# Heat Transfer Limitations of Heat Pipes

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## Revision as of 19:56, 12 March 2014

There are various parameters that put limitations and constraints on the steady and transient operations of heat pipes [1]. In other words, the rate of heat transport through a heat pipe is subject to a number of operating limits. Physical phenomena that might limit heat transport in heat pipes are due to capillary, sonic, entrainment, boiling, frozen startup, continuum vapor, vapor pressure and condenser effects. The heat transfer limitation can be any of the above limitations depending on the size and shape of the pipe, working fluid, wick structure, and operating temperature. The lowest limit among the eight constraints defines the maximum heat transport limitation of a heat pipe at a given temperature. The physical phenomena for each limitation are briefly presented below. A detailed presentation of the criteria for the heat transfer limitations for heat pipes are provided in Faghri [1].

## Capillary Limit

The ability of a particular capillary structure to provide the circulation for a given working fluid is limited [2][1]. This limit is commonly called the capillary limitation or hydrodynamic limitation. The capillary limit is the most commonly encountered limitation in the operation of low-temperature heat pipes. It occurs when the pumping rate is not sufficient to provide enough liquid to the evaporator section. This is due to the fact that the sum of the liquid and vapor pressure drops exceed the maximum capillary pressure that the wick can sustain. The maximum capillary pressure for a given wick structure depends on the physical properties of the wick and working fluid. Any attempt to increase the heat transfer above the capillary limit will cause dryout in the evaporator section, where a sudden increase in wall temperature along the evaporator section takes place.

## Sonic Limit

The evaporator and condenser sections of a heat pipe represent a vapor flow channel with mass addition and extraction due to the evaporation and condensation, respectively. The vapor velocity increases along the evaporator and reaches a maximum at the end of the evaporator section. The limitation of such a flow system is similar to that of a converging-diverging nozzle with a constant mass flow rate, where the evaporator exit corresponds to the throat of the nozzle. Therefore, one expects that the vapor velocity at that point cannot exceed the local speed of sound. This choked flow condition is called the sonic limitation. The sonic limit usually occurs either during heat pipe startup or during steady state operation when the heat transfer coefficient at the condenser is high. The sonic limit is usually associated with liquid-metal heat pipes due to high vapor velocities and low densities. Unlike the capillary limit, when the sonic limit is exceeded, it does not represent a serious failure. The sonic limitation corresponds to a given evaporator end cap temperature. Increasing the evaporator end cap temperature will increase this limit to a new higher sonic limit. The rate of heat transfer will not increase by decreasing the condenser temperature under the choked condition. Therefore, when the sonic limit is reached, further increases in the heat transfer rate can be realized only when the evaporator temperature increases. Operation of heat pipes with a heat rate close to or at the sonic limit results in a significant axial temperature drop along the heat pipe.

## Boiling Limit

If the radial heat flux in the evaporator section becomes too high, the liquid in the evaporator wick boils and the wall temperature becomes excessively high. The vapor bubbles that form in the wick prevent the liquid from wetting the pipe wall, which causes hot spots. If this boiling is severe, it dries out the wick in the evaporator, which is defined as the boiling limit. However, under a low or moderate radial heat flux, low intensity stable boiling is possible without causing dryout. It should be noted that the boiling limitation is a radial heat flux limitation as compared to an axial heat flux limitation for the other heat pipe limits. However, since they are related through the evaporator surface area, the maximum radial heat flux limitation also specifies the maximum axial heat transport. The boiling limit is often associated with heat pipes of non-metallic working fluids. For liquid-metal heat pipes, the boiling limit is rarely seen.

## Entrainment Limit

A shear force exists at the liquid-vapor interface since the vapor and liquid move in opposite directions. At high relative velocities, droplets of liquid can be torn from the wick surface and entrained into the vapor flowing toward the condenser section. If the entrainment becomes too great, the evaporator will dry out. The heat transfer rate at which this occurs is called the entrainment limit. Entrainment can be detected by the sounds made by droplets striking the condenser end of the heat pipe. The entrainment limit is often associated with low or moderate temperature heat pipes with small diameters, or high temperature heat pipes when the heat input at the evaporator is high.

## Vapor Pressure Limit

At low operating temperatures, viscous forces may be dominant for the vapor moving flow down the heat pipe. For a long liquid-metal heat pipe, the vapor pressure at the condenser end may reduce to zero. The heat transport of the heat pipe may be limited under this condition. The vapor pressure limit (viscous limit) is encountered when a heat pipe operates at temperatures below its normal operating range, such as during startup from the frozen state. In this case, the vapor pressure is very small, with the condenser end cap pressure nearly zero.

## Frozen Startup Limit

During the startup process from the frozen state, the active length of the heat pipe is less than the total length, and the distance the liquid has to travel in the wick is less than that required for steady state operations. Therefore, the capillary limit will usually not occur during the startup process if the heat input is not very high and is not applied too abruptly. However, for heat pipes with an initially frozen working fluid, if the melting temperature of the working fluid and the heat capacities of the heat pipe container and wick are high, and the latent heat of evaporation and cross-sectional area of the wick are small, a frozen startup limit may occur due to the freezing out of vapor from the evaporation zone to the adiabatic or condensation zone.

## Condenser Heat Transfer Limit

In general, heat pipe condensers and the method of cooling the condenser should be designed such that the maximum heat rate capable of being transported by the heat pipe can be removed. However, in exceptional cases with high temperature heat pipes, appropriate condensers cannot be developed to remove the maximum heat capability of the heat pipe. Due to the presence of noncondensible gases, the effective length of the heat pipe is reduced during continuous operation. Therefore, the condenser is not used to its full capacity. In both cases, the heat transfer limitation can be due to the condenser limit.

## Vapor Continuum Limit

For heat pipes with very low operating temperatures, especially when the dimension of the heat pipe is very small such as micro heat pipes, the vapor flow in the heat pipe may be in the free molecular or rarefied condition. The heat transport capability under this condition is limited, and is called the vapor continuum limit.

## Flooding Limit

The flooding limit is the most common concern for long thermosyphons with large liquid fill ratios, large axial heat fluxes, and small radial heat fluxes [3]. This limit occurs due to the instability of the liquid film generated by a high value of interfacial shear, which is a result of the large vapor velocities induced by high axial heat fluxes. The vapor shear hold-up prevents the condensate from returning to the evaporator and leads to a flooding condition in the condenser section. This causes a partial dryout of the evaporator, which results in wall temperature excursions or in limiting the operation of the system.

## References

1. 1.0 1.1 1.2 Faghri, A., 1995, Heat Pipe Science and Technology, 1st ed., Taylor & Francis, Washington, D.C.
2. Faghri, A., and Thomas, S., 1989, "Performance Characteristics of a Concentric Annular Heat Pipe: Part I-Experimental Prediction and Analysis of the Capillary Limit," Journal of Heat Transfer, 111(1-4), 844-850. http://dx.doi.org/10.1115/1.3250795
3. Faghri, A., Chen, M. M., and Morgan, M., 1989a, "Heat Transfer Characteristics in Two-Phase Closed Conventional and Concentric Annular Thermosyphons," Journal of Heat Transfer, 111(3), 611-618. http://dx.doi.org/10.1115/1.3250726