1. Design of Heat Pipe Heat Exchanger
Dr. P. R. Dhamangaonkar
Associate Professor in Mechanical Engineering
Ref: Bahman Zohuri, “Heat Pipe Design and Technology”
Modern Applications for Practical Thermal Management
Second Edition, Springer International Publishing Switzerland
ISBN (eBook)
Department of Mechanical Engineering
College of Engineering Pune
Forerunners in Technical Education

2. The three basic components of a heat pipe are:
1. The container
2. The working fluid
3. The wick or capillary structure
Selection of the container material depends on many factors.
Compatibility (both with working fluid and external environment)
Strength to weight ratio
Thermal conductivity
Ease of fabrication, machineability, and ductility
Porosity
Wettability

3. The prime requirements are:
Working Fluid
The prime requirements are:
• Compatibility with wick and wall materials
• Good thermal stability
• Wettability of wick and wall materials
• Vapor pressure not too high or low over the operating range
• High latent heat
• High thermal conductivity
• Low liquid and vapor viscosities
• High surface tension
• Acceptable freezing or pour point
With the various limitations to heat flow occurring within the heat pipe such as viscous, sonic, capillary, entrainment, and nucleate boiling levels.

4. Wicker or Capillary Structure

5. How the Heat Pipe Is Working
Heat Pipe Assemblies Design Guidelines
Orientation with Respect to Gravity
For the best performance, the application should have gravity working with the system; that is, the evaporator section (heated) should be lower, with respect to gravity, than the condenser (cooling) section.
3. Depending on the wick structure, pipes will operate in environments with as low as -40 oC. Upper temperature limits depend on the fluid, but 60–80 oC is the average limit.

6. How the Heat Pipe Is Working
Heat Removal
Air cooling or liquid cooling
Reliability
Forming or Shading
Effects of Length and Pipe Diameter
The larger the diameter, the more cross-sectional area available to allow vapor to move from the evaporator to the condenser. This allows for greater power carrying capacity. Shorter heat pipes carry more power than longer pipes when used in application not assisted by gravity
8. Wick Structure

7. Certain limitations that one has to look upon
Viscous limit: In long pipes and at low temperatures, the vapor pressure is low, and the effect of viscous friction on the vapor flow may dominate over the inertial forces. In this situation, the circulation of the working fluid is limited, which, consequently, limits the heat transfer through the pipe.
2. Sonic limit: At low vapor pressures, the velocity of the vapor at the exit of the evaporator may reach the speed of sound. Then the evaporator cannot respond to further decrease in the condenser pressure. That is, the vapor flow is chocked, which limits the vapor flow rate.
3. Capillary limit: A capillary structure is able to provide circulation of a given fluid up to a certain limit. This limit depends on the permeability of the wick structure and the properties of the working fluid.

8. 4. Entrainment limit: The vapor flow exerts a shear force on the liquid in the wick which flows opposite the direction of the vapor flow. If the sheer force exceeds the resistive surface tension of the liquid, the vapor flow entrains small liquid droplets. The entrainment of liquid increases the fluid circulation but not the heat transfer through the pipe. If the capillary force cannot accommodate the increased flow, dry out of the wick in evaporator may occur.
5. Boiling limit: At high temperatures, nucleate boiling may take place which produces vapor bubbles in the liquid layer. The bubbles may block the wick pores and decrease the vapor flow. Furthermore, the presence of the bubbles decreases the conduction of heat through liquid layer which limits the heat transfer from the heat pipe shell to the liquid which is by conduction only

9. The best design and fabrication of a heat pipe is where it operates within these envelope limits which is the area below all the curves.
This area is known as best optimum design of heat pipe for the particular application of designer.

10. Decide Design Parameters
Select case material
Select working fluid
Select wick type, size and material
Calculate operating limits
Check Qmax > Q?
Evaluate thermal resistances, hence:
Th − T1 = f (Q)
Or Q = f (Th − T1)
Performance adequade?
Select thermal design and complete mechanical design or test alternatives to obtain optimum

11. Design Example
A heat pipe is required which will be capable of transferring a minimum of 15W at a vapour temperature between 0 oC and 80 oC over a distance of 1m in zero gravity (a satellite application). Restraints on the design are such that the evaporator and condenser sections are each 8 cm long, located at each end of the heat pipe and the maximum permissible temperature drop between the outside wall of the evaporator and the outside wall of the condenser is 6 oC. Because of weight and volume limitations, the cross-sectional area of the vapour space should not exceed 0.197cm2. The heat pipe must also withstand bonding temperatures.
Design a heat pipe to meet this specification.

12. Selection of materials and working fluid
As this is an aerospace application, low mass is important.
Hence aluminum alloy 6061 (HT30) is chosen for the wall and stainless steel for the wick.
The maximum vapour space area of 0.197cm2 .
If it is assumed that the heat pipe is of a circular cross section then radius is 2.5 mm.
Freon 11, Freon 113, Acetone, Ammonia are the working fluids compatible with these materials.
Water must be dismissed.
The operating limits for each fluid must now be examined.

13. Sonic limit
The minimum axial heat flux due to the sonic limitation will occur at the minimum operating temperature, 0 oC, and can be calculated by setting Mach number to unity.

14. Similar calculations carried out for the other candidate fluids, to get
The sonic limit would not be encountered for any of the candidate fluids.

15. Entrainment limit

16. Properties of candidate fluids at 80 oC
L (kJ/kg)
σl (mN/m)
ρv kg/m3
Qent (kW)
Freon 11
221
10.7
27.6
0.98
Freon 113
132
10.6
18.5
0.48
Acetone
495
16.2
4.05
1.04
Ammonia
891
7.67 34
3.75

17. Wicking limit A qualitative comparison of the
potential performance of the four fluids can be obtained by evaluating the Merit number

18. Radial heat flux
Boiling in the wick may result in the vapour blocking the supply of liquid to all parts of the evaporator. In arterial heat pipes, bubbles in the artery itself can create even more serious problems. It is therefore desirable to have a working fluid with a high superheat ΔT to reduce the chance of nucleation.

19. Freon 11, ΔT= 0.13K
Freon 113, ΔT= 0.31K
Acetone, ΔT= 0.58K
Ammonia, ΔT= 0.02K
These figures suggest that the freons and ammonia require only very small superheat temperatures at 80 oC to cause boiling. Acetone is the best fluid from this point of view.

20. A further factor in fluid selection is the priming ability.
Priming of the wick
A further factor in fluid selection is the priming ability.
A comparison of the priming ability of fluids may be obtained from the ratio ρl/ρv.
Acetone and ammonia are shown to be superior to the freons over the whole operating temperature range.

21. Wall thickness The heat pipe may reach 170 oC during bonding.
At this temperature, the vapour pressures of ammonia and acetone are 113 and 17 bar, respectively.
Taking the 0.1 per cent proof stress, Ω of HT30 aluminum as 463MN/m2 (allowing for some degradation of properties in weld regions), and using the thin cylinder formula,
There is therefore a mass penalty attached to the use of ammonia

22. Conclusions on selection of working fluid
Acetone and ammonia both meet the heat transport requirements, ammonia being superior to acetone in this respect.
Nucleation occurs more readily in an ammonia heat pipe, and the pipe may also be heavier.
The handling of ammonia to obtain high purity is difficult, and the presence of any water in the working fluid may lead to long-term degradation in performance.
Acetone is therefore selected in spite of the somewhat inferior thermal performance.

23. Detail design ΔPl+ΔPg= ΔPc Wick selection
Two types of wick structure are proposed for this heat pipe, homogeneous and arterial types.
To determine the minimum flow area to transport 15 W, equate the
maximum capillary pressure to the sum of the liquid and gravitational pressure drops (neglecting vapour P).
ΔPl+ΔPg= ΔPc

24. The effective capillary radius for the wick is 0.029 mm;

25. The wick permeability, K, is calculated using the Blake–Koseny equation

26. The gravitational pressure is ΔPg,
ΔPg = ρl.g.h = 719×9.81×0.01 = 70N/m2
The required wick area 0.26 cm2 > the available vapour space area 0.197cm2,
Hence the homogeneous type of wick is not acceptable.
An arterial wick must be used.

27. Arterial diameter
Thus, the maximum permitted value is 0.58 mm. To allow for uncertainties in fluid properties, wetting (θ assumed 0) and manufacturing tolerances, a practical limit is 0.5 mm.

28. Circumferential liquid distribution and temperature difference
The circumferential wick is the most significant thermal resistance in this heat pipe.
The temperature drop between the vapour space and the outside surface of the heat pipe and vice versa should be 3 oC maximum.
Using the steady state conduction equation the thermal conductivity of the wick is:

29. Thermal conductivity of steel=ks = 16W/m oC
Thermal conductivity acetone= kl= 0165W/m oC
∴ β = −10.2
The volume fraction ε of the solid phase is approximately 0.3
Using the basic conduction equation

30. Coarser meshes are too thick, resulting in unacceptable temperature differences across the wick in the condenser and evaporator.
We have found that the maximum permissible artery depth is 0.5 mm.
In order to prevent nucleation in the arteries, they should be kept away from the heat pipe wall and formed of low conductivity material.
It is also necessary to cover the arteries with a fine pore structure.
It is desirable to have several arteries to give a degree of redundancy.
Hence two configurations are considered, one having six arteries and the other having four arteries.
In case of 6 arteries each groove is nominally 1.0-mm wide, and in the 4 arteries case 1.5 mm.

31. Machined Stainless former
Mesh lining and inner wall artery

32. Final analysis
Let’s now predict the overall capability of the heat pipe, to check that it meets the specification.
It is shown that entrainment and sonic limitations will not be met
and that the radial heat flux is acceptable.
The heat pipe should also meet the overall temperature drop requirement, and the arteries are sufficiently small to allow repriming at 20 oC. The wall thickness requirement for structural integrity (0.1mm minimum) can easily be satisfied.
For performance assessment the core pressure drop to be assessed.

33. ΔPla+ Δ Plm+ Δ Pg+ Δ Pv= Δ Pc
The axial flow in the mesh will have little effect and can be neglected.
For the pressure loss in a rectangular duct having depth/width ratios aa/ba of 0.05−1.0.

35. The summed pressure loss in the condenser and evaporator is given by

37. The vapour pressure loss, which occurs in two near-semicircular ducts of the hydraulic radius is given as

38. Vapour Temperature, o C
Transitional load (W)
31.1 20
31.2 40
30.6 60
30.2 80
30.00
The transitional load is always greater than the design load of 15 W , it is necessary to investigate the turbulent regime.

39. For Rez > 1000 and for two ducts

40. The gravitational pressure drop =ΔPg =

41. Summarizing

42. ΔPc=ΔPlm+Δpla{6channel/4 channel}+ΔPg+ΔPv {laminar/turbulent}
Using properties at each temperature (in 20 oC increments) over the operating range, the total capability is determined:
ΔPc=ΔPlm+Δpla{6channel/4 channel}+ΔPg+ΔPv {laminar/turbulent}
Vapour
temperatures oC
Q(W)
Laminar 4 Channel
Turbulent 4 Channel
Turbulent 6Channel
21.6
21.9 20
34.0
32.5
22.6
22.0 40
42.6
40.2
27.9
27.0 60
49.1
45.8
33.0
32.0 80
51.4
47.6
36.4
35.0

43. In this example, it is assumed that the maximum resistance to heat transfer is across the wick hence the other thermal resistances have not been calculated explicitly.
This heat pipe was constructed with six grooves in the artery structure and met the specification.

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