ESDU (3)

ESD

U C

opyr

ight

mat

eria

l. F

or c

urre

nt s

tatu

s co

ntac

t ESD

U.

ESDU 79013

Endorsed byThe Institution of Mechanical EngineersThe Institution of Chemical Engineers

Heat pipes – properties of commonsmall-pore wicks

Issued November 1979

ESD

U C

opyr

ight

mat

eria

l. F

or c

urre

nt s

tatu

s co

ntac

t ESD

U.

ESDU 79013ESDU DATA ITEMS

Data Items provide validated information in engineering design and analysis for use by, or under the supervisionof, professionally qualified engineers. The data are founded on an evaluation of all the relevant information, bothpublished and unpublished, and are invariably supported by original work of ESDU staff engineers or consultants.The whole process is subject to independent review for which crucial support is provided by industrial companies,government research laboratories, universities and others from around the world through the participation of someof their leading experts on ESDU Technical Committees. This process ensures that the results of much valuablework (theoretical, experimental and operational), which may not be widely available or in a readily usable form, canbe communicated concisely and accurately to the engineering community.

We are constantly striving to develop new work and review data already issued. Any comments arising out of youruse of our data, or any suggestions for new topics or information that might lead to improvements, will help us toprovide a better service.

THE PREPARATION OF THIS DATA ITEM

The work on this particular Item was monitored and guided by the following Working Party:

on behalf of the Heat Transfer Steering Group which first met in 1966 and now has the following membership:

The Steering Group has benefited from the participation of members from several engineering disciplines. Inparticular, Mr E.C. Firman has been appointed to represent the interests of mechanical engineering as the nomineeof the Institution of Mechanical Engineers and Dr G.F. Hewitt has been appointed to represent the interests ofchemical engineering as the nominee of the Institution of Chemical Engineers.

The work on this Item was carried out in the Heat Transfer Group of ESDU under the supervision of Mr N. Thompson,Group Head. The member of staff who undertook the technical work involved in the initial assessment of the availableinformation and the construction and subsequent development of the Item was

Dr D. Chisholm — National Engineering LaboratoryMr J.B. Goodacre — Marconi Research Laboratories, ChelmsfordMr G. Rattcliff — Isoterix LtdMr D.A. Reay — International Research and Development Co. LtdDr G. Rice — Reading University

ChairmanDr G.F. Hewitt — HTFS, Atomic Energy Authority, Harwell

Vice-ChairmanProf. V. Walker — Bradford University

MembersDr T.R. Bott — Birmingham UniversityMr E.C. Firman — IndependentMr J.A. Hitchcock — Central Electricity Research LaboratoriesProf. R.H. Sabersky*

* Corresponding Member

— California Institute of Technology, USAMr E.A.D. Saunders — Whessoe LtdMr R.A. Smith — Imperial Chemical Industries LtdMr M.A. Taylor — B.N.O.C. (Developments) LtdMr N.G. Worley — Babcock and Wilcox (Operations) Ltd.

Dr A. Acton — Senior Engineer.

ESD

U C

opyr

ight

mat

eria

l. F

or c

urre

nt s

tatu

s co

ntac

t ESD

U.

i

ESDU 79013HEAT PIPES – PROPERTIES OF COMMON SMALL-PORE WICKS

CONTENTS

Page

1. NOTATION AND UNITS 1

2. INTRODUCTION 2

3. EFFECTIVE THERMAL CONDUCTIVITY 2

4. MINIMUM CAPILLARY RADIUS 3

5. PERMEABILITY 4

6. REFERENCES AND DERIVATION 4

7. EQUATIONS FOR WICK PROPERTIES 77.1 Table of Equations 77.2 Notes on Equations 11

FIGURES 1 AND 2 13

ESD

U C

opyr

ight

mat

eria

l. F

or c

urre

nt s

tatu

s co

ntac

t ESD

U.

ESDU 79013
HEAT PIPES – PROPERTIES OF COMMON SMALL-PORE WICKS
1. NOTATION AND UNITS

Excepting angles (degrees), the SI system of units is used throughout.

cross-sectional area m2

width of groove in rectangular-groove wick m

constants in equation for permeability of metal-felt wick m2 , 1/m2

width of land (ridge) between grooves in rectangular-groove wick m

equivalent diameter, 4 A/P for a duct or 4(volume of pores)/(surface area of pores) for a porous material

m

wire diameter, average particle diameter, fibre diameter m

permeability factor

fluid permeability of wick m2

length of wick m

mass flow rate kg/s

number of apertures per unit length of mesh screen 1/m

perimeter of duct m

axial Reynolds number for liquid in wick,

minimum capillary radius m

wick thickness m

superficial liquid velocity in wick, m/s

aperture of mesh screen m

term in equation for permeability of metal-felt wick

half angle of triangular-section wick degrees

pressure drop in liquid Pa

maximum capillary pressure difference Pa

porosity, (volume of pores)/(volume of porous material)

A

b

C1 , C2

c

DE

d

F

K

l

M·

N

P

RelρlVlDEl/ εµl( )

rσ

tw

Vl M· / Awρl( )

w

y

α

pl∆

pσ∆

ε

1

Issued November 1979

ESD

U C

opyr

ight

mat

eria

l. F

or c

urre

nt s

tatu

s co

ntac

t ESD

U.

ESDU 79013

2. INTRODUCTION

This Data Item, which is one of a series concerned with heat pipes, gives data on the effective thermalconductivity, the minimum capillary radius and the permeability of small-pore wicks that are commonlyused in heat pipes. A small-pore wick is one in which capillary forces can support a height of liquid that iscomparable with the wick length, l, along which liquid flows. This length is usually equal to the length ofthe heat pipe. The Data Item is primarily intended for use with a companion Data Item in the series(Reference 3) for calculating the thermal performance of capillary-driven heat pipes whenever experimentalwick property data are unavailable. However, the data also apply to other types of heat pipe.*

The individual properties are briefly discussed in Sections 3, 4 and 5 and equations for these properties aregiven in Section 7. Accuracy information in terms of scatterbands containing 80 per cent of the experimentaldata are also included in Section 7 for the equations giving the minimum capillary radius and thepermeability. The experimental data for the effective thermal conductivity show large scatter and in extremecases the equations for the thermal conductivity can be in error by a factor of ten.

3. EFFECTIVE THERMAL CONDUCTIVITY

Many wick structures are anisotropic and the effective thermal conductivity is different for differentdirections of heat flow. It is the effective conductivity, , in the direction through the wick thicknessnormal to the heat-pipe wall that is usually required; approximate equations for are given in Section 7.In the few cases in which effective thermal conductivities in other directions are required (e.g. to establishwhether or not axial conduction in a heat pipe is important), it is almost always sufficiently accurate to use

, as defined here.

contact angle degrees

thermal conductivity W/(m K)

liquid dynamic viscosity N s/m2

liquid density kg/m3

surface tension N/m

Subscripts

refers to liquid or liquid flow-channel

refers to solid material of wick

refers to wick

refers to wick capillary

* It is intended to issue a Data Item giving introductory information on common types of heat pipe. Other planned Data Items will dealwith the physical properties of working fluids and with the performance of two-phase closed thermosyphons.

θ

λ

µl

ρl

σ

l

s

w

σ

λwλw

λw

2

ESD

U C

opyr

ight

mat

eria

l. F

or c

urre

nt s

tatu

s co

ntac

t ESD

U.

ESDU 79013
The effective thermal conductivity of a liquid-saturated wick is generally a function of the porosity, , andthe thermal conductivities, and , of the two components present, the working liquid and the solidmaterial. In any two-component mixture, lies between two extremes, a lower limit obtained assumingthat the components are effectively in series,
, (3.1)

and an upper limit obtained assuming that the components are effectively in parallel,

. (3.2)

Equations (3.1) and (3.2), whilst providing limits for that are sometimes useful, do not properly takeaccount of the structure of most wicks. This becomes important if and are appreciably different fromone another (e.g. for a water working fluid and a porous copper wick) because the two limits are then toofar apart to be of any practical use. In such cases, the equations in Section 7, by taking account of the wickstructure, represent a significant improvement on the use of Equations (3.1) and (3.2).

The thermal conductivities of some nearly-pure solid metals can be considerably reduced by smallpercentages of impurity; the effect is most significant at sub-ambient temperature, but can be important atambient temperature. For example, less than 2 per cent by mass of phosphorus reduces the thermalconductivity of copper by almost a factor of ten at 288 K (15 °C), see Derivation 17. It is therefore unsafeto use the thermal conductivity of the pure metal if there is impurity present even in small quantities.

4. MINIMUM CAPILLARY RADIUS

The shape of the pores in many small-pore wicks is complex but, for the calculation of capillary pumpingproperties, these wicks can be characterised by the minimum capillary radius of the structure, . Thisradius is a function of the pore size and shape but it is independent of the nature of the fluid in the wick; itis defined by the equation

. (4.1)

The equations for in Section 7 correlate data obtained by “falling column”, “rising column” and “bubbletest” experiments, all of which measure the maximum capillary pressure difference, . Systematicdifferences between data obtained using the different experimental methods are sometimes reported, butthese differences are small in comparison with the scatter of the data from the various sources. In very fewcases is information on the contact angle, , reported. Therefore, the equations have been obtained withthis angle set equal to zero. The contact angle should, in most cases, have been small or zero because theexperimental data are generally for thoroughly cleaned surfaces and fluids that wet these surfaces easily.

From the practical point of view it is worth noting that oxidised surfaces usually give smaller contact anglesthan unoxidised surfaces with the same fluid; consequently it may be worthwhile using oxidised surfacesin order to obtain a high value of .

ελl λs

λw

λw λlλs 1 ε–( )λl ελs+[ ]⁄=

λw ελl 1 ε–( )λs+=

λwλl λs

rσ

rσ 2σ θ ∆pσ⁄cos=

rσpσ∆

θ

pσ∆

3

ESD

U C

opyr

ight

mat

eria

l. F

or c

urre

nt s

tatu

s co

ntac

t ESD

U.

ESDU 79013
5. PERMEABILITY
The permeability is a function of the size and shape of the channels through which liquid flows. Providedthat the flow rate is sufficiently low, so that the flow can be considered to be laminar and so that inertialeffects are insignificant, the permeability is independent of flow rate and the nature of the liquid in thewick. This is usually the case for heat-pipe wicks. Layered wicks, such as multiple mesh screens and metalfelts, are anisotropic and the permeability is different for different directions of liquid flow. These wicksare normally used in heat pipes with the flow in the plane of the layers, and it is the permeability in thisplane that is required. The permeability is defined by the equation

. (5.1)

The equations in Section 7 correlate experimental permeability data for typical heat-pipe wicks. Themaximum Reynolds numbers up to which these equations are valid and equations for the equivalentdiameters on which the Reynolds numbers are based are also given in Section 7.

The permeability data were obtained for a uniform mass flow rate in the wick whereas in an operating heatpipe the mass flow rate varies along the lengths of the evaporator and condenser. The maximum mass flowrate occurs in the adiabatic section or at the junction of the evaporator and the condenser if there is noadiabatic section. Pressure drops along a heat pipe are obtained from the maximum mass flow rate inconjunction with effective lengths rather than the true evaporator and condenser lengths; the Reynoldsnumber is also calculated from the maximum mass flow rate. Assuming that all of the heat input to the heatpipe goes towards evaporating liquid, the maximum mass flow rate equals the overall rate of heat transferby the pipe divided by the specific latent heat of vaporisation of the working fluid.

6. REFERENCES AND DERIVATION

References

The References given are recommended sources of information supplementary to that in this Data Item.

Derivation

The Derivation lists selected sources that have assisted in the preparation of this Data Item.

1. UHLEMANN, H.MARKS, C.J.A.Th.SPIGT, C.L.

Flow resistance in screen wick structures. Proceedings of the 1stInternational Heat Pipe Conference, Stuttgart, West Germany, Paper6-3, 1973.

2. BSI Specification for test sieves, BS 410, British Standards Institution,London, 1976.

3. ESDU Heat pipes – performance of capillary-driven designs. Data Item No.79012, ESDU International plc, London, 1979.

4. GORRING, R.L.CHURCHILL, S.W.

Thermal conductivity of heterogeneous materials. Chem. Eng. Prog.,Vol. 57, No. 7, pp. 53-59, 1961.

5. ESDU Friction losses for fully-developed flow in straight pipes. Data Item No.66027, ESDU International plc, London, 1966.

K lM· µl / Aw∆plρl( )=

4

ESD

U C

opyr

ight

mat

eria

l. F

or c

urre

nt s

tatu

s co

ntac

t ESD

U.

ESDU 79013
6. KATZOFF, S. Heat pipes and vapor chambers for thermal control of spacecraft. Am.
Inst. Aeronaut. Astronaut., Paper 67-310, 1967.

7. FREGGENS, R.A. Experimental determination of wick properties for heat pipeapplications. Proceedings of the 4th Intersociety Energy ConversionEngineering Conference, Washington D.C., USA, pp. 888-897, 1969.

8. LANGSTON, L.S.KUNZ, H.R.

Liquid transport properties of some heat pipe wicking materials. Am.Soc. mech. Engrs, Paper 69-HT-17, 1969.

9. PHILLIPS, E.C.HINDERMAN, J.D.

Determination of properties of capillary media useful in heat pipedesign. Am. Soc. mech. Engrs, Paper 69-HT-18, 1969.

10. FERRELL, J.K. ALLEAVITCH, J.

Vaporization heat transfer in capillary wick structures. Chem. Eng.Prog. Symp. Series, Vol. 66, No. 102, pp.82-91, 1970.

11. SOLIMAN, M.M.GRAUMANN, D.W.BERENSON, P.J.

Effective thermal conductivity of dry and liquid-saturated sintered fibermetal wicks. Am. Soc. mech, Engrs, Paper 70-HT/SpT-40, 1970.

12. TIEN, C.L. SUN, K.H.

Minimum meniscus radius of heat pipe wick materials. Int. J. HeatMass Trans., Vol. 14, pp.1853-1855, 1971.

13. CHUN, K.R. Some experiments on screen wick dry-out limits. Trans. am. Soc. mech.Engrs, Series C, J. Heat Transfer, Vol. 94, pp. 46-51, 1972.

14. MARCUS, B.D. Theory and design of variable conductance heat pipes. NASA CR-2018,National Aeronautics and Space Administration, USA, 1972.

15. ROBERTS, C.C.FELDMAN, Jr, K.T.

Predicting performance of heat pipes with partially saturated wicks.Am. Soc. mech. Engrs, Paper 72-WA/HT-38, 1972.

16. BIRNBREIER, H. GAMMEL, G.

Measurement of the effective capillary radius and the permeability ofdifferent capillary structures. Proceedings of the 1st International HeatPipe Conference, Stuttgart, West Germany, Paper 5-4, 1973.

17. CHILDS, G.E.ERICKS, L.J.POWELL, R.L.

Thermal conductivity of solids at room temperature and below (areview and compilation of the literature). NBS Monograph No. 131,U.S. Dept. of Commerce/National Bureau of Standards, 1973.

18. FELDMAN, Jr, K.T.BERGER, M.E.

Analysis of a high-heat-flux water heat pipe evaporator. TechnicalReport ME-62(73) ONR-012-2, University of New Mexico,Albuquerque, New Mexico, USA, 1973.

19. FERRELL, J.K.ALEXANDER, E.G.PIVER, W.T.

Vaporization heat transfer in heat pipe wick materials. AIAA progress inastronautics and aeronautics: thermal control and radiation, Vol. 31,pp. 3-18, Editor C.L. Tien, MIT Press, Cambridge, Mass., 1973.

20. HOOGENDOORN, C.J. NIO, S.G.HARDY, H.J.J.

Permeability studies on wire screens and grooves. Proceedings of the1st International Heat Pipe Conference, Stuttgart, West Germany, Paper5-3, 1973.

21. KESER, D. Experimental determination of properties of saturated sintered wicks.Proceedings of the 1st International Heat Pipe Conference, Stuttgart,West Germany, Paper 6-1, 1973.

22. DUL’NEV, G.N.ZARICHNYAK, Yu.P.

Thermal conductivity of blends and compound materials. Energiya(USSR), 1974 (in Russian).

5

ESD

U C

opyr

ight

mat

eria

l. F

or c

urre

nt s

tatu

s co

ntac

t ESD

U.

ESDU 79013
23. GOODACRE, J.B. Study of heat pipe wick structures – phase 2. Final Technical Report on
Contract No. K/GW31a/135, Marconi Ltd, UK, 1974.

24. SEMENA, M.G.KOSTORNOV, A.G.et al.

Investigation of the structural and hydrodynamic characteristics of thewicks of heat pipes. High Temperature, Vol. 13, No. 1, pp.137-140,1975.

25. VANSANT, J.H.MALET, J.R.

Thermal conductivity of some heat pipe wicks. Lett. Heat Mass Trans.,Vol. 2, pp.199-206, 1975.

26. CHI, S.W. Heat pipe theory and practice. Hemisphere Publishing Corporation,Washington/London, 1976.

27. DEAN, D.J. An integral heat pipe package for microelectronic circuits. Proceedingsof the 2nd International Heat Pipe Conference, Bologna, Italy,pp.481-502, 1976.

28. DUNN, P.D.REAY, D.A.

Heat pipes. Pergamon Press, Oxford, 1976.

29. FINLAY, I.C.LOY, B.CREE, D.G.

Manufacture and performance of a water filled heat pipe with a sinteredcopper wick. Proceedings of the 2nd International Heat PipeConference, Bologna, Italy, pp. 93-101, 1976.

30. SEMENA, M.G.ZARIPOV, V.K.

Influence of the diameter and length of fibres on material heat transferof metal-fibre wicks of heat pipes. Thermal Engineering, Vol. 24, No. 4,pp. 69-72, 1977.

31. CHAIKOVSKY, V.SMIRNOV, G.et al.

Complex investigation of characteristics and processes inartery-grooved heat pipes. A collection of technical papers – 3rdInternational Heat Pipe Conference, Palo Alto, California, USA,pp. 426-433, 1978.

32. EASTMAN, G.Y.ERNST, D.M.

High performance, high temperature heat pipes. A collection oftechnical papers – 3rd International Heat Pipe Conference, Palo Alto,California, USA, pp. 268-273, 1978.

33. – Product data from Brunswick Corporation, Florida, USA, 1979.

6

ESD

U C

opyr

ight

mat

eria

l. F

or c

urre

nt s

tatu

s co

ntac

t ESD

U.

ESDU 79013
7. EQUATIONS FOR WICK PROPERTIES
7.1 Table of Equations

Wick Type*

* In the sketches the axis of the heat pipe and therefore the direction of fluid flows are normal to the plane of the paper unless stated otherwise.

Thermal conductivity

PorosityEquation†

† Figures in brackets refer to notes in Section 7.2.

Derivation Numbers(see Section 6)

Single-layer wire mesh screens (heat-pipe axis in plane of paper in this sketch)

N = number of apertures per unit (m) of screen

–

(1)

18, 31

26, 28

Multiple wire mesh screens‡, plain orsintered (screen dimensions as forsingle layers illustrated above)

‡ These wicks are positioned so that the layers follow the contour of the inner surface of the heat-pipe wall.

(2)

19, 21, 25, 26

Best obtained experimentally, but can be estimated from the equation for single screens

Unconsolidated packed spherical particles (d = average particle diameter)

Plain

(3)

4, 26

Depends on packing mode and should be measured. A very rough estimate can be obtained assuming cubic packing,

Sintered 19, 21, 28

Sintered felted metal fibres‡

(d = fibre diameter)

(4)

11, 19, 22, 30, 33Obtain experimentally or use manufacturer’s data

d

w

1N---- d w+=

twScreen

Annular

λw λl= ε 1=

tw

αα

Screen

Screen-covered grooves(isosceles triangle)

λw 0.85λs λl/ λs αsin( )[ ]0.63≈ε 0.5=

tw

b

c

Screen

Screen-covered grooves(rectangle)

λw ελl 1 ε–( )λs+≈ ε bb c+-----------=

tw λw

λl λl λs 1 ε–( ) λl λs–( )–+[ ]

λl λs 1 ε–( ) λl λs–( )+ +--------------------------------------------------------------------≈

ε 1πNd

4----------–≈

twλw

λl 2λl λs 2 1 ε–( ) λl λs–( )–+[ ]

2λl λs 1 ε–( ) λl λs–( )+ +---------------------------------------------------------------------------≈

ε 0.48≈λw

λs 2λs λl 2ε λs λl–( )–+[ ]

2λs λl ε λs λl–( )+ +---------------------------------------------------------------≈

tw λw ε2λl 1 ε–( )2λs

4ε 1 ε–( )λlλsλl λs+

---------------------------------+ +≈ ε

7

ESD

U C

opyr

ight

mat

eria

l. F

or c

urre

nt s

tatu

s co

ntac

t ESD

U.

ESDU 79013

Wick Type*


Minimum Capillary Radius

Equation†

† Figures in brackets refer to notes in Section 7.2

Derivation Numbers (see Section 6)

Accuracy Information



(5), (6), (7)

6, 9, 12, 15, 23, 27

80% of data lie within 0.8to 1.2 times value given byequation



(5), (8)

7, 8, 13, 15, 16, 19, 20, 2180% of data lie within 0.5 to 1.5 times value given by equation


Plain

(9)

7, 8, 10, 16, 21, 23, 29, 3280% of data lie within 0.7 to 1.3 times value given by equation

Sintered



(10)

7, 8, 19, 2380% of data lie within 0.5 to 1.5 times value given by equation

d

w

1N---- d w+=

twScreen

Annular

rσ1

2N-------=

tw

αα

Screen


tw

b

c

Screen


twrσ

12N-------=

tw

rσ 0.21d=

tw

rσd

2 1 ε–( )------------------=

8

ESD

U C

opyr

ight

mat

eria

l. F

or c

urre

nt s

tatu

s co

ntac

t ESD

U.

ESDU 79013

Wick Type*


Permeability

Equation†

† Figures in brackets refer to notes in Section 7.2.

Derivation Numbers (see Section 6)

Accuracy information



(11)

5

Equations apply strictlyto these shapes withsmooth surfaces in placeof screens and are thenaccurate to within %.The effect of screens isuncertain but it isexpected to be small

where F is given in Figure 1

where F is given in Figure 2



(8), (12)

7, 8, 13, 14, 15, 16, 19, 21

Equation from Derivation 14; 80% of data from other Derivations lie within 0.5 to 2.0 times value given by equation


Plain

(13)

7, 8, 10, 14, 16, 21, 29, 32

Equation from Derivation 14; 80% of data from other Derivations lie with in 0.8 to 1.7 times value given by equation Sintered



(14)where

7, 8, 19, 23, 24, 33

80% of data lie within 0.75 to 1.25 times value given by equation

d

w

1N---- d w+=

twScreen

Annular

Ktw3

12------=

5±

tw

αα

Screen


K F tw2 ε=

tw

b

c

Screen


K Fbtwε=

twK

d2ε3

122 1 ε–( )2----------------------------=

tw Kd

2ε3

150 1 ε–( )2----------------------------=

twK

C1 y2

1–( )

y2

1+--------------------------=

y 1C2d

2ε3

1 ε–( )2-------------------+=

C1 6.0 1010–

m2×=

C2 3.3 107× 1/m

2=

9

ESD

U C

opyr

ight

mat

eria

l. F

or c

urre

nt s

tatu

s co

ntac

t ESD

U.

ESDU 79013

Wick Type*

* In the sketches the axis of the heat pipe and therefore the direction of fluid flows are normal to the plane of thepaper unless stated otherwise.

EquivalentDiameter

ReynoldsNumberCriterion


N = number of opertures per unit (m) of screen

(15)

Multiple wire mesh screens†, plain orsintered (screen dimensions as forsingle layers illustrated above)

† These wicks are positioned so that the layers follow the contour of the inner surface of the heat-pipe wall.


Plain

Sintered



d

w

1N---- d w+=

twScreen

Annular

DE 2tw=

Rel 2000<

tw

αα

Screen


DE

2tw αsin

1 αsin+---------------------=

tw

b

c

Screen


DE

2btwb tw+--------------=

tw DEdε

1 ε–----------=

Rel 10<tw

DE2dε

3 1 ε–( )------------------=

tw

DEdε

1 ε–----------=

10

ESD

U C

opyr

ight

mat

eria

l. F

or c

urre

nt s

tatu

s co

ntac

t ESD

U.

ESDU 79013
7.2 Notes on Equations
(1) This equation has been established for grooves that are not screen-covered for and. A screen made of a material with a higher thermal conductivity than that of

the liquid would be expected to enhance .

(2) Data in Derivation 21 show that this equation predicts conservative (low) values of for sinteredwicks. Data in Derivation 25 show that for plain (unsintered) copper and stainless steel wicks theequation sightly overpredicts if the mechanically applied pressure is less than about 10 kPa(averaged over the wick surface).

(3) Data in Derivation 4 indicate that this equation predicts conservative (low) values of . A moreaccurate, but rather complex equation is given in Derivation 4.

(4) Measured data, which should be used for accurate work in preference to this equation are availablefor water-filled copper felts in Derivation 30.

(5) The BS sieves are now characterised by the aperture dimension, . Preferred values of the wirediameter, , are given in Reference 2. The ASTM standard for sieves is characterised by a meshnumber equal to the number of apertures per inch and earlier BS sieves were similarly designated.Therefore for these standard sieves, × (ASTM or BS mesh number).

(6) This equation has been established for ASTM mesh numbers in the range from 50 to 635.

(7) This equation gives the effective capillary radius of the screen pores; it is applicable only when nolarger opening exists between the liquid and vapour spaces. Furthermore, the ability of these wicksto fill with liquid against gravity depends on the effective capillary radius of the liquid space(s) ifthis radius is larger than that of the screen pores.

(8) This equation has been established for ASTM mesh numbers in the range from 50 to 325.

(9) This equation has been established for wicks made of metal beads and metal powders with 40 × 10–6

< d < 10–3, 0.27 < < 0.66 and a maximum to minimum particle size ratio not exceeding 2.5.

(10) This equation has been established for metal felts with 8 × 10–6 < d < 46 × 10–6 and 0.6 < <0.9.

(11) This equation applies for ratios of screen diameter to container internal diameter exceeding 0.5provided that the eccentricity of screen and container is less than 0.08tw . If these conditions arenot both met, the permeability is larger than predicted by the equation, see Derivation 5.

(12) This equation applies to flow that is essentially parallel to the warp or weft wires of the meshes.The equation has been established for tightly wrapped wicks of 3 layers or more and for which0.62 < < 0.75. The equation is expected to predict conservative (low) values of for looselywrapped wicks with > 0.75, and wicks with < 0.62 rarely occur in practice. Further data areavailable from Reference 1 for cases in which the above conditions are not met.

(13) This equation has been established for wicks made of metal powders (mainly copper) with50 × 10–6 < < 3 × 10–4, 0.27 < < 0.66 and a maximum to minimum particle size ratio notexceeding 2.5. On the whole, the equation predicts conservative (low) values of , but a few dataon nickel samples reported in Derivations 8 and 32 are up to one order of magnitude lower thanpredicted.

20° α 45°< <0.001 λl/λs 0.1< <

λw

λw

λw

λw

wd

N 39.4=

ε

ε

ε Kε ε

d εK

11

ESD

U C

opyr

ight

mat

eria

l. F

or c

urre

nt s

tatu

s co

ntac

t ESD

U.

ESDU 79013
(14) This equation has been established for metal felts with 8 × 10–6 < < 55 × 10–6 and 0.6 < < 0.95.
(15) Rarely, inertial effects may become important at lower Reynolds numbers than this. The presuredrop in the condenser of a heat pipe due to acceleration of liquid in an annular or grooved wick isroughly equal to . This pressure drop should be compared with the pressure drop due tofriction (calculated from the permeability) and if it is signficant (say in excess of 5 per cent) thevalue should be added to the frictional pressure drop in the condenser and subtracted from thefrictional pressure drop in the evaporator.

d ε

ρlVl2/ε2

12

ESD

U C

opyr

ight

mat

eria

l. F

or c

urre

nt s

tatu

s co

ntac

t ESD

U.

ESDU 79013

FIGURE 1 PREMEABILITY FACTOR FOR TRIAGULAR SECTION

FIGURE 2 PERMEABILITY FACTOR FOR RECTANGULAR SECTION

0 10 20 30 40 50 60 70 80

F

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

α (degrees)

αα

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

F

0.000

0.005

0.010

0.015

0.020

0.025

0.030

0.035

0.040

twb

btw

or

tw

b

13

ESD

U C

opyr

ight

mat

eria

l. F

or c

urre

nt s

tatu

s co

ntac

t ESD

U.

ESDU 79013KEEPING UP TO DATE

Whenever Items are revised, subscribers to the service automatically receive the material required to updatethe appropriate Volumes. If you are in any doubt as to whether or not your ESDU holding is up to date, pleasecontact us.

Please address all technical engineering enquiries and suggestions to:

For users in the USA, please address all Customer Service and Support enquiries and suggestions to:

ESDU International plc Tel: 020 7490 5151 (from the UK)+44 20 7490 5151 (from outside the UK)

Fax: 020 7490 2701 (from the UK)+44 20 7490 2701 (from outside the UK)

E-Mail: [email protected]: www.ihsesdu.com

IHS Engineering Products Tel: 1 800 447 3352 (toll free number)and Fax: 1 303 397 2599Global Engineering Documents Website: www.ihs.com

global.ihs.com

ESD

U C

opyr

ight

mat

eria

l. F

or c

urre

nt s

tatu

s co

ntac

t ESD

U.

All rights are reserved. No part of any Data Item may be reprinted, reproduced, ortransmitted in any form or by any means, optical, electronic or mechanical includingphotocopying, recording or by any information storage and retrieval system withoutpermission from ESDU International plc in writing. Save for such permission allcopyright and other intellectual property rights belong to ESDU International plc.

© ESDU International plc, 2008

ESDU 79013Heat pipes - properties of common small-pore wicksESDU 79013

ISBN 978 0 85679 257 1, ISSN 0141-402X

Available as part of the ESDU Series on Heat Transfer. For informationon all ESDU validated engineering data contact ESDU International plc,27 Corsham Street, London N1 6UA.

ESDU 79013 is one of a group of five on heat pipe performance. It givesequations for calculating the effective thermal conductivity, minimumcapillary radius and permeability of a wide range of wicks for use incapillary-driven heat pipes including single-layer and multiple-layer wiremesh, unconsolidated packed particles and sintered felted metal fibres.ESDU 79012 deals with performance prediction of capillary-driven heatpipes, ESDU 81038 deals with performance prediction of two-phaseclosed thermosyphons, ESDU 80013 introduces the use of heat pipesand includes practical design experience, and ESDU 80017 givesproperties of fluids relevant to heat pipe operation at temperatures of 210to 570 K.

ESDU (3)

Documents

Transcript of ESDU (3)