant thermal resistances for heat conduction through the machine were the stator lamination stack and the thermal contact resistance (TCR) between the stator and case [3]. For this reason, there was a need to experimentally measure the in-plane lamination thermal conductivity and the TCR of the stator-to-instance interface.
The coolant jacket for the electric car was mounted to the stator through an interference fit between the coolant jacket and stator. For the motorcar of interest, the stator-to-case interference fit resulted in a compressive force per unit area on the joint ranging from 5.52 to 9.65 MPa. The laminated silicon steel used in the stator gives the outer bore of the stator a ridged surface. The inner diameter of the instance in contact with the stator is a machined aluminum surface. Examples from a similar electrical machine are shown in Fig. 2, showing the stator'due south outer bore surface and the cooling jacket's inner diameter surface.
Fig. two
Pinnacle: motorcar stator surface. Bottom: case interior surface.
Fig. 2
Top: machine stator surface. Bottom: example interior surface.
Shut modal
In that location are a number of models and experimental data for calculating TCR. The simplest apply an effective air gap with suggestions for values based on surface roughness [4,five]. Using these techniques yields a pressure level-independent TCR ranging from 840 to 1400 mm2 K/Due west. Theoretical models will have into account factors such as the pressure level on the joint, the hardness of the two materials, the surface roughness, and interstitial gas [6,7]. Using such a model gives a pressure level-dependent TCR ranging from 354 to 244 mmtwo K/W for the 5.52–9.65 MPa force per unit area range. The disadvantage of such a model is the requirement to obtain upwards of fifteen parameters, some of which may be obscure or difficult to obtain or require specialized equipment to measure. Finally, extrapolating from previously published experimental information [8] gives a TCR of 157–149 mm2 K/W for the same pressure range.
The large range in the calculated TCR values (149–1400 mm2 K/W) causes a challenge in the electrical auto thermal pattern. A TCR of 150 mm2 K/W corresponds to a temperature drop across the stator-to-jacket interface of 5 °C–10 °C. A TCR of 1400 mm2 Thousand/W across the same interface results in a temperature drib near 7 times college. Therefore, obtaining an accurate value for the stator-to-instance TCR is critical in the thermal pattern of example-cooled electric machines.
This paper presents an experimental method to measure out thermal contact resistance at pressures representing interference fits. Pressures from 5.52 to 9.65 MPa and two types of ordinarily used machine laminations were studied. The experimental information were used to select a model that can be used with easily obtained parameters, while giving an accurate issue that can be used in relevant electrical auto thermal models.
Experimental Appliance and Procedures
To measure the TCR of the instance-to-stator interference fit, a high-pressure transmittance setup was constructed in accord with ASTM International (ASTM) Method D5470 [nine] using a high-capacity hydraulic clamp, as shown in Fig. 3 [x]. The setup includes a lamination coupon with the laminations stacked horizontally. The laminations are sandwiched betwixt two 4-mm-thick aluminum contact plates that simulate the aluminum example. The aluminum contact plates on the elevation and bottom of the fixture are pressed against copper metering blocks with thermal grease applied at the interface. The setup was validated confronting both an existing thermal transmittance setup at the National Renewable Energy Laboratory for lower pressures described by Narumanchi et al. [11] and a xenon flash diffusivity measurement system using the 4-mm-thick aluminum contact plates to be used in the experiment. The setup uses resistance temperature detectors (RTDs) placed into the copper metering blocks located on the acme and bottom of the examination sample. Oestrus is provided to ane side of the sample through electrical heaters inserted into an aluminum heater block. The test apparatus is thermally isolated from the large pneumatic press using a cold plate on the bottom. Both cold plates are cooled with a bath circulator using manifestly water.
Fig. 3
Loftier-pressure thermal transmittance setup showing cutaway view of sample stabilizing rig
Fig. 3
High-force per unit area thermal transmittance setup showing cutaway view of sample stabilizing rig
Close modal
For the experiments, the laminations were manufactured with a tolerance of 0.1 mm. A stabilizing rig was built to hold the laminations together. The stabilizing rig provided a method to concord the laminations level without welding or adhesion such that the surface was "self-leveling." The stabilizing rig consisted of an aluminum frame with thermally insulating Teflon bumpers held against the lamination stack with set screws.
The objective of the experiment was to measure the TCR betwixt the steel laminations and the aluminum contact plate in addition to the lamination thermal conductivity parallel to the in-aeroplane direction of the laminations. The primary test factors for the experiment included force per unit area and lamination material. The sample temperature ranged from 45 °C to 115 °C. A temperature gradient must be applied to the sample to obtain results using the thermal transmittance method, and the temperature was limited by the safe operating temperature of the heaters in the heater block shown in Fig. 3. The highest safe temperature was used to maximize the heat flux beyond the sample to ameliorate the accurateness of the measurement results. Electric machines volition operate beyond a wide range of temperatures, but the impact of temperature on the thermal contact resistance was not included as part of the pattern infinite of this experiment.
Test Pressures.
The pressures practical during the tests were intended to correspond an interference fit between the case and stator where the stator diameter is larger than the inner diameter of the case. The pressure was calculated based on the geometry of the UQM epitome electric machine. The tested pressures covered a range of values that encompassed the force per unit area estimate of the UQM prototype machine, which included five.52 MPa, 6.89 MPa, viii.27 MPa, and 9.65 MPa. Each information point at the listed pressure was repeated three times to aid in the measurement doubt analysis. Thermal contact resistance is affected by hysteresis or the loading history of the contact. Thermal cycling, load cycling, and extended time nether load can reduce thermal contact resistance [12]. To minimize hysteresis effects, measurements were taken immediately after thermal steady-land was reached. Steady-state was divers by a maximum temperature change of less than 0.03 °C for a x-min period. Pressures were but increased throughout each test (i.e., a higher-force per unit area test could non precede a test at lower pressure).
The high pressures involved necessitated investigation into whether the surface of the contact plate would become indented from the lamination coupon surface. This was done by using a laser profilometer to scan the surface and so using spatial 2-dimensional fast Fourier transform to transform the surface data into the frequency domain. Analyzing the surface in the frequency domain allows differentiation between tool marks and indentation caused by the lamination coupon surface. If the experiment caused an indentation in the aluminum, it would necessitate replacing the aluminum for each experimental test to ensure repeatability. Whether or not the aluminum plates could be reused affects the number of experiments that tin can exist performed due to the potential expense of having to cut or refinish plates for each repetition should they non exist reusable. The laminations were too tested for possible work hardening by comparison thermal properties before and after awarding of pressure.
Lamination Materials.
Two types of laminations were used: 29-estimate M15 material and 0.2-mm high-frequency textile from JFE Steel Corporation. Both laminations were laser cut to get the shapes needed. The dissimilar edges are the result of unlike feed rates and/or intensity used by the vendor in the cut process to ensure samples were non damaged due to thinner laminations beingness more brittle. Figure four shows the edges of the two lamination materials included in the experimental measurements. The JFE textile is thinner, and the resulting edge has a serrated appearance.
Fig. 4
Edge views of lamination materials. The microscope stage is labeled for clarity.
Fig. iv
Edge views of lamination materials. The microscope phase is labeled for clarity.
Close modal
Surface Properties of Contact Plates.
Ii surfaces for the contact plates were tested and compared to determine the significance of the surface stop. The commencement was a factory-ground surface with no special handling with an average surface roughness of 0.6 μm. In an actual machine case, the inner surface is lathed to a specified tolerance. Ideally, the second surface would exactly replicate a lathed machine design. However, it was not possible to exactly indistinguishable a lathed car pattern on a flat surface without specialized equipment. Instead, the 2d surface approximated a lathed surface by machining the aluminum contact block surface with a fly cut. Fly cutting results in surface tooling (ridges) like to what would exist obtained with lathing; using a very large bit results in most straight ridges. The feed speed gives control over the surface roughness and was adjusted to lucifer the surface roughness of the stator instance, which was 1.6 μg. Figure v shows a surface topography map of the fly cut surface obtained using a light amplification by stimulated emission of radiation profilometer. The data were postprocessed in matlab to obtain the expanse-average surface roughness.
Fig. 5
Ten-mm square sample area surface profile of the contact plate
Fig. 5
10-mm foursquare sample expanse surface profile of the contact plate
Close modal
Data Analysis Procedure.
The test apparatus measures the thermal resistance of the total stack-up between the two metering blocks shown in Fig. three. The stack-up can be represented by Eq. (i). The TCR is obtained by subtracting the thermal resistances due to the other layers.
R GL represents the thermal grease layer between the copper metering blocks and the contact plates shown in Fig. 3. The grease layer improves the thermal contact betwixt the copper metering block and contact plate. R CP represents the thermal resistance of the aluminum contact plate shown in Fig. three. The thermal resistance of the contact plate was characterized using a xenon wink transient technique. R LS represents the thermal resistance of the lamination stack coupon shown in Fig. 3.
The challenge with the thermal transmittance setup is that the measurement incertitude is a stock-still percent of R tot. Therefore, care must be taken to minimize the subtractions from Rtot to obtain the value of interest, in this example, TCR. Intendance must also exist taken to minimize variations in R tot due to variations of private layers (eastward.1000., grease layer thickness).
The grease layer between the metering cake and contact plate was characterized at all four pressures using only a contact plate and obtained using Eq. (2). Using a contact plate instead of simply characterizing the grease layer independently simulates the experimental atmospheric condition of the grease layer exactly between the copper metering block and the aluminum contact plate
While estimates and measurements for the bulk lamination material thermal electrical conductivity were available, the direction-dependent thermal electrical conductivity of the lamination stack parallel with the laminations was not known. For this reason, it was not possible to subtract the thermal resistance of the lamination stack as shown in Eq. (ane) with sufficient confidence. To overcome this claiming, 3 sizes of laminations were used to generate a thermal resistance versus sample elevation curve like to what is shown in Fig. 6. Past fitting a first-lodge bend, the lamination stack's thermal resistance can be extracted independently of other parameters using Eq. (three), and TCR tin can be extracted from the stack using Eq. (four)
(3)
Fig. half-dozen
Thermal resistance every bit a role of lamination coupon thickness
Fig. six
Thermal resistance as a role of lamination coupon thickness
Close modal
Results and Give-and-take
The experimental results are described in the following sections. To validate the experimental design and the test procedure, a series of preliminary tests was performed. The results of the preliminary testing provided confidence in the experimental approach. Once the experimental design was finalized, the experimental results were recorded as described in the following.
Preliminary Test Results.
Earlier the high-force per unit area tests were conducted, an initial examination was performed on the existing thermal transmittance setup to check if the random dubiousness of the measurement would be acceptable before constructing the high-pressure setup. The test yielded an adequate uncertainty and work proceeded to build the high-pressure experimental setup.
The thermal resistance of the grease layer in Eq. (4) was determined experimentally every bit described previously. The results of the measurements are shown in Table 1. The consequence is the average of three experiments. The values are modest compared to the expected measurements. Information technology is worth noting that the thermal resistance decreases with pressure, which follows the expected behavior.
Table 1
Meter block-to-contact plate thermal resistance with thermal grease interface
| Examination force per unit area (MPa) | Grease thermal resistance (mm2 K/W) |
|---|---|
| 5.52 | viii.4 |
| six.89 | viii.1 |
| 8.27 | seven.8 |
| 9.65 | seven.6 |
| Examination pressure (MPa) | Grease thermal resistance (mmii K/W) |
|---|---|
| 5.52 | 8.iv |
| half dozen.89 | 8.1 |
| 8.27 | 7.8 |
| 9.65 | seven.half-dozen |
To test for indentations in the contact plates, the experiment was performed at 9.65 MPa for the aforementioned temperature and fourth dimension conditions used in the experiment. The surface was then analyzed using a spatial two-dimensional fast Fourier transform technique. Transforming the surface data into spatial frequency space allows elementary differentiation between a potential indentation due to a lamination stack and existing tool marks that both run in the aforementioned direction. At that place was no indication of whatsoever indentation or change in surface properties due to the experiment. Samples were also periodically analyzed throughout the experiment to ensure that no cumulative damage occurred to the plate surface that would affect results. In improver, the laminations were tested on the xenon flash before and after the preliminary test to ensure no thermal property changes due to potential work hardening had occurred.
To highlight the effect the lathed surface on the interior of the case had on the contact resistance, a series of tests was run using a smoothen contact plate and the fly-cutting contact plate. The results are shown in Fig. 7. For the TCR calculation in Fig. seven, a value for the lamination coupon was calculated based on the known bulk thermal properties of the laminations as a preliminary guess. As seen in Fig. vii, the surface cease significantly impacts the measured contact resistance. For this reason, the tests proceeded with the fly-cutting surface to more closely represent the lathed surface properties.
Fig. seven
Comparison of contact plate surface finish effect on TCR
Fig. vii
Comparison of contact plate surface end result on TCR
Close modal
Thermal Holding Experimental Results.
Figure 8 shows a plot of the data for the M15 29-gauge lamination coupons at the lowest of the 4 pressures tested. Three data points were nerveless for each of the iii coupon thicknesses. The information were fit with a starting time-order curve with the curve fit data points weighted according to the systematic error of the experiment. The thermal properties for both the lamination stack and the stator-to-case contact resistance were extracted using the gradient and intercept of the fit, respectively, using Eqs. (iii) and (four).
Fig. 8
Total thermal resistance measurements for M15 29-gauge coupons at v.52 MPa with extrapolation to 0 lamination coupon thickness
Fig. viii
Total thermal resistance measurements for M15 29-guess coupons at five.52 MPa with extrapolation to 0 lamination coupon thickness
Close modal
As described previously, the thermal resistances of the grease and contact plate are subtracted from the intercept to obtain the contact resistance. To summate the uncertainty of the measurements, the bend fit is weighted on systematic fault, which includes RTD calibration error, estimated spatial temperature variation calculated using a thermal finite chemical element model of the setup, and RTD location error. The RTDs were calibrated to a National Institute of Standards and Technology traceable reference probe using a static temperature calibration bathroom. The bend fit yields random error and the 95% conviction interval (U95) is calculated [12,xiii]. Effigy nine summarizes the results for both the stator-to-case contact and the bulk thermal electrical conductivity for the laminations as calculated from the slope-intercept technique.
Fig. 9
Acme: stator-to-case TCR results. Bottom: lamination effective thermal conductivity results. Error bars correspond the 95% confidence interval.
Fig. 9
Top: stator-to-case TCR results. Bottom: lamination effective thermal conductivity results. Error bars stand for the 95% conviction interval.
Shut modal
The results shown in Fig. ix are generally consistent with expectations, which give confidence in the technique. The thermal conductivity of the laminations does not vary with pressure level and is near the majority value measured with the xenon flash technique of 22 W/m K for both materials. The contact resistance decreases with increasing pressure level. The contact resistance is significantly lower than what is predicted by effective air gap models, only agrees well with pressure-dependent models for TCR. The dubiousness in the results shown past the fault bars in Fig. ix precludes making further conclusions virtually the results. However, in that location is a clear trend of pressure dependence, and the different surface of the JFE equally shown in Fig. 4 may affect TCR.
Theoretical Model.
The model described in Madhusudana [vii] appeared to requite the best agreement with the experimental results for TCR in the 5–10 MPa pressure range. The purpose here is not to propose a new model or a physically comprehensive model only to summarize the existing model as it pertains to a stator-to-instance TCR. The model includes both solid [6] and fluid [14] components to summate the inverse of TCR or thermal contact conductance (TCC)
The solid spot conductance (h s) is described by Eq. (vi) as
where one thousand is the harmonic hateful of the thermal conductivities of the two materials; C and n are coefficients, which are 1.xiii and 0.94, respectively [6]; σ is the centerline average roughness of the two contacting surfaces and is 1.25σRMS; σRMS is the root hateful square of the average surface roughness of the two contacting surfaces; tan Θ is the mean slope of the surface asperities; P is the applied pressure; and H is the contact microhardness of the softer of the two materials. P and H accept units of MPa.
The surface roughness of the case plate was 1.half dozen μone thousand. The surface roughness of the laminations was determined using the aforementioned technique and yielded 10.ix μm and 11.8 μm for the M15 and JFE materials, respectively. Any roughness tester could be used to measure out the surface roughness provided it has the range needed. Measuring tan Θ is nontrivial, and motor designers are unlikely to possess the necessary equipment. As an alternative, tan Θ can be calculated based on the surface roughness correlations [15]. However, the surface roughness is outside the valid range for the correlation to be valid. Furthermore, the correlation assumes a Gaussian, random surface, which is not necessarily the example for this contact. Because of this, tan Θ was adamant empirically to exist 0.12. Typical values for tan Θ range between 0.03 and 0.18 [seven,fifteen]. Annotation that bulk properties for k are used (22 W/m Thou for both types of laminations), non the effective backdrop reported in Fig. 9, which are a function of the stacking factor and include a minor amount of interstitial air. The aluminum thermal conductivity was measured to be 195 W/k K. The aluminum microhardness was estimated to be 930 MPa, derived from typical Brinell hardness for Al 6061-T6. Surface microhardness is dependent on the history of the surface, including how it was finished, estrus treatment, or piece of work hardening. The actual surface microhardness may differ from the estimated value and requires specialized equipment to measure out. The gaseous fluid conductance (h g) is described by Eq. (7) as
where k g is the thermal conductivity of the interstitial gas, in this example air at 80 °C. δ is calculated using Eq. (viii) [14]
Effigy ten shows a comparison of the model to the information for both sets of laminations. The model shows proficient agreement with the data. Although not included in the plot, the model agrees with the preliminary test at 0.22 MPa. The range of 150–250 mm2 K/Due west is on the lower end of the estimates of 149–1400 mm2 M/W for the interface. More importantly, it reduces the uncertainty of the value past 90%, which leads to more accurate motorcar design.
Fig. 10
Pinnacle: Comparison of TCR model to M15 29-gauge data. Bottom: comparison of TCR model to JFE (0.2 mm) data. Root mean foursquare surface roughness of the contacting surfaces used in the model is noted on the plot. Error bars bespeak 95% conviction interval for the information.
Fig. 10
Top: Comparison of TCR model to M15 29-gauge data. Bottom: comparison of TCR model to JFE (0.two mm) data. Root hateful square surface roughness of the contacting surfaces used in the model is noted on the plot. Error bars indicate 95% confidence interval for the data.
Close modal
Thermal contact resistance calculated past the model agrees reasonably well (17% difference) with the experimental results reported past Kulkarni et al. [viii] for 13.28 MPa, but the model results are lower than their results when extrapolating to college pressures (21–39 MPa). Notation that values were not given for the material and surface properties, and so it is possible they differed from what is presented here.
Conclusions
The TCR between auto laminations and an aluminum cooling jacket under interference loading was measured using a simulated stack within a high-pressure ASTM D5470 setup. The results for two commonly used auto lamination types are presented and compared to existing contact resistance models. It was constitute that the TCR ranged from 150 to 250 mmtwo One thousand/Westward for interference fit pressures between 5.52 and ix.65 MPa. A model was presented with parameters that can be obtained using standard equipment and agrees closely with the experimental data.
Pressure-independent models (such as effective air gap models) are valid for pressures below 500 kPa. For pressures exceeding 500 kPa, the air gap model overestimates TCR proportional to the pressure. For the interference fit pressures investigated, the pressure-independent models overestimated TCR by a factor of four to seven compared to the pressure level-dependent model presented. The model presented was validated to 10 MPa, but should exist valid for whatever pressure well beneath the textile yield signal.
The stator-to-case TCR is a disquisitional parameter in high-performance and meaty motorcar designs, especially those that depend on case cooling. Without an accurate value for the stator-to-case TCR, the cooling organisation may be optimized incorrectly or additional expense invested in alternative cooling or oversizing the motor that may non be necessary. This work helps electric machine designers accurately estimate the stator-to-case TCR for a range of electric machines without having to resort to expensive experimental tests or overly conservative estimates.
Acknowledgment
We acknowledge fiscal support for the work provided by Susan Rogers and Steven Boyd, Engineering science Managers for the Electric Bulldoze Technologies Plan, Vehicle Technologies Office, U.S. Department of Energy, Office of Energy Efficiency and Renewable Energy (EERE). The significant contributions from Doug DeVoto (NREL) and Charlie King (NREL) to the project are acknowledged.
This work was supported by the U.Southward. Section of Energy under Contract No. DE-AC36-08GO28308 with the Alliance for Sustainable Energy, LLC, the Managing director and Operator of the National Renewable Free energy Laboratory.
Nomenclature
-
C =
-
H =
-
hg =
gaseous fluid conductance
-
hs =
-
k =
-
n =
-
P =
-
R =
-
RTD =
resistance temperature detector
-
tanΘ =
-
TCC =
thermal contact conductance (1/TCR)
-
TCR =
thermal contact resistance
-
δ =
-
σ =
Subscripts
-
CP =
-
GL =
-
LS =
-
RMS =
-
Tot =
Subscripts
References
1.
Stone G. C. Boulter E. A. Culbert I. Dhirani H.
2004
,
Electrical Insulation for Rotating Machines: Design, Evaluation, Aging, Testing, and Repair
,
Wiley
, Hoboken, NJ.
2.
Popescu 1000. Staton D. A. Boglietti A. Cavagnino A. Hawkins D. Goss J.
2016
, "
Modern Heat Extraction Systems for Ability Traction Machines—A Review
,"
IEEE Trans. Ind. Appl.
,
52
(
3
), pp.
2167
–
2175
.
four.
Lindström J.
1999
,
Thermal Model of a Permanent-Magnet Motor for a Hybrid Electric Vehicle
,
Chalmers Academy of Engineering
, Gothenburg, Sweden.
v.
Staton D. Boglietti A. Cavagnino A.
2005
, "
Solving the More Difficult Aspects of Electric Motor Thermal Analysis in Small and Medium Size Industrial Induction Motors
,"
IEEE Trans. Free energy Convers.
,
twenty
(
3
), pp.
620
–
628
.
six.
Mikić B. B.
1974
, "
Thermal Contact Conductance; Theoretical Considerations
,"
Int. J. Heat Mass Transfer
,
17
(
ii
), pp.
205
–
214
.
7.
Madhusudana C.
2014
,
Thermal Contact Conductance
, 2nd ed.,
Springer
, Cham,
Switzerland
.
8.
Kulkarni D. P. Rupertus G. Chen E.
2012
, "
Experimental Investigation of Contact Resistance for Water Cooled Jacket for Electric Motors and Generators
,"
IEEE Trans. Energy Convers.
,
27
(
1
), pp.
204
–
210
.
eleven.
Narumanchi Due south. Mihalic M. Kelly K. Eesley G.
2008
, "
Thermal Interface Materials for Power Electronics Applications
,"
11th Intersociety Conference on Thermal and Thermomechanical Phenomena in Electronic Systems
(
ITHERM
), Orlando, FL, May 28–31, pp.
395
–
404
.
12.
Kirkup L.
2002
,
Data Analysis With Excel®: an Introduction for Physical Scientists
,
Cambridge University Press
, Cambridge, UK.
13.
Dieck R. H.
2007
,
Measurement Uncertainty: Methods and Applications
,
ISA
, Research Triangle Park, NC.
14.
Madhusudana C. V. Fletcher 50. South.
1981
, "Gas Conductance Contribution to Contact Oestrus Transfer,"
AIAA
Paper No. 81-1163.
fifteen.
Antonetti V. West. Whittle T. D. Simons R. East.
1993
, "
An Approximate Thermal Contact Conductance Correlation
,"
ASME J. Electron. Packag.
,
115
(
i
), pp.
131
–
134
.
Source: https://asmedigitalcollection.asme.org/thermalscienceapplication/article/10/4/041016/369591/Experimental-Characterization-and-Modeling-of
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