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Research Papers

A Stepped-Bar Apparatus for Thermal Resistance Measurements

[+] Author and Article Information
Sameer R. Rao

George W. Woodruff School
of Mechanical Engineering,
Georgia Institute of Technology,
Atlanta, GA 30332

Baratunde A. Cola

George W. Woodruff School
of Mechanical Engineering,
Georgia Institute of Technology,
Atlanta, GA 30332;
School of Materials Science Engineering,
Georgia Institute of Technology,
Atlanta, GA 30332

Contributed by the Electronic and Photonic Packaging Division of ASME for publication in the JOURNAL OF ELECTRONIC PACKAGING. Manuscript received March 15, 2013; final manuscript received June 24, 2013; published online August 13, 2013. Assoc. Editor: Mehmet Arik.

J. Electron. Packag 135(4), 041002 (Aug 13, 2013) (8 pages) Paper No: EP-13-1019; doi: 10.1115/1.4025116 History: Received March 15, 2013; Revised June 24, 2013

A stepped-bar apparatus has been designed and constructed to characterize the thermal resistance of materials using steady-state heat transfer techniques. The design of the apparatus is a modification of the ASTM D5470 standard where reference bars of equal cross-sectional area are used to extrapolate surface temperatures and heat flux across a sample of unknown thermal resistance. The design modification involves intentionally oversizing the upper reference bar (URB) of the apparatus to avoid contact area uncertainty due to reference bar misalignment, which is difficult to account for, as well as the high cost that can be associated with equipping the apparatus with precise alignment controls (e.g., pneumatic alignment). Multidimensional heat transfer in the upper reference bar near the sample interface is anticipated using numerical modeling. The resulting nonlinear temperature profile in the upper reference bar is accounted for by fitting a second order regression line through thermocouple readings near the sample interface. The thermal resistances of commercially available thermal gap pads and thermal pastes were measured with the stepped-bar apparatus; the measured values were in good agreement with published results, and exhibited a high degree of reproducibility. The measurement uncertainty of both the standard and stepped-bar apparatus decrease with increased thermocouple precision. Notably, the uncertainty due to reference bar misalignment with the standard apparatus becomes more pronounced as thermocouple precision and the number of thermocouples increases, which suggests that the stepped-bar apparatus would be especially advantageous for enabling accurate, high-precision measurements of very low thermal resistances.

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References

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Figures

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Fig. 1

(a) Schematic of model geometry used in 2D heat transfer model. Constant temperature boundary conditions at top of URB and bottom of URB. Zero heat flux boundary conditions on all sides of stepped-bar apparatus. Simulated temperatures in URB recorded along dotted line. (b) Simulated center-line (see dotted line in Fig. 1(a)) temperature profile in URB of stepped-bar apparatus.

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Fig. 2

Stepped-bar thermal measurement apparatus. (a) Photograph of apparatus with screw press in place. (b) Schematic of apparatus (Two 0.5 in. thick aluminum base plates (a, b), each measuring 12 in. × 12 in. Four vertical steel rods (c) of 0.5 in. outer diameter. Bottom base plate mounted on rubber feet (d) to provide extra stability. Third plate (e) mounted in between base plates using Rulon sleeve bearings and the steel rods as guide rails. Assembly connected to mechanical transducer (f) comprised of 3/8 in.–12 size acme threaded rod, acme nut and a steel hand wheel. Load cell (g) of maximum load 500 N positioned between free plate and thermal test sections (h, i) to monitor the pressure being applied to the sample. Cartridge heater (150 W 120 V) embedded in a block (j) of oxygen free high conductivity copper (OHFC) and connected to a constant temperature PID controller to maintain the set point and the heat rate through the system. OFHC block (k) machined to allow coolant (water) to flow through it. Blocks j and k serve as the high and low temperature reservoirs, respectively). (c) Annotated drawing of URB with thermocouple positions (dimensions in mm). (d) Annotated drawing of LRB with thermocouple positions (dimensions in mm).

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Fig. 3

Curve-fitting procedure in upper reference bar of modified apparatus. The slope of the blue dashed line is used to determine the input heat rate. The red dashed-dot curve is used to extrapolate the interface temperature.

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Fig. 4

Cross-sectional view of the custom insulation system surrounding the reference bars. Fiberglass insulation is added to each surface of the nylon foam halves (not seen in the photo). The photo also shows the thermocouples in their measurement positions in each reference bar.

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Fig. 5

Measured thermal resistance of commercially available thermal paste. The dashed orange and blue lines estimate the lower bounds of the measured thermal resistances for Ceramique and Arctic Silver 5, which occur at high pressures.

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Fig. 6

Frequency histogram of 18 independent thermal resistance measurements (red) of TC100 thermal interface material. The sample was removed and reloaded in the system after each measurement. Manufacturer-specified thermal resistance of TC100 sample was 12.12 cm2 K/W. The dotted red line indicates the average value of the thermal resistance measurements. Also shown is the upper set point temperature (blue shaded region) used in each measurement.

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Fig. 7

(a) Top-view of lateral and rotational misalignment of upper reference bar. (b) Top-view of 1D misalignment of upper reference bar.

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Fig. 8

Comparison of measurement uncertainty for standard and stepped-bar apparatus with Al 2024 meter bars and a graphite pad TIM. Solid lines and dotted lines represent measurement uncertainties when 0.5 K and 0.001 K temperature probes are used, respectively. ASTM D-5470-06 and conventional reference bar curves overlap for high-precision (0.001 K) thermal probes.

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