Heat Pipes – Part III Operating principles: heat transfer limits
This newsletter represents the third part of a series dedicated to Heat Pipes, it follows the one dedicated to the hydraulic behaviour of this passive device, entitled: “Heat Pipes – Part II Operating principles: capillary pumping pressure”, where we introduced and described the fundamental role played by the capillary structure on the performance of a Heat pipe.
Once again Fig. 1 recalls a simple Heat Pipe configuration indicating the evaporation, adiabatic and condensation regions, as well as the liquid and vapour flow directions.
Figure 1: Heat pipe schematic.
The heat transfer characteristic of a heat pipe can be assumed to be similar to that of a very efficient thermal conductor with a very low thermal resistance, as:
where R is the total thermal resistance [k/W], which accounts for all the thermal resistances throughout the heat pipe. The most important thermal resistances are those associated to the external heat transfer on the hot and cold sides, then there are those linked to the heat pipe itself: the wall thermal resistances and the capillary structure thermal resistance on both sides.
Generally speaking, if the heat flux increases too much the Heat Pipe may fail, the evaporator dries out and the liquid cannot be pumped back from the condenser region. There are different heat transport limits, which are clearly shown in Fig. 2.
Figure 2: Heat transport limits.
First of all, the operating temperature must be in the range between the melting point Tfreeze and the critical one Tcrit; if this condition is satisfied, the maximum heat transport capacity qmax is limited by several different phenomena. The area delimited by the curves plotted in Fig. 2 represents the steady state operating conditions for a heat pipe.
The phenomena that affect a heat pipe are: viscous limit, sonic limit, capillary limit, entrainment limit, and boiling limit.
Viscous limit: this condition occurs when the operating temperatures are very close to Tfreeze; in such conditions, the vapour pressure and density are very low and the viscous forces dominate the flow behaviour. The vapour pressure drop cannot be higher than the absolute pressure near the evaporator end.
Sonic limit: this limit might be important for high temperature heat pipes with metallic fluids. If one decreases the temperature and thus the pressure in the condenser at a constant evaporator temperature a rising heat flow and rising fluid flow velocities will be the results. The sonic limit is reached when the vapour velocity at the evaporator exit reaches the sonic one. In these conditions, the heat flow cannot be further increased by a pressure or temperature reduction in the condenser.
Capillary limit: this condition was studied in the second part of these newsletter’s series; to keep the fluid circulating, the capillary pumping pressure provided by the capillary structure must be higher, at least, equal to the pressure drops generated in the vapour and liquid phases, plus, if present, the gravitational pressure drop.
∆Pc1max ≥ ∆PL + ∆Pv + ∆Pg
In normal operation, the capillary limit is the most important and fixes the limiting conditions. If the analysis of a designed heat pipe shows that the capillary structure is not able to ensure the liquid to be returned to the evaporator, the design itself must be changed.
Entrainment limit: this limit can be reached only in heat pipes with open capillary structures where the vapour and liquid flow counter-currently generating a shear force at the fluid interface. When increasing heat flux, the vapour and liquid velocities rise until the shear forces might destabilized the interface and surface waves may be generated. The vapour flowing toward the condenser can entrain some liquid droplet from the liquid interface. This situation occurs when shear forces exceed the surface tension forces.
Boiling limit: when increasing the heat flux the wall superheats in the evaporator region activating potential nucleation sites at the solid-liquid interface and vapour bubbles might be generated inside the capillary structure. If the capillary structure is open, the vapour can easily escape; otherwise, in sintered structures, covered grooves, or meshes the growing bubbles might interrupt the capillary driven condensate flow or even cause a local dry out.
In order to have an order of magnitude of the different limits, we can consider a heat pipe used for electronic cooling in a satellite. It is designed for a heat flux of 50 W at 10 °C of saturation temperature using ammonia as working fluid. The heat pipe is made of an aluminum tube with 32 rectangular axial open grooves (w=0.5 mm and h=0.8 mm). The tube has a ID= 9 mm and OD=14 mm. The length of the adiabatic zone is 780 mm whereas the evaporator and condenser regions are 100 mm long.
In the previous newsletter, the maximum capillary pumping pressure was calculated and it was equal to 107 Pa. At the design conditions the capillary pressure difference is equal to around 40 Pa, which is lower then the maximum capillary pumping pressure.
By applying the correlations proposed for the evaluation of the viscous, sonic, capillary, entrainment, and boiling limits, the results listed in Table can be obtained.
From the analysis of the data in Table, we can state that the capillary limit controls the heat pipe operation; the boiling limit is not relevant in this case because the capillary structure is open.
The heat pipes represent a smart and efficient way to transfer heat from one zone to another where it can be easily rejected without any moving part; their design must be carefully considered in order to avoid any failure during their operation.
References
- G.P. Paterson, An introduction to heat pipes. Modeling, Testing, and Applications, Ed. John Wiley and Sons, 1994, New York, USA.
- D. Reay, P. Kew, Heat Pipes – Theory, Design and Applications, 5th ed., Ed. Elsevier, 2006, Burlington, MA , USA
- P. Stephan, Heat Pipes, N5 VDI
Correlated Topics
- Heat Pipes – Part I: from aerospace to air conditioning applications
- Heat Pipes – Part II Operating principles: capillary pumping pressure.
- Wraparound Heat Pipes for air conditioning applications
