### 新闻分类

### 联系我们

- 地 址：哈尔滨市南岗区南通大街256号
- 电 话：13704813968
- 传 真：0451-82552085
- 邮 箱：2004777@qq.com

**CRITICAL ASPECTS OF MODELING HEAT PIPE ASSISTED HEAT SINKS
Geoffrey Thyrum, Thermacore**

**Nomenclature
**K thermal conductivity (W/m°C)

Q power (Watts)

L length

A area

dT delta-T (°C)

*Subscripts*

eff effective

evap evaporator

cond condenser

**Introduction**

Many of today’s electronic devices require cooling beyond the capability of standard cast or extruded metalheat sinks. In many applications, heat pipes have enhanced heat sink performance and have become a mainstream thermal management tool. The purpose of this paper is to provide general guidelines and highlight potential pitfalls for those who wish to perform steady state thermal analyses of heat pipe assisted heatsinks.

Reasonably accurate overall heat sink to ambient temperature gradients can be estimated utilizing simple modeling techniques, provided that the proper size and number of simulated heat pipes are included in the model. This paper will describe how to model the effect of heat pipes in a system but will not provide details of how to model the internal workings of the heat pipe. However, the limits affecting heat pipe performance shall be qualitatively reviewed to provide the reader with an understanding of heat pipe

operation and an appreciation for the complexity of predicting heat pipe performance.

**Heat pipe operation**

The cross-section of a typical heat pipe is shown in Figure 1. A heat pipe consists of a vacuum tight envelope, a wick structure and a working fluid. The heat pipe is fully evacuated and then back filled with a small quantity of

working fluid, just enough to saturate the wick. Since 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 temperatures 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 with very low thermal gradients. A heat pipe’s operation is passive, being driven only by

the heat that it transfers. This passive operation results in high reliability and long life. The details and equations describing the internal workings of heat pipes can be found in heat pipe design books (e.g., Chi,1976; Dunn and Reay, 1980; Peterson, 1994).

**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.

The maximum heat transport capability of the heat pipe is governed by several limiting factors. The following are the five primary heat pipe transport limitations (which are a function of the heat pipe operating temperature): viscous, sonic, capillary pumping, entrainment/flooding, and boiling. Each heat transport limitation is described in Table 1 (Garner, 1996). Figure 2 provides a graph of the axial heat transport limits as a function of operating temperature for a typical heat pipe with a powder metal wick. The

specific parameters of the heat pipe in Figure 2 were chosen to match the parameters of heat pipes used in a prototype design that will be discussed later in the paper.

As shown in Figure 2, the capillary limit is usually the factor limiting the heat transfer capability of a heat pipe. The capillary limit is determined by the pumping 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 can’t 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 evaporator becomes depleted of working fluid and the evaporative path for heat removal is exhausted. The only mechanism 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” (Xie et al., 1994).

The capillary limit is a strong function of the type of wick structure and the operating orientation. For example, Figure 2 shows that the capillary limit is reached at approximately 50 W for the specified heat pipe when it is at a temperature of 75 °C and in a horizontal position. If the heat pipe orientation were changed so the evaporator was vertically above the condenser, the exact same heat pipe would only be able to transport about 20 W.

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 heat pipes is:

Keff = Q*Leff/(A*dT)

Where: Leff = (Levap + Lcond)/2 + Ladiabatic

A = the cross-sectional area of the heat pipe

Q = power transported by the heat pipe

dT = the measured temperature difference across the heat pipe

This section illustrates the effective thermal conductivities of heat pipes used in three heat sink designs(Garner and Toth, 1997). Figure 3 shows the first design example used for cooling a Pentium chip that dissipates 6 to 10 Watts 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 natural convection through the case of the notebook. Figure 4 shows the second heat pipe heat sink example that cools a high-end processor for workstation and server applications. This design dissipates 75 Watts by forced convection. Figure 5 shows the third heat pipe heat sink example that was designed to cool IGBT's dissipating 4 kilowatts by forced convection.

Figure 3

Figure 4

Figure 5

Table 2 summarizes the effective thermal conductivities of the three design examples and makes the comparison with other high thermal conductivity materials (Garner and Toth, 1997). Table 2 shows that heat pipe effective conductivities 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 6 compares the predicted dT across a 31.2 cm long, 0.95 cm diameter, solid copper bar to a similarly sized heat pipe under the exact same conditions as presented in Figure 2 (operating at 75°C). As discussed in a previous section, this particular heat pipe will transport heat effectively up to 50 W before the capillary limit is reached and the evaporator end of the heat pipe starts to “dry out”. This can be seen on Figure 6 by the radical change in the heat pipe dT after 50 W. Figure 6 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 in all thermal design, the first step is to obtain as much information as possible including size and packaging constraints, estimated electrical power dissipation, velocity of air flow, required operating ambient temperature range, and maximum allowable sink to ambient temperature rise. Because of the complexity involved with heat pipe sizing and performance prediction, it is suggested that a thermal designer considering heat pipes should contact a heat pipe vendor to estimate the size and number of heat pipes required to transport the power dissipation for the particular application. This will require an initial

rough estimate of the average heat pipe operating temperature because heat pipe performance is a function of temperature. Working with the thermal designer, the heat pipe vendor can also determine the best wick material, working fluid, and attachment method for the application.

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/m-K. 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.

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, the heat pipe vendor can check the initially recommended size and number of heat pipes required for the system. Figure 2 shows that 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.

The temperature gradient across the heat pipes should also be checked to determine if they are in the expected range. The temperature gradient along a heat pipe is a function of numerous variables but is commonly in the range of 1 to 8 °C. A rough rule of thumb for estimating the heat pipe dT (for

copper/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 (Garner, 1996). 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 (See Garner, 1996, for an example calculation).

**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 effect heat pipe power transport performance. These changes in heat pipe performance won’t be accounted for in the simplified thermal model and could result in serious heat sink performance prediction errors.

This simple modeling technique provides reasonable results when the heat pipe dT is only a small fraction of the overall heat sink temperature rise. This is the case for many air cooled systems where an error of a few degrees in the predicted heat pipe dT will not create a large percentage error in the estimated overall heat sink dT. However, for liquid cooled systems where the overall heat sink dT can be much smaller, the heat pipe dT could be a larger percentage of the overall heat sink dT. Therefore, for heat sink systems requiring small overall dT’s - more effort should be made in accurately estimating the effective heat pipe conductivity.

The modeling technique presented is not adequate for transient or cold start conditions. 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

system such as the mounting block and fins. This is because the heat pipe has a high effective thermal conductivity and very little mass. For cold case thermal analyses when the ambient temperature is lower than the freezing point of the working fluid, the response of the heat pipe is more difficult to predict because the heat pipe has to thaw out. The modeling of transient or cold start conditions is beyond the scope of this paper.

**Thermal Model Example**

Figure 7 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.

This heat pipe assisted heat sink was modeled using Flotherm, version 1.4. Figure 8 shows the generated temperature predictions. The ambient temperature in the model was 23 °C and radiation was not included.The thermal model was run using three different values of effective thermal conductivity for the heat pipes.A breakdown of the predicted temperature gradients is provided 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).

As can be seen in Table 3, varying the effective thermal conductivity of the heat pipes from 10,000 to 100,000 W/m-K resulted in predicted heat pipe dT’s 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.

**Potential Pitfall Example**

As discussed earlier, problems will occur if the proper size and number of heat pipes required are not accounted for in the thermal model. To demonstrate this potential pitfall, the thermal model was modified by removing three of the four heat pipes. This was done in an attempt to simulate what could occur if the

thermal designer does not start with a good initial estimate regarding the proper size and number of heat pipes required. Using only one heat pipe with an effective thermal conductivity of 50,000 W/m-K, the predicted overall temperature rise was estimated at 59.5 °C. This prediction is only 8 °C higher than that predicted using four heat pipes. However, in reality if only one heat pipe was used, the capillary limit of the heat pipe would be exceeded making the heat pipe an ineffective heat transfer device. Figures 2 and 6 show

the predicted performance for the heat pipes used in the prototype. As discussed earlier, each heat pipe can transport a maximum of 50 W under the prescribed conditions. If the prototype actually had only one pipe and 100 W of power was applied, the heat pipe would dry out and the temperature of the copper mounting

block would probably increase until the electronic components failed.

**Conclusion**

Heat pipes offer an attractive approach in supplementing conventional heat sink solutions. Although predicting heat pipe performance is complicated, a relatively simple approach can be applied to modeling heat pipes 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.

References

? Chi, S. W., Heat pipe Theory and Practice, Hemisphere Publishing Corporation, 1976

? Dunn, P.D. and Reay, D.A., Heat Pipes, 3rd Edition, Permagon Press, 1982

? Garner, S.D., Heat Pipes for Electronics Cooling Applications, Electronics Cooling, V2, N3, Sept.

1996

? Garner, S.D., and Toth, J.E., Heat Pipes: A Practical and Cost Effective Method for Maximizing Heat

Sink Effectiveness, INTERPACK, 1997

? Peterson, G.P., An Introduction to Heat Pipes Modeling, Testing, and Applications, John Wiley and

Sons, Inc., 1994.

? 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.