COVER STORY
A simplified technique for modeling heat pipe assisted heat sinks
BY GEOFFERY THYRUM AND ELLEN CRUSE
The trend in the electronics industry of packing more power into smaller packages has created increasing thermal management challenges. Many of today's electronic devices require cooling beyond the capability of standard cast or extruded metal heat sinks. In many applications, heat pipes have enhanced heat sink performance and have become a mainstream thermal management tool.
Heat Pipe Operation
A heat pipe consists of a vacuum tight envelope, a wick structure and a working fluid (Figure 1). The heat pipe is fully evacuated and then back-filled with a small quantity of working fluid, just enough to saturate the wick. Because the working fluid – typically water in electronics cooling – is the only dynamic component in the heat pipe, the pressure inside the pipe is equal to the saturation pressure associated with the heat pipe temperature. As heat enters at the evaporator, equilibrium is upset, generating vapor at a slightly higher pressure and temperature. The higher pressure causes vapor to travel to the condenser end where the slightly lower temperature causes the vapor to condense and give up its latent heat of vaporization. The condensed fluid is then pumped back to the evaporator by the capillary forces developed in the wick structure. This continuous cycle can transfer large quantities of heat even with very low thermal gradients. A heat pipe's operation is passive, being driven only by the heat that it transfers, which results in high reliability and long life.1-3
Limits to Heat Transport
Heat pipes can be sized or designed to carry a few watts or several kilowatts, depending on the application. For a given temperature gradient, heat pipes can transfer significantly more heat than even the best metal conductors. When driven beyond its rated capacity, however, the effective thermal conductivity of the heat pipe will be drastically reduced. Therefore, it is important to design the heat pipe to safely transport the required heat load.
 Figure 1. The structure and functioning of a heat pipe. |
The maximum heat transport capability of the heat pipe is governed by several limiting factors (which are a function of the heat pipe operating temperature): viscous, sonic, capillary pumping, entrainment/flooding and boiling (Table 1).4
 Figure 2. The heat pipe for example 1, a 25 W microprocessor. |
The capillary limit is usually the factor limiting the heat transfer capability of a heat pipe. It is determined by the pump-ing capacity of the wick structure. The capillary limit is exceeded when the heat flux into the pipe is so high that the pumping force provided by the wick structure does not provide for an adequate flow of working fluid back to the evaporator. When the mass flow rate of the vapor leaving the evaporator is greater than the mass flow rate of the working fluid returned to the evaporator through the wick structure, the wick in the evapo-rator becomes depleted of working fluid and the evaporative path for heat removal is exhausted. The only mecha-nism left for heat removal from the evaporator is conduction through the thin wall and wick structure of the heat pipe. When this occurs, the effective thermal conductivity of the heat pipe is drastically reduced and the heat pipe is often referred to as being “dried out.”5
Heat Pipe Effective Conductivity
Because heat pipes are two-phase heat transfer devices that do not have relatively constant thermal conductivities like solid materials, an effective thermal conductivity is used. The equation used to calculate the effective thermal conductivity for a heat pipe is:
Keffective = QLeffective/(A ΔT)
Where: Leff = (Levaporator + Lcondenser)/2 + Ladiabatic
K = thermal conductivity
L = length
A = the cross-sectional area of the heat pipe
Q = power transported by the heat pipe
ΔT = the measured temperature difference across the heat pipe.
Three examples discussed here illustrate the effec-tive thermal conductivities of heat pipes used in differ-ent applications.6 Figure 2 shows an example designed for cooling an 800+ MHz Pentium processor with a heat load of 25 W in a notebook computer. The heat pipe transfers the high heat flux at the die interface to a large condenser area where the heat is dissipated by forced convec-tion using fans with 3 cfm of airflow. Another heat pipe heat sink can cool a high-end processor for workstation and server applications. This design can dissipate 90 W by forced convec-tion. A third heat pipe heat sink type can cool isolated gate bipolar transistors (IGBTs) dissi-pating 4 kW by forced convection.
 Table 1. Heat pipe heat transfer limitations. |
Table 2 summarizes the effective thermal conductivities of the three design examples and makes the comparison with other high ther-mal conductivity materials.6 Table 2 shows that heat pipe effective con-ductivities range in value but are significantly higher than some of the best thermally conductive materials available. The effective thermal conductivity of heat pipes is high until one of the heat pipe limits is reached. Once the heat pipe power limit is reached, the heat pipe becomes an ineffective heat transfer device. For example, Figure 3 compares the predicted ΔT across a 31.2 cm long, 0.95 cm diameter, solid copper bar to a similarly sized heat. This particular heat pipe will transport heat effectively up to 50 W before the capillary limit is reached and the evapora-tor end of the heat pipe starts to “dry out.” Figure 3 also demonstrates how poorly a solid copper bar performs compared to the heat pipe operating within its design range.
Guidelines for Modeling Heat Pipe Assisted Heat Sinks
As demonstrated previously, heat pipe performance is a function of numerous variables and a heat pipe's effective thermal conductivity varies with different designs. However, with a reasonably good estimate of the size and number of heat pipes required for the application, the heat pipe can be approximated by modeling it as a solid bar with a high thermal conductivity. As a first approximation for most applications, it is recommended that the heat pipes be modeled with a thermal conductivity of 50,000 W/mK. It is common for heat pipes to be soldered or epoxied to the evaporator plate and/or the heat sink. Typically, epoxy interface resistances range from 0.75 to 1.5°C/(W/cm2), and solder interface resistances range from 0.25 to 0.75°C/(W/cm2). The interface resistances should be included in the model to determine their impact on the thermal performance.
 Figure 3. Copper/water heat pipe performance, compared to a copper bar of the same dimensions. |
The next step is to generate and run the heat sink system model. From this first iteration, a good estimate of the average heat pipe temperature can be obtained. With this information, it is possible to check the size and number of heat pipes in the initial design because, for example, heat pipe performance varies significantly with average heat pipe temperature. If the initial rough estimate of the average heat pipe operating temperature was significantly off, the initial heat pipe sizing could be significantly off, and the model may need to be updated to include a more accurate representation of the size and number of heat pipes required.
 Figure 4. The design of the heat pipe assisted heat sink discussed. |
The temperature gradient along a heat pipe is a function of numerous variables but is com-monly in the range of 1 to 8°C. A rough rule of thumb for estimating the heat pipe ΔT (for cop-per/water heat pipes) is to use 0.2°C/(W/cm2) for thermal resistance at the evaporator and condenser, and 0.02°C/(W/cm2) for axial resistance.4 The evaporator and condenser resistances are based on the outer surface area of the pipe. The axial resistance is based on the cross-sectional area of the vapor space. This design guide is only useful for powers at or below the design power for the given heat pipe.
Modeling Constraints
Because the heat pipes are being modeled as simple bars with high thermal conductivities, the thermal model must be re-examined if the design criteria is altered. Changes in the heat sink orientation, power dissipation, air flow, or ambient operating temperatures can significantly affect heat pipe power transport performance. These changes in heat pipe performance will not be accounted for in the simplified thermal model and could result in serious heat sink performance prediction errors.
 Table 2. Heat pipe effective thermal conductivities. |
This simple modeling technique provides reasonable results when the heat pipe ΔT is only a small fraction of the overall heat sink temperature rise. This is the case for many air cooled sys-tems where an error of a few degrees in the predicted heat pipe ΔT will not create a large percentage error in the estimated overall heat sink ΔT. However, for liq-uid cooled systems where the overall heat sink ΔT can be much smaller, the heat pipe ΔT could be a larger percentage of the overall heat sink ΔT. Therefore, for heat sink sys-tems requiring a small overall ΔT, more effort should be made in accurately esti-mating the effective heat pipe conductivity.
 Table 3. Thermal predictions with varying heat pipe effective thermal conductivity. |
The modeling technique presented is not adequate for transient or cold start condi-tions. For hot case transient thermal analyses when the ambient temperature is higher than the freezing point of the working fluid, the response time of the heat pipe is typically much faster than the other components of the heat sink sys-tem such as the mounting block and fins. This is because the heat pipe has a high effective thermal con-ductivity and very little mass. For cold case thermal analyses when the ambient temperature is lower than the freez-ing point of the working fluid, the response of the heat pipe is more difficult to predict because the heat pipe has to thaw out.
Thermal Model Example
Figure 4 provides a drawing of a prototype heat pipe assisted heat sink. The assembly consists of a copper block for mounting the electrical components, four 0.95 cm diameter heat pipes soldered into the copper block, and 17 aluminum fins. This prototype was designed to dissipate 100 W using natural convection.
 Figure 5. Temperature contours in the modeling output for the heat pipe assisted heat sink discussed in the text and illustrated in Figure 4. |
This heat pipe assisted heat sink was modeled using Flotherm, version 1.4 (Figure 5). The ambient temperature in the model was 23°C and radiation was not included. The ther-mal model was run using three different values of effective thermal conductivity for the heat pipes. A breakdown of the predicted tempera-ture gradients is pro-vided in Table 3. The prototype was tested with 100 W of power dissipation and the measured heat sink rise above ambient was 50°C which compares well to the predicted values (ranging from 51.0 to 54.5°C).
Varying the effective thermal conductivity of the heat pipes from 10,000 to 100,000 W/mK resulted in a predicted heat pipe ΔT of 4 to 0.5°C. In this natural convection air cooled assembly, the bulk of the overall temperature rise comes from the fin to air resistance. Therefore, large differences in the estimation of the heat pipe thermal conductivity resulted in relatively small changes to the predicted total rise above ambient.
Conclusion
Heat pipes offer an attractive approach in supplementing conventional heat sink solutions for some applications. Although predicting heat pipe performance is complicated, a relatively simple approach can be applied to modeling heat pipe assisted heat sinks. The simplified modeling technique does not account for heat pipe limitations and can provide overly optimistic thermal performance predictions if the design parameters change and the thermal model is not re-evaluated and appropriately updated to account for these changes. AP
References for this article are available at www.apmag.com.
References
- Chi, S. W., Heat Pipe Theory and Practice, Hemisphere Publishing Corporation, 1976.
- Dunn, P.D. and Reay, D.A., Heat Pipes, 3rd Edition, Pergamon Press, 1982.
- Peterson, G.P., An Introduction to Heat Pipes: Modeling, Testing, and Applications, John Wiley and Sons, Inc., 1994.
- Garner, S.D., “Heat Pipes for Electronics Cooling Applications,” Electronics Cooling, Vol. 2, No. 3, Sept. 1996.
- Xie, H., Aghazadeh, M., and Toth, J., “The Use of Heat Pipes in the Cooling of Portables with High Power Packages – A Case Study with the Pentium Processor-Based Notebooks and Sub-notebooks,” 1994 Intersociety Energy Conversion Engineering Conference, www.thermacore.com/papers.htm.
- Garner, S.D., and Toth, J.E., “Heat Pipes: A Practical and Cost Effective Method for Maximizing Heat Sink Effectiveness,” INTERPACK, 1997.
Geoffrey Thyrum, market development manager, and Ellen Cruse, marketing communications manager, can be contacted at Thermacore, 780 Eden Road, Lancaster, PA 17604-3243; 717-569-6551; Fax: 717-569-8424; E-mail: [email protected] and [email protected].
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