Author Archives: Josh Perry

Optimizing Heat Sink Base Spreading Resistance to Enhance Thermal Performance

Posted on August 13, 2018 | 2 comments

(This article was featured in an issue of Qpedia Thermal e-Magazine, an online publication dedicated to the thermal management of electronics. To get the current issue or to look through the archives, visit http://www.qats.com/Qpedia-Thermal-eMagazine.)

Heat sinks are routinely used in electronics cooling applications to keep critical components below a recommended maximum junction temperature. The total resistance to heat transfer from junction to air, R_ja, can be expressed as a sum of the following resistance values as shown in Equation 1 and displayed in Figure 1.

Where, R_jc is the internal thermal resistance from junction to the case of the component. R_TIM is the thermal resistance of the thermal interface material. R_f is the total thermal resistance through the fins. The final term in Equation 1 represents the resistance of the fluid, e.g. air, going through the heat sink where m is the mass flow rate and C_p is the heat capacity of the fluid. As Equation 2 shows, R_cond and R_conv are the conduction and convection resistance respectively through the heat sink fins respectively.

Fig. 1 – Resistance network of a typical heat sink in electronics cooling. [1]

Fig. 2 – Heat source on a heat sink base. [2]

R_s stands for the spreading resistance that is non-zero when the heat sink base is larger than the component. The next few sections show the full analytical solution for calculating spreading resistance, followed by an approximate simplified solution and the amount of error from the full solution and finally the use of these solutions to model and optimize a heat sink.

Analytical Solution of Spreading Resistance

Lee et al. [2] derived an analytical solution for the spreading resistance. Figure 2 shows a cross-section of a circular heat source with radius a on the base with radius b and thickness t. The heat, q, originates from the source, spreads out over the base and dissipates into the fluid on the other side with heat transfer coefficient, h. For heat transfer through finned heat sinks, the effective heat transfer coefficient is related to thermal resistance of the fins, R_f as shown in Equation 3. For square heat source and plates, the values of a and b can be approximated by finding an effective radius as shown in equations 4 and 5.

Where,
h = heat transfer coefficient [W/m²K]
a = effective radius of the heater [m]
A_heater = area of the heater [m²]
b = effective radius of the heat sink base [m]
A_base = total area of the heat sink base [m²]

The derivation of the analytical solution starts with the Laplace equation for conduction heat transfer and applying the boundary conditions. Equation 6 shows the final analytical solution for spreading resistance. The values for the eigenvalue can be computed by using the Bessel function of the first kind at the outer edge of the plate, r=b as shown in Equation 7.

Where,
k = Thermal Conductivity of the plate or heat sink [W/mK]
J₁ = Bessel function of the first kind
λ_n = Eigenvalue that can be computed using Equation (3) at r = b
t = thickness of the heat sink base [m]

Lee et al. [2] also offered an approximation as shown in Equation 8 along with the approximation for the eigenvalues as shown in Equation 9. This approximation eliminates the need for calculating complex formulas that involve the Bessel functions and can be computed by a simple calculator.

Approximation vs. Full Solution

Simons [3] compared the full solution (Equations 6 and 7) with the approximations shown in (Equations 8 and 9). The problem contained a 10 mm square heat source on a 2.5 mm thick plate with a conductivity of 25 W/mK, 20 mm width and varying length, L as shown in Figure 3. Figure 4 shows that the percentage error increases with length but stays relatively low. Less than 10% error is expected for lengths up to 50 mm; five times the length of the heater. This is acceptable for most engineering problems since analytical solutions are first-cut approximations that should later be verified through empirical testing and/or CFD simulations. However, the full analytical solution should be used if the heater-to-heat sink base area difference gets much larger or if a more accurate solution is desired.

Fig. 3 – Example problem for comparing analytical and approximate solutions for spreading resistance. [3]

Fig. 4 – Percent error between the analytical and the approximate solution of spreading resistance for the example shown in Figure 3. [3]

Optimizing Heat Sink Performance

The goal of any electronic cooling solution is to lower the component junction temperature, T_j. For a given R_jc and R_TIM, the objective is to maximize heat sink performance by reducing the spreading resistance, R_s, and the fin resistance R_f.

The spreading resistance can be reduced by increasing base thickness. However, most electronics applications are limited by total heat sink height and thus any increase in base thickness leads to shorter fins which reduce the total area of the fins A_fins. For a fixed heat transfer coefficient (the heat transfer coefficient is a function of fin design and air velocity and we can assume it is fixed for this exercise) a reduction in the fin area increases R_f as shown in Equation 2. Equation 10 shows this combined heat sink resistance, R_hs, as a function of the spreading and fin resistance.

Thus, for a given fin design, the thermal engineer must choose the appropriate heat sink base thickness to optimize heat sink performance. To illustrate this point, let’s take an example of an application with the parameters as shown in Table 1.

Table 1 – Example Heat Sink Application

Figure 5 shows a graph of the total thermal resistance of the heat sink, R_hs and spreading resistance, R_s as a function of base thickness for copper and aluminum material. (Note that the final term from Equations 1 and 10 is ignored because it is constant and does not contribute to the understanding of spreading resistance). The graph shows that spreading resistance improves monotonically with increased base thickness. However, the total thermal resistance has an optimal point between 2-4 mm base thicknesses. For base thicknesses less than 2 mm, there is a sharp increase in spreading resistance which leads to a higher overall thermal resistance.

Fig. 5 – Total and spreading resistance of the example shown in Table 1 for a 50 mm heat sink.

On the other hand, increasing the base thickness above 4 or 5 mm gives diminishing marginal returns; the improvement in spreading resistance is minimal compared to the increase in thermal resistance due to the reduced fin area. Additionally, the graph also shows that higher conductivity materials such as copper, improves thermal performance across the entire domain.

Conclusion

The heat spreading resistance is an important factor when designing a heat sink for cooling electronics components. The full analytical solution for calculating the spreading resistance, shown in Equations 6 and 7, can be substituted with the approximations shown in Equations 8 and 9 with minimal error. The error increases with increased difference between the heat sink base and heater size and the complete analytical model should be used if needed. The analytical model can be used to choose the right heat sink base thickness that optimizes heat sink performance as shown in Figure 5.

Techniques such as higher conductivity materials, embedded heat pipes, vapor chambers etc. are available if the spreading resistance is major obstacle in the cooling. Thermal engineers must balance the increased weight and cost of such techniques against the benefits for each application.

References
1. “Spreading Resistance of Single and Multiple Heat Sources,” Qpedia. September 2010
2. Seri Lee et al. “Constriction/Spreading Resistance Model for Electronics Packaging,” 1995.
3. Simons, Robert http://www.electronics-cooling.com/2004/05/simple-formulas-for-estimating-thermal-spreading-resistance

For more information about Advanced Thermal Solutions, Inc. (ATS) thermal management consulting and design services, visit https://www.qats.com/consulting or contact ATS at 781.769.2800 or [email protected].

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Posted in heat sink, Heat Sinks, Thermal Design, Thermal resistance

Tagged heat sinks, Spreading Resistance, thermal resistance

ATS and Future Facilities Hosting Workshop

Posted on July 31, 2018 | Leave a comment

ATS and Future Facilities have announced a hands-on workshop on Wednesday, Sept. 12 at the ATS headquarters (89 Access Rd. Norwood, MA). “A Comprehensive Approach to Thermal Design and Validation” will teach engineers how to tackle thermal challenges in modern electronics from concept to final validation. Click here to learn more and to register for this workshop. Sign up today because space is limited.

Rethinking Thermocouples: Creating Micro-Scale High Precision Sensors

Posted on July 26, 2018 | Leave a comment

In the Qpedia Issue 99 article, “Minimizing Thermocouple Errors in Electronics Thermal Characterization,” we examined how the use of thermocouples can alter the measurements that are made, whether it is because the thermocouple itself acts as a fin that dissipates heat, or any of a number of other reasons [1]. We saw that even use of a very fine 36-gauge thermocouple wire can introduce measurement error of more than 5%.

The influence of the sensor on the measurement can be even more challenging as the item under test becomes smaller and more sensitive to ambient influences. As an example, a thin film made of carbon nanotubes presents an extreme challenge, as the film is only 100 nm thick, or about 1/1000 of the diameter of an average human hair. At this scale, the material has practically no thermal mass, so the temperature of the film can easily be affected by most temperature transducers. In order to create a sensor small enough to measure temperatures on the thin film, Shrestha et al. chose to use a glass micropipette as a base [2]. A sensor was then fabricated by creating a junction of dissimilar metals, using the same thermoelectric principles as a thermocouple.

Thermocouple sensors had been made using micropipettes previously, but past examples used materials that were much more expensive, and the construction was very complex. The platinum and gold materials were chosen because of their use in a biological environment, but as a thermocouple junction, they had a low voltage output in response to temperature differences [3,4]. The sensors that Shrestha et al. created were meant to address these issues.

Glass micropipettes can be made with tips so small that they are commonly used to inject substances into individual living cells. The tip diameters that Shrestha et al. created ranged from 2 to 30 µm. The micropipettes were made using a micropipette puller which heated a 1.5mm glass tube and then pulled the tube apart, creating a finely tapered section (see Figure 1a). The micropipettes were then filled with a tin based soldering alloy (Figure 1b), and a micropipette beveler was used to sharpen and achieve the finished tip shape (Figure 1c).

Fig. 1 – Creating a Micropipette Thermocouple. [2]

The next step in the construction was to coat the outside of the micropipette with a nickel film using a sputtering process (Figure 1d). On the end of the tip where the tin was exposed, the deposition of nickel created the working thermocouple junction. The deposition conditions were varied to create different film thicknesses, which we will examine later. Finally, lead wires made of tin and nickel were attached to the respective materials in the sensor (Figure 1e).

The sensors were calibrated in a water bath at temperatures from 21 to 40°C, while the cold junction was maintained at a constant 24.5°C. The voltages generated by the sensors at each temperature were recorded using a Nano voltmeter, as the measurement scale was in the range of 100µV. The calibration curves for some of the sensors are shown in Figures 2 and 3 below, where a linear response is clearly demonstrated. It can also be seen that the thicker layer of nickel significantly increased the sensitivity of the sensor, more than doubling its voltage output for a given temperature.

Fig. 2 – Voltage response of a Micropipette Thermocouple with most-nickel deposition. [2]

Fig. 3 – Voltage response of a Micropipette Thermocouple with least-nickel deposition. [2]

Shrestha et al. [2] saw sensitivities as high as 8.9 µV/°C, compared to the average of 2.1 µV/°C for the platinum-gold thermocouples made by Kakuta et al. [4]. Fish et al. [3] achieved about 7 µV/°C from their Pt-Au thermocouples, but as a point of reference, a standard J-type thermocouple has a sensitivity of about 40 µV/°C [4]. With all of the thin film-based thermocouples, the output signal is low, and measurement noise can become a problem if the environment is not well controlled. Some of the researchers found it necessary to use preamplifiers to boost the output voltage of the sensors, which complicates setup and can introduce noise.

It should also be noted that because of the sizes of all of these sensors and the test subjects, the micropipette sensors need to be positioned with micromanipulators, a basic version of which is shown in Figure 4 below.

Fig. 4 – Sutter MM-33 Micromanipulator. [6]

Clearly these are not quite like the standard thermocouples that we use for standard thermal measurements, and the setup and fabrication of the sensors is more involved. The payoff is sensors that have an extremely fast response time to temperature changes, only a few microseconds in air [3], as well as very little thermal influence on the samples they are testing, which is critical at the small scales that Shrestha et al. examined. In addition, Shrestha et al. determined that the measurement accuracy of their sensors was 0.01°C, which compares very favorably to a standard J-type thermocouple. Even with the “special limits of error” grade wire, J-type accuracy is only about 1ºC. [5]

None of the three researchers quantified the possible heat transfer through the sensor, but they were confident that it was negligible even in the context of their micrometer-scale measurements. With sensor diameters from 2 to 30 µm, the cross-sectional area is so small that the thermal resistance via conduction is very high.

This approach may be excessive for most electronics thermal management purposes, but it does illustrate that even something as familiar as a thermocouple can be approached in many different ways. The sizes of these sensors allow them to make temperature measurements with pinpoint precision, and to identify very small heat sources and heat flow paths. One such application could be localizing hot spots on a CPU die, for example. Such small sensors could generate a temperature map by traversing the surface of a die.

They could also be used to measure any small component or heat sink where a standard thermocouple would draw too much heat away. As Shrestha et al. show with their temperature measurements on a 100 nm thick film [2], the applications can vary widely, and are limited only by our preconceptions of what thermocouples are capable of.

References
1. Advanced Thermal Solutions, Inc. (ATS), “Inaccuracies in Thermocouple Measurements,” Qpedia, Issue 99.
2. Shrestha, R., Choi, T. Y., Chang, W. S., “Measurement of Thermal Conductivity of Thin and Thick Films by Steady State Heat Conduction,” University of North Texas, Denton, TX, 2012.
3. Fish, G., Bouevitch, O., Kokotov, S., Lieberman, K., Palanker, D., Turovets, I., Lewis, A., “Ultrafast Response Micropipette-Based Submicrometer Thermocouple,” The Hebrew University of Jerusalem, Jerusalem, Israel, 1994.
4. Kakuta, N., Suzuki, T., Saito, T., Nishimura, H., Mabuchi, K., “Measurement of Microscale Bio-Thermal Responses by Means of a Micro-Thermocouple Probe,” University of Tokyo, Tokyo, Japan, 2001.
5. “Thermocouple – Thermocouple types – J,” http://www.thermometricscorp.com/thermocouple.html, [Dec. 16, 2015].
6. “Sutter Instrument Company – MICROMANIPULATION,” http://www.sutter.com/MICROMANIPULATION/mm33.html, [Dec. 22, 2015].

Technical Note: Effect of Vacuum and Fill Ratio on Performance of Heat Pipes

Posted on July 17, 2018 | 7 comments

The discussion generally arises as to what would be the heat pipe performance as a function of liquid fill ratio and vacuum. Before we show some results, let’s see how a heat pipe works. The thermodynamic cycle of a heat pipe is shown in figure 1 in a T-S diagram. [1]

Fig. 1 – Thermodynamic cycle of a heat pipe. [1]

Liquid at state 1 enters the evaporator and after absorbing the heat vaporizes to a mixture at 2 or to a saturated vapor at 2’. This vapor travels through the length of the heat pipe and enters the condenser at state 3. This vapor after losing its heat in the condenser exits at state 4 which is saturated liquid and upon travelling through the wick loses its temperature until it reaches point 1, which the cycle begins. If one looks at the phase diagram for a liquid, for example water in figure 2, it is apparent that the state of the liquid should be very close to the liquid vapor line in order for the liquid to promptly changes phase from liquid to gas upon heating. The triple point of water is at 4.58 Torr at temperature of 0.0075℃.

Fig. 2 – Phase diagram of water.

The state of liquid pressure should be in the region below atmosphere (vacuum) and above the complete vacuum. To obtain lower operating temperature the heat pipe pressure should be decrease and vice versa. The state of liquid after the condenser has to be saturated liquid, so the wick can create the liquid motion.

Lin, et al. [2] have shown that maximum heat transfer in a heat pipe is an exponential function of vacuum pressure according to the following formula:

Where,
Q_max,0 = maximum heat transfer at 0 pressure (no condensable gas)
P_NCG = pressure of the non-condensable gas
∆P_cg = pressure drop difference between capillary and gravity

This equation clearly shows that by decreasing vacuum pressure, Q_max increases.

Another important factor is the amount of liquid in the heat pipe which is commonly called the fill ratio or inventory. If there is too much liquid, evaporation will not happen or delayed, and if there is not enough liquid, the dry out condition will happen. The rule of thumb is the volume of the liquid should be higher than the volume of the pore volume of the wick.

Figure 3 shows that as the pressure decreases from 10 Torr to 1 Torr the Q_max increases. The graph also shows that as the inventory (fill ratio) increases from 0.7 ml to 1.1 ml, Q_max peaks at 0.8 ml. This corresponds to a fill ratio of 26.4%, which is the ratio of the liquid volume to total volume of the heat pipe when it is empty. This graph shows the importance of fill ratio. If the fill ratio is not optimized as is shown for example for 1 Torr, Q_max drops from 8 W to 4 W, a 50% drop that can be catastrophic for the application. Mozumder et al. [3], in their experiment, measured the thermal resistance of a heat pipe for different fill ratios and power.

Fig. 3 – Q_max as a function of vacuum pressure and fill ratio for a heat pipe. [2]

Figure 4 shows that as the fill ratio increases from dry run to 85% (in their experiment fill ratio is defined as the volume of liquid to the volume of the evaporator section), thermal resistance decreases, but then increase with further increase of fill ratio.

Fig. 4 – Heat pipe thermal resistance as a function of fill ratio. [3]

The aforementioned arguments demonstrate that the fill ratio and vacuum pressure are very important in the proper design of a heat pipe. There is not much data in the literature about the effect of these two factors on the performance of the heat pipe. And it appears that most heat pipe manufacturers either resort to a try and error procedure or use the information from past experience. This topic needs further research.

Advanced Thermal Solutions, Inc. (ATS) is an industry-leader in heat pipe technology and has recently expanded its offering of high-performance, off-the-shelf heat pipes to provide the broadest selection on the market. Use the heat pipe selection tool to find the right fit for your project and avoid the cost and time for custom solutions. Learn more at https://qats.com/Products/Heat-Pipes.

References
1. Ong, S., “Heat Pipes”, Jurutera, April 2008.
2. Lin, W., Chao, C., Calvin, Y., Hsu, G., Chou, S., “Effect of vacuum pressure and the Working Fluid Inventory to the Maximum Heat Loading (Q_max) of the Heat Pipe”, 10th IHPS, Taipei, Taiwan, Nov. 6-9, 2011.
3. Mozumder, A., Akon, A., Chowdhury, M. Banik, S., “Performance of Heat Pipe with Different Working Fluids and Fill Ratios”, Journal of Mechanical Engineering, Vol. ME 41, No. 2 December 2010.

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ATS Hosting Thermal Management Webinars

Posted on July 12, 2018 | Leave a comment

Advanced Thermal Solutions, Inc. (ATS) has announced a series of monthly, online webinars covering different aspects of the thermal management of electronics. The webinars are presented by Dr. Kaveh Azar and begin on Thursday, July 26 at 1:00 p.m. Learn more and register here https://qats.com/Training/Webinars.

Author Archives: Josh Perry

Optimizing Heat Sink Base Spreading Resistance to Enhance Thermal Performance

ATS and Future Facilities Hosting Workshop

Rethinking Thermocouples: Creating Micro-Scale High Precision Sensors

Technical Note: Effect of Vacuum and Fill Ratio on Performance of Heat Pipes

ATS Hosting Thermal Management Webinars

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Author Archives: Josh Perry

Optimizing Heat Sink Base Spreading Resistance to Enhance Thermal Performance

ATS and Future Facilities Hosting Workshop

Rethinking Thermocouples: Creating Micro-Scale High Precision Sensors

Technical Note: Effect of Vacuum and Fill Ratio on Performance of Heat Pipes

ATS Hosting Thermal Management Webinars

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