Indian 10urnal of Fibre & Textil e Research Vol. 27, September 2002, pp. 2 17-223

Thermal conductivity of unidirectional fibre composites made from yarns and computation of thermal conductivity of yarns

S Kawabata & R S Rengasamy"

Department of Material Science, The University of Shiga Prefecture, 2500 Hassaka, Hikone 522-8533, Japan

Received 1 March 2001; accepTed 6 luly 2001

Measu rement of thermal conductivity of fibre composites made from differe nt fibre assemblies (yarns) consisting of apparcl, industrial and hi gh pcrformance fibres is described. From the measured thermal conducti vity va lues of compos ites, the computation of longitudinal and transve rse conductivity of yarns is reported. The thermal conducti vity of yarn along its axis is much higher than the thermal conductivity in transverse direction for all types of fibres, except E-Glass, showing that the phenomenon of thermal conductivity of fibres is anisotropic in nature. The behaviour of E-Glass in conducting the heat is close to isotropic. Pol yethylene filament yarn shows the hi ghest ani sotropy followed by Vectron , Kevlar, Technora, linen, hi gh-tenacity polyester and jute. For the fibres of same chemica l structure, hi gh-tenacity fibres have sli ghtly highcr longi tudinal and lower transverse thermal conductivity values compared to apparel-grade fibres. Indust ri al-grade polyestcr and nylons have high ani sotropy in cond ucting heat than the apparel-grade fibres. The effect of fibre chemistry on the thermal conducti vity of fibres is predom inant than the effect of orientation of the molecu les.

Keywords: Anisotropy, Composites, Longitudinal conducti vity, Thermal conduct ivi ty. Transverse conducti vity

1 Introduction Thermal conductivity of fibres (apparel, industrial

and high performance) is important for designing various fibrous products. So far, there is no preci se data available on the thermal conductivity of different yarns/fibres and their anisotropic behaviour. Previous studies have shown that the thermal conductivity va lues along the fibre axis are much higher than the values in the transverse direction l

-2

. Direct measure­ment of the the rmal conductivity of fibres/yarns is very difficult due to the followin g reasons: (i) fibres are too delicate to handl e during measurement, (ii) it is very difficult to create a smooth transverse plane (normal to the direction of heat flow) on them, which brings down area of contact between fibres and heat source, (iii) it is very difficult to orient the fibres/ ya rns in a specified direction during experiment, and (iv) as the fibres are poor in conducting the heat, the heat flow through them during measurement is very low compared to convection and radiation losses in the measuring system. This leads to inaccuracies in the measurement of their thermal conductivity. Initia l

a To whom all the correspondence should be addressed. Present address: Department of Tex tile Technology, Indian Insti ­tute of Technol ogy. New Delhi 110016, India. Phone: 659 141 8; Fax: 0091-011-6581103; E-mail: rsr60 @hotmail.com

attempts made in this direction were not successful and therefore aborted.

An alternate method involves preparation of unidirectional fibre composites made from yarn s, measurement of the the rmal conductivity of composites and the computation of the thermal conductivity of yarns using mode ls or finite e lement analysis . ]n the present study , this indirect approach was adopted . Unidirectional fibre-epoxy composites were prepared and an improved methodology for the measurement of the thermal conductivity o f composites was adopted using an instrument reported earlier2

.

2 Materials and Methods The detail s of fibre assemblies used in this study

are given in Table 1. The mate rials (yarns and rovings) were wound paralle l to each other into a sheet form on a mandrel in a winding machine, especially designed for the purpose. The traverse rate of winding was adjusted depending on yarn tex .

2.1 Fibre Composite Preparation 2.1.1 Preparation of Epoxy Solution

Epoxy (Epikote 819) and a curing agen t (triethylcnetctramine) were mixed in the ratio of 10: I by weight. After stirring , the solution was subjected to vacuum for 30 min to remove air particles .

218 INDIAN J. FIBR E TEXT. RES ., SEPTEMBER 2002

Table I-Detail s of fibre asse mbl ies used in mak ing the composites

Fibre type

Tekmilon (hi gh-modulus po lyethy le ne)

Vectron (polyester-po lyary late)

Kev lar 49

Kev lar 29

Technora

Carbon (T300B)

Nomex

Nieron

E-G lass

Linen

Jute

Cotton

Cotto n

Colton

Colton

Cotton

Vi scose rayon

Ny lon 66 (industria l grade)

Ny lon 66 (appare l grade)

Nylon 6 (industri al grade)

Ny lon 6 (appare l grade)

Polyester (hi gh tenac ity)

Polyes ter (appare l grade)

Acry li c

Si lk

Wool

"No of fil aments is not know n

Detail s of fibre assembly

Illtex, 100 filaments

167 tex, 300 filament s

240 tex, I 000 fi laments

250 tex"

167 tex, 1000 fi laments

67 tex"

133 tex , 600fi larnent s

2 17 tex"

4570 tex"

36 1 tex (spun yam)

178 tex (spun yarn)

493 tex (rov ing)

197 tex (rov ing)

15 tex (two-fold ring-spun yarn )

20 tex (combed ring-spun yarn )

6 tex (combed ri ng-spun ya rn )

13 tex, 24 fi laments

140 tex, 204 fi laments

7 .7 tex"

140 tex, 204 fil aments

7.7 tex"

8.3 tex, 36 fil aments

15.6 tex, 68 filaments

16.6 tex, 120 fi laments

11 .8 tex (twisted ya rn )

15.6 tex (spun yarn)

2.1.2 Preparation of Fibre Composites for Measurement of Transverse Thermal Conductivity of Yarns

Volume fraction of fibres in the fibre composites Transverse Long itudinal specimen

0.94

0.93-0.95

0.67

0.8-0.85

0.77

0.77

0.87

0.72

0.77

0.73-0.85

0.94

0.92

0.94

0.87

0.89

0.87

0.96

0 .84

0 .84-0 .93

0.87-0.90

0.94

0 .85

0.93

0.91

0.88

0.9 1-0.94

specimen

0.54

0.5 1

0 .51

0 .51

0.60

0.4

0.55

0.20

0.53

0.30

0.34

0.30-0 .33

0.32

0 .31 -0.33

OAO 0.54

0.54

0.5 1-0.54

0.55

0.5 1

0.54

0.55

0.23-0.3 1

0.3 1-0.33

Section ABCO sho .... s fibres The prepared soluti on was app lied on both the sides

of yarn layers. The epoxy coated yarn layers were placed between two molding plates, already sprayed with mold releasing agent. Then these were subjected to vacuum for one hour to remove the entrapped air in the yarns to fac ilitate the solution to penetrate into the voids in between the fibres. Molding was carri ed out at a pressure of 300 kg/cm" and temperature of 1000 C for 45 min. Arter cooling, the fibre epoxy composite sheet was removed from the molding plates. From thi s fi bre composite sheet. the speci mens were cut mostly in the

fo rm of square shape (15mm x 15mm) using knife cut­ter These composite ~pecimens have yarns orien ted in a plane normal to the direction of' heat flow through the composIte duri ng measurements (Fig. I ) and are re­f'erred as '"transve:se specimens".

Fig. I--Cross-section of a fibre cO lllpositl: used for measuring the trallsverse thermal conductivity of yarns (trans verse spec llllen)

KAWABATA & RENGASAM Y: THERM AL CONDUCTIVIT Y OF UNIDIRECTIONAL FIBRE COM POSITES 2 19

2.1.3 Preparation of Fibre Composites for Measurement of Longitudinal Thermal Conductivity of Yarns

The yarn layers were dipped in the epoxy solution and then subj ected to vacuum for 45 min. Thereafter, the yarns were pulled through a Tefl on tube with an inner di ameter of 10mm. Care was taken during thi s operation to avoid the twisting together of yarns. The Tefl on tube was placed in a circular tank and then the tank was fill ed with the epoxy solution. The tank was placed in a vacuum and the air was removed fo r 3 h to fill the voids in the fibre assembl y with the epoxy resin . Curing was carried out at 100°C for 45 min . After cooling, the cy lindrica l shaped cured epoxy containing Tefl on tube was removed. This cy lindrical shaped cured epoxy was cut into various lengths using a ceramic cutter, with the cutting plane perpendicul ar to the yarn axes . From these cut pieces, fibre epoxy composites were pushed out. All these fibre compos ites were in the fo rm of solid cy linders with yarns parall el to the cy lindrical axes (Fig. 2) and are referred as "longitudinal spec imens" .

2.2 Description of the Measuring System The apparatus used to measure the thermal

conductivity of fibre composites is shown in Fig. 3. It consists of top and bottom units. The top unit consists of a heat source plate, called top plate (heat plate), whi ch suppli es heat to the composite specimen. Surrounding the top unit is a circul ar strip of al uminum heat source, called top guard (heat guard), to contro l convecti on heat fl ow from the top pl ate to the top guard . The segment between the top plate and the top guard is fill ed with an insulating material. The bottom unit consists of a bottom plate (base plate) and a guard. The temperature of the base plate can be controll ed by circul ating water through the bottom unit. The temperatures of both the plates and top guard can be set independentl y. The fibre composite specimens can be pl aced in between the top plate and the bottom plate.

2.3 Measurement of Thermal Conductivity of Composites Heat source to the top plate and top guard was

switched on. The temperature of both these was set at 3SOC. The top unit was placed over a thick polys tyrene sheet for 30 min to avoid heat losses and to reach the set temperature va lues .

The temperature of the bottom plate was set at 25°C. High conducti vity silicone grease was applied on the top and bottom sllIfaees of the specimen and on both the pl ates. The purpose of applying the silicone grease was to cover the mjcroaspel1ies present on the surfaces

Fibres

Fig. 2 --Cross-sec ti on of a fi bre composite uscd for measuring the long itudinal thermal conduc ti vity of ya rns (longitud inal spec ime n)

~--- - ----..

(' " \,.-Heat insulat ing case

"" I

! -'-- ~ - /j , I

I =-..---- --i'- --- _Temp. sensor : , .. \ . ./ ...... '\ ... .... . . . .... .. - --.. - Heater

I -_J-=~:-::tTem ~. se nsor I : Hea er I

L· Hea t gaurd

~q..f--/---Hea t pla te ~,::,...:-t_- S pe ci men

_-.+-- Base plate

__ Tem p. se nso r : __ ..... :.:,- - - Heater

q Wa ter / / ......... Heat insulating case

' .......... ,-_._-/

Fig. 3 - Apparatus to measure the thermal conductivit y of fibre composi tes

of the plates and specimens. The specimen was then placed over the bottom plate and turned several times to squeeze out the excess grease and to increase the area of contact between them.

The top unit was placed over the specimen, pressed and turned several times. Initiall y, there was a sudden drop in temperature of the top plate and rise in the temperature of the bottom plate. When the tempera­tures of both the top and bottom plates were stab i­lized, these were reset at 35° and 25°C respecti vely. Weights were also placed over the top unit to increase

220 INDIAN J. FIBRE TEXT. RES., SEPTEMBER 2002

the area of contact between specimen and plates. After a few minutes, the system reached a state of equilibrium and there was no change in the heat flo w and temperature levels of both the plates.

Under the steady state condition, the heat supplied to the top plate (QT in Watts) was measured . Each specimen was tested four times. Each time, the specimens were turned upside down. The heat sup .. plied to the top plate consists of radiati on heat loss (QR), convection heat loss (Qc) and the heat con­ducted by the fibre composite specimen from top to bottom plate (Qs) .

.. . ( I)

The thermal conductivity of the composite (Ks in W/m.K) can be calculated using the following equation:

Ks = (Qs . L)/(T.A) ... (2)

where L is the spec imen thickness (m); 7~ the temperature gradient (K) across the specimen; and A, the cross-sectional area of the spec imen (m2

)

Heat suppl ied to the top plate (QT) versus the in verse of spec imen thick ness (C l

) was plotted . The best line fit fo llows the equation:

QT =[C + (lIl. C l)] ... (3)

where III is the slope; and C, a constant = QR + Qc = total heat loss.

The fit is similar to the one shown for cotton longitudinal specimens in Fig. 4 . The es timated heat losses for transverse spec imens of circular (22mm diam.) and square shapes ( 15mm x 15mm) are around 40-80 and 20-30mW respectively. These losses are very low compared to the total heat supplied to the top plate during therma l conductivity measurement of the composites, which was few hundred milli watts to more than one watt. The heat loss estimated for longitudinal spec imens ( I Omm diam.) is around 10-35 mW, whi ch is al so very low compared to the total heat suppli ed to the top plate during measurements with composi tes.

The thermal conductivity of the composites can be calcul ated from the slope as:

Ks =[lIl/(T. A)] ... (4)

2.4 T hermal Conductivity of Yarns

The thermal res istance of the yarn in a fibre com­posi te is parallel to the resistance of epoxy matrix when the heat flo w through the composite is al ong the yarn axes (longitudin al specimens). The thermal res is-

25 -'" 3 + E

20 w ..... <t -' a. a. + f2 15

w I

+ .....

+ >-en 10 +

0 w :::::; a. a. ~ V1

~ w I

u......~:........,..J...,.-----;"='=---;;::~--;~ .....--l 800 1200 1600 2000

INVERSE DISTANCE BE1WEEN PLATES 1m-1)

Fig. 4 - Heal suppli ed to the top plate versus the inverse thi ck­ness o r the fibre-compos ite specimens (collon long itudinal specimens)

Fib re

Res in

Pa rallel Model

! Se rie s Mode l

~ I

Rf

Rf Rr Rr

I

Fig. 5 - Phys ical mode ls or thermal resistance o r fibre and epoxy matri x in a ribre composite flU- Fibre resistance, and H.r- resi n resis tance I

tance of ya rns in a fibre composite is both parallel and in se ri es to the resistance of the epoxy matrix when the heat flow through the composite is normal to the ya rn axes (transverse spec imens). The model s are shown in Fig. 5.

The thermal conductivity of yarn, Ky (para ll el ), can be calculated assuming that the re~ i ·tance of both

KAWAB ATA & RENGAS AMY: THERMAL CONDUCTIVITY OF UN IDIRECTIONAL f i BRE COMPOS ITES 22 1

yarn and cured epoxy res in are parallel to each other, 10'[ as fo ll ows:

Ky (parallel) = (Ks - v,. K,)1 Vr ... (5)

The thermal conductiv ity o f yarn , Ky (series), can be calculated , assu ming that the res istance of both the yarn and cured epoxy res in are in seri es to each other, as follows:

Ky (series) = (vr)/ I( I/Ks) - (v,lK,) l . . . (6)

where I ' "~ is the vo lu me fraction o f fibres in the compos ite; \ 'r, the vo lume fraction of cured res in in the composi te; and K" the thermal conducti vity of cured epoxy res in (W/m. K).

To measure the thermal conducti vity of epoxy resin , cured 100% epoxy sheets of different thi ck ness were prepared by cas ting. The thermal conducti vity o f cured epoxy resin was ca lculated using the method described in section 2.3. The thermal conductivity of cured epoxy res in was 0. 167 W/m. K.

The volume fraction of f ibre (vr) for transverse specimens was ca lculated using the following equation:

... (7)

The volume fracti on of fibre (VI) for longitudinal specimens was ca lcu lated uSlllg the fo l lowing equation:

vr = ( 1.273 N.c. x I ( 5)/(Pr.D\ ) ... (8)

where N is the number of yarns in the specimen; C, the count of the yarn (tex); Pr, the density of fibre (g /cm\ I , the thickness o f the compos ite (cm); IV, the width of the compos ite (cm); and Dc the diameter of the composite (cm).

The longitud inal therma l conductivity of yarn was calculated using the Eq . (5). The transverse thermal conductivity of yarn should li e in between the values calculated from the Eqs (5) and (6). In the transverse specimens, the exact proporti on o f the composite having both the res istances o f yarn and resin , either in parallel or in seri es to each other, is not known. Because of thi s, the finite element analys is was used to calculate the transverse thermal conductivity of yarns from the values o f K s, Vr and K,. A diagram showing the pattern of heat fl ow through the compos ite produced by the finite element method is depicted in Fig. 6.

The thermal conductivity of fibre composite can be predicted i f thc fibre vol ume fraction and the conductivity of fibre and res ins are known (Fig. 7). In this figure, the K Il: indicates the tran sverse thermal

I ______ ~=~FIBRE==----~­~--Vf = 0.67--~--\-~

-- JTF =0 .4~7- --

8 ·c

Fig. ()--Fin itc clcmcnt of a fibrc compos itc showi ng pallern of

heal fl ow for a tClllpcraturc gradi cnt of 10° K 1(- ) 0.25°C. and (---) l OCI

KT F 1.05

1. 0 0 .95

"" o.as

E O.S 3- 0.75 u.> I-

0·65 Vi ~ 0· 6 :>:

0·5 5 C) LJ

u.. C) 0.45

~ :> 0·35 6 :::> '2 0.2, 8

0.15

0·10

VOLUME FRACTtON OF FIBRE

Fig. 7- Pl ots of thcrmal conducli vit y va lues of fibrc compos ite using finit c clcmen t mcthod for va rious valucs of transvcrse ther­mal conducti vi ty of fibrc and fibre vo lumc fracti on

conducti vity of fibre, and the direction of heat flow th rough the composite is normal to the axes of f ibre (s imilar to that in transverse specimens).

The longitudinal (KLY) and transverse (KTY )

therma l conducti vity va lues of vari ous yarns with

222 IND i A J. FIBRE TEXT. RES .. SEPTEMB ER 2002

Tab lc 2 ~ Thcrillal conducti vit y vallics or fibrc assc illbl ics (yarn s)

f ibrc typc Therillal conductivity . W/m.K Anisotropy va luc or therma l conducti vit y (KL\.IK i•y ) Long itudina l (K I.\' ) T ran sverse (K n·)

Tckmilon (h igh-Illodulus polyc thyknc)

Veetron (polyes ter- pol yary latc)

Kev lar 49

Kev lar 29

Technora

CarbonT300 B

Nomex

Nicron

E-G lass

L inen

Jutc

Cotton

Vi scose rayon

Nylon 66 ( industria l grade)

Ny lun 66 (apparcl grade)

Ny lon 6 ( industrial grade)

Ny lun 6 (apparel grade)

Polyester (high tenacit y)

Polyes tcr (apparcl grade)

Acry lic

Silk

Wool

"A ve ragc for all eollon f i brc assembl ies.

15 .656

2A 7 1

3.5 13

3.1 39

1.9RR

6.722

() .649

Ull)9

1.233

1.1\36

1.7 12

1. 81\2"

1.077

1.065

I .00

1.055

0.933

1.056

1.009

0.930

0.846

0.566

their thermal conductivity an isotropy va lucs (KLy/K ry rati o) are given in Table 2.

3 Results and Discussion The anisotropy va lues of thermal conducti vity

ind ica te that the high-modulus polyethyl ene (Tekmi lon) has the highest ani so tropy followed by other high performance f ibres Vectron , Kev lar 49, Kev iar 29 and Teehnora. The ani sotropy va lue for E­Glass is j.4, the lowest among all the fibres tes ted. This indicates that the behaviour of E-G lass fibres in conducting the heat is close to isotropic .

High-modulus polyethylene has the highest longitudinal thermal conductivity and the wool has the lowest longitudinal thermal conducti v ity among the f ibres tested. Carbon T 300B has the highest transverse thermal conductivity, fo llowed by E-G lass and N icron. Vectron (po lyes ter-po lyary late) and

echnora (para artttnide) have poor transverse thermal conductivity compared to other fibres tes ted .

A mong the natural f ibres tested in this study, the highest ani sotropy is exhibited by li nen fo llowed by

0.30 1

o 132

0.2 17

0.2 17

0. 14 1

1.20 1

0.2 19

0.793

0.87R

0.25 1

0.261\

0.363"

0.326

0.204

0.22 1

0.236

0.239

0.1 57

0. 179

0.20 1

0.209

0.25.+

52,0

11\ .7

16.2

1.+.5

1'+. 1

5.6

3.0

2A

IA

7.3

SA 5.2

3.3

5.2

.+.5

4.5

3.9

6.7

5.6

4.6

4.0

2.2

jute and cotton . Among the apparel fi bres, cotton has the highest transverse thermal conductiv ity fo llowed by viscose, woo l, ny lon 6, ny lon 66, acry li c, silk and polyester. The longitudinal thermal conducti vity va lues o f apparel fibres indicate that the cotton has the highest conductivity, fo llowed by viscose, polyes ter, ny lon 66, ny lon 6, acry li c and silk in a narrow range and lastly the woo l.

T he fibre assemblies of co tton, linen, jute, wool and silk used in making the compos ites were twisted yarns, The fibre compos ites made from these yarns fo r the measurement o f longitudinal thermal conducti vity of yarns have fibres/f ilamen ts whose axes lie at a range of angles to the heat flow direc ti on

(8;), However, the angle between yarn s and heat fl ow direction is zero. Therefore, fo r the twi sted ya rn s, the longitud i nal thermal conduct i vi ty o f fibres is ex pected to be more than the longitudinal thermal conducti vity o f yarns. For other f ibre assembli es (multi-filament yarns with produc.er 's twi st) used in the composites, the longitudinal thermal conducti v ity of yarns and fi bres will be the same.

KAWABATA & RENGASAMY: THERMAL CONDUCTIVITY OF U !DIRECTIONAL FIBRE COM POSITES 223

Pred icti on of longitudina l conductivity va lues o f fibres (Ku :) from the thermal conductivity va lues of spun yarns based on fibre hel ix angles in th e yarn is

1 reported elsewhere' .

The transverse specimens made from multifil ament yarns (except silk) have fibres configured in the compos ite, normal to the heat now direct ion as they have neg ligible amount of twi st. T herefore, for these samples, the transverse thermal conduct iv ity of f ibres is equa l to the transverse thermal conductivity of yarns. In the case of transverse spec imens made from fibre assemblies, vi z. wool , cotton, jute and sil k, the fibre volu me frac ti ons in the composites are 0.9 1-0.94,0.87-0.94, 0.94 and 0.88 respectively. T hese are very close to the theoreti ca l packi ng fraction of closely packed cy linders. Hence, these fibres in the transverse specimens are very nearl y aligned in a plane normal to the heat flow di rec ti on. Consequentl y, for these fi bre assembl ies, the transverse thermal conducti vity of fibres and yarns w i II be the same.

Therefore, the Kry va lues reported in Table 2 can also be referred as tran sverse thermal conducti vity of fibres, except fo r cot ton and linen yarns.

The longitudinal thermal conduct i vity va lues of industri al-grade ny lon 66, nylon 6 and polyester yarn s are 1.065, 1.055 and 1.056 W/m.K respecti ve ly. These are marginall y higher than the values for corresponding apparel-grade yarns ( 1.00, 0.933 and 1.009 W/m. K respectively). The transverse thermal conducti vity values of industrial-grade ny lon 66 and polyester fibres (0.204 and 0.157 W/m.K respectively) are marginall y lower than the values for the apparel-grade fibres (0.22 1 and 0.179 W /m. K ). Thi s indicates that the high drawn fibres have slightly higher longitudinal and lower transverse thermal conductivity values and ex hibit higher anisotropy in conducting the heat compared to the fibres with less molecular ori entation.

4 Conclusions An indirect method of calcu lating the thermal

conductivity of yarn s/fibres from the measured va lues of thermal conductivity of fib re compos ites is reported . l ndustrial -grade fibres have marginall y higher longi tud inal and lower transverse thermal conductivity val ues th an for th e appare l-grade fibres. Th is may be due to the molecular \-ve ight and orientation of molecules. The effect of f ibre chemistry on the thermal conduct ivity is more pronounced than the ori entation of molecules or molecul ar wei ght in the f ibre. Protein fibres and omex have low longitudinal thermal conductivity va lues compared to other fibres.

Except the high-modu lus po lyethy lene, all other yarns tested, viz. Carbon T300B , Vectron, Technora , Nicron , cotton, E-G lass and viscose rayon, have transverse thermal conducti vity va lues in a narrow range. Vec tron, Technora and polyester have poor transverse thermal conductiv ity compared to the other fi bres stud ied .

The anisotropy of thermal conducti vity (K u '/ Kry ratios) shows that the high-modulus polyethy lene has very high anisotropy, followed by Vectron, Kevlar 49, Kev lar 29, Technora, linen, polyes ter (high drawn), jute, Carbon T 300B, Dacron, Nylon 66 (industrial grade) and cotton. The anisotropy va lue for E-Glass is l A, the lowest among all the f ibres tested. This shows that the thermal conducti vity behaviour of E-Glass is very close to isotropic.

References I Kawabata S, j Text Mach Soc japall, 39 ( 12) ( 1986) T 18-1. 2 Rengasa my R S, Yoshi da S & Kawabata S, Measurell/ellt of

therll/al cOllducti l' ity oj" COl/Oil pbre, paper presented at the 22 nd Tex tile Resea rch Sy mpos ium. Mount Fuji, Shi/.uob , Japan , 8 August 1993.

3 Rengasamy R S & Kawab.na S, Computati on of thermal CO Il­

ducti vi ty of fibres from the thermal cond ucti vity of twisted yarn , Illdiall j Fibre Text Res (in press).