85 

Al-Khwarizmi 
Engineering   

Journal 

Al-Khwarizmi Engineering Journal, Vol. 4, No. 3, PP 85-97 (2008) 

 

 

Studying the Effect of Volume Fraction of Glass Fibers 

on the Thermal Conductivity of the Polymer Composite Materials 
 

Mohammed Sellab Hamza 
Material Engineering Departement /University of Technolog 

 

(Received 11 March 2008; accepted 18 June 2008) 

 

 

Abstract 
 

In this study the effect of fiber volume fraction of the glass fiber on the thermal conductivity of the polymer 

composite material was studied. Different fiber volume fraction of glass fibers were used (3%, 6%, 9%, 12%, and 15%). 

Specimens were made from polyester which reinforced with glass fibers .The fibers had two arrangements according to 

the direction of the thermal flow. In the first arrangement the fibers were parallel to the direction of the thermal flow, 

while the second arrangement was perpendicular; Lee's disk method was used for testing the specimens. The 

experimental results proved that the values of the thermal conductivity of the specimens was higher when the fibers 

arranged in parallel direction than that when the fibers arranged in the perpendicular direction. The percentage of 

increasing of experimental thermal conductivity was 96.91% for parallel arrangement and 13.33% for perpendicular 

arrangement comparison with its original value before the using of glass fibers.  
Also the experimental results indicated that the thermal conductivity increases with the increasing of the fiber 

volume fraction. Minimum value was (0.172 W/m.C) for perpendicular arrangement at fiber volume fraction 3% and 

maximum value was (0.327 W/m.C) for parallel arrangement at fiber volume fraction 15%. 

 

Keywords: Polymer, Glass fibers, Thermal conductivity. 

 

 

Introduction 
 
Thermal conductivity is a phenomena of the heat 

transfer phenomenon, so the thermal conductivity is 

defined as the transfer of heat from area of high 
temperature to that of low temperature. The rate of 

heat transfer depends upon the temperature gradient 

and the components of materials. The direction of 
heat transfer will be opposite to the temperature 

gradient since the net energy transfer will be from 

high temperature to low.  

The thermal conductivity of solids materials is 
greater than that of liquids and gases materials.  

For solid materials it is four times than that of 

gases material. This is due to the difference between 
the voids of the two materials. Gases transfer heat by 

direct collisions between molecules, and as would be 

expected, their thermal conductivity is low compared 

to most solids since they are dilute media. Metals 
have better thermal conductivity than non-metals 

because the same mobile electrons which participate 

in electrical conduction also take part in the transfer 
of heat. Non-metallic solids transfer heat by lattice 

vibrations so that there is no net motion of the 
media as the energy propagates through. Such 

heat transfer is often described in terms of 

"phonons", quanta of lattice vibrations [1].  
The free electrons are responsible for the 

transferring the thermal power through the 

conduct materials, while for the insulating 
materials such as polymers, the photons is 

responsible for this phenomena [1]. 

Zhan-Sheng et. al. [1] used the finite 

element formulation of transient heat transfer 
problem for polymeric matrix composite 

materials from the heat transfer differential 

equations to study the experimental and 
numerical temperature distribution of thick 

polymeric matrix laminates during an 

autoclaves vacuum bag process.  

Murthy et. al. [2] studied the distribution of 
the temperature and the analysis of thermal 

stresses across the composite thick plates by 

using two-dimensional finite and physical 
model element model for this analysis in both 



Mohammed Sellab Hamza                                      Al-Khwarizmi Engineering Journal, Vol. 4, No. 3, PP 85-97 (2008) 

 

 86 

longitudinal and transverse directions for three 
different filter materials with epoxy as matrix 

material. 

Rondeaux et al. [3] improved a specific thermal 
conductivity measurement facility for solid materials 

at low temperature where the thermal conductivity 

measurements on pre-impregnated fibers glass epoxy 

composite are tested in the range of temperature (4.2  
to 14 K) in order to extract the thermal boundary 

resistance for different thicknesses. 

Raimund [4] studied the analysis of temperature 
fields for hybrid and conventional composite 

structures by using the two-dimensional and three-

dimensional finite element formulations for the 

analysis of temperature fields for hybrid and 
conventional composite structures. 

Khalaf [5] studied the thermal conductivity and 

the mechanical and physical properties for 
unsaturated polyester reinforced by fiber glass and 

nylon fiber composites and found that  the thermal 

conductivity decrease with increase of nylon fiber 
layers and also decreases with the increase the 

volume fraction, for the samples of laminar 

reinforced system. 

Pilling et. al. [6] studied the effect of orientation 
of fiber and the fiber volume fraction on the thermal 

conductivity of composite materials reinforced with 

fiber of carbon. They proved that the thermal 
conductivity increases with increasing of the fiber 

volume fraction and were higher in the parallel 

arrangement of the fibers than that for perpendicular 
arrangement.  

Elie [7] studied the thermal conductivity and 

mechanical properties for polymer composite 

material reinforced by aluminum and aluminum 
oxide particles and found that the thermal 

conductivity increased with the increase of the weight 

fraction of metallic and ceramic particles and reach a 
maximum value at a weight fraction of (20 %) and 

for the composite material reinforced with (Al) was ( 

0.407 W/m.

C) and for the composite material 

reinforced with (Al2O3) was (0.319 W/m.

C) at the 

same weight fraction.  

James and Harrison [8] calculated heat flow and 

distribution of temperature by using the finite 
difference method in composite materials made from 

anisotropic materials by taking in to account the local 

re-orientation of the grid and the temperature 
distribution. Heat flow was derived for a composite 

material made from two materials with anisotropic 

thermal conductivities 
The aim of this study is to study the effect of fiber 

volume fraction and their direction (parallel or 

perpendicular to heat flow) of the reinforcement 

material (glass fibers) on the thermal conductivity. 
The specimens were made from polyester reinforced 

with five different volume fraction of glass 
fiber (3%, 6%, 9%, 12% and 15%). 

The reinforcement material (glass fiber) 

was arranged in two methods. In the first 
method the glass fibers was aligned in the 

parallel  direction to the heat flow  while in the 

second method the glass fibers was aligned 

perpendicular to its. 
 

 

Theoretical analysis   

The volume fraction of matrix and 

reinforcement material is calculated from the 

following equations [9]. 
a- Volume fraction of matrix   

                                                               ...(1) 

               

b- Volume fraction of glass fibers 
                                                               ...(2)                                                                    

 

The electric power pass through the heating 
coil is calculated by the following formula. 

       P=V.I                                             …(3) 

The transferring of the thermal energy is 

carried out in two ways. These are: 
1- The vibrating waves of the lattice. 
2- The movement of the free electrons. 
The thermal conductivity is defined by the 

following formula [9]: 

q= -k dT/dx                                                 ...(4) 

The equation (4) used only for steady state 
of thermal flow and when the thermal flux is 

fixed and does not change with time. The 

minus sign means that the transfer of heat is 

starting from hot part to the cold part. The 
direction of heat transfer will be opposite to the 

temperature gradient since the net energy 

transfer will be from high temperature to low. 
This direction of maximum heat transfer will 

be perpendicular to the equal-temperature 

surfaces surrounding a source of heat. 
The theoretical thermal conductivity is 

calculating by the following equation [9, 10]. 

 

                                                               ...(5) 
 

The heat loss (e) through the unit time 

(second) and through the area (m
2
) is 

calculated by the following formula [11]: 

                                                               ...(6) 

 

 The theoretical thermal conductivity of 
composite materials is estimated from the 

following equations [12, 13, 14]:- 

1-heat flow is parallel to the glass fibers: 

%
c

m
m

V





%
c

f

f
V





































 


2
T

s
d

r

1

1
T

s
d

2

1

1
d

r

2

1
Te

s
d

1
T

2
T

K

    









3
T

3
d

2
T

2
d

2
T

1
T

s
d

2

1

1
T

1
derπ2

3
T

1
Te

2
rπVI



Mohammed Sellab Hamza                                      Al-Khwarizmi Engineering Journal, Vol. 4, No. 3, PP 85-97 (2008) 

 

 87 

                                                          …(7) 
2- heat flow is perpendicular to the glass fibers: 

 

                                                       ....(8) 

 

 

Experimental Work  
 
The samples were manufactured from 

unsaturated polyester (thermosets) which 

reinforced with different values of fiber volume 
fraction of fiber glass.  

The hardener type of MEKP (Methyl Ethyl 

Keto Peroxide ) was added by 2% of resin and the 
Cobalt Octeate also added by 0.5% to speed up 

the reaction and increases the solidification of the 

samples. 

In this studying, the Lee's disk method is used 
for measuring the thermal conductivity. Figure (1) 

shows the electric circuit which used for this 

method. Figure (2) shows the instrument used for 
this method. The instrument is consist of heating 

coil and three brass disks (1, 2, 3). The specimen 

was fixed between brass disks (1,2) while the 
heating coil was fixed between brass disks (2,3) as 

shown in figure (1).  

The cylindrical specimens were made from 

polyester matrix material which reinforced by 

glass fibers, the geometry of the specimens are  r 
=0.02m, ds =0.007m.  

The first group of specimens reinforced with 

the glass fibers parallel to the direction of thermal 

flow and the second group of the specimens are 
perpendicular to the thermal flow. The 

experimental temperature T1, T2, and T3 were 

measured by means of Lee`s disk method. The 
applied voltage across the terminal of the heating 

coil is (6 Volt) and the current is (0.2 Amper). 

The heating coil was used to heat the brass disks 

(1, 2, 3) and heat transfer across the specimen 
from the bass disk (2) to brass disk (1).The 

temperatures of all disks increases gradually and 

the temperatures recorded every (5 minutes) by 
using thermometers until reach the equilibrium 

temperature of all disks (i.e. T2=T3).  

The losses in heat (e) was calculated from 
equation (6).The thermal conductivity (k) was 

calculated from equation (5) by using the 

experimental temperatures (T1, T2, T3) and the 

dimension of specimen (r,ds). 

 

 

 

 

 

                          

 

 

 

 

Fig.1. Thermal Conductivity Measurment. 

 

 

 

 

 

 

 

 

 

 

Fig. 2. Test Apparatus with Specimens Test.

m
V

m
K

f
V

f
K

c1
K 

f
V

m
K

m
V

f
K

m
K

f
K

c2
K






3 
 

 1     S      2       H   

T1           T2               T3      

A 

T2 T1 
Heater Specimen 

T3 

Brass Disks 



Mohammed Sellab Hamza                                      Al-Khwarizmi Engineering Journal, Vol. 4, No. 3, PP 85-97 (2008) 

 

 88 

Results and Discussions 
 

The properties of the unsaturated polyester and 

glass fibers are presented in table (1). Table (2) 
illustrates the theoretical thermal conductivity of 

composite material for parallel and perpendicular 

arrangement and the difference between them. This 
table indicated that the difference increase with the 

increasing the fiber volume fracture and this leads to 

that the thermal conductivity of composite materials 
improve with the addition of glass fibers.    

Tables (3, 4) show some properties of the 

manufactured composite specimens at different fiber 

volume fraction for both directions parallel and 

perpendicular respectively. These tables show 
that the properties of manufactured specimens 

were improved and increase with the 

increasing of the fiber volume fraction of glass 
fibers.     

Figure (3) shows the relationship between 

the experimental temperature of the wall 

surface (T1and T2) of the tested specimens and 
the time for the unsaturated polyester. It is 

clear from these figures that the experimental 

temperatures of wall surface (T2 and T3) 
increase with time until it reach the 

equilibrium temperature (T2=T3). 

 

Table 1 

Properties of Unsaturated Polyester and Glass Fibers[12].  

Percent 

Elongation 

% 

Poisson's 

Ratio 

Thermal 

conductivity 

(W/m.
 o

C) 

Tensile 

Stress 

(MPa.) 

Modulus of 

Elasticity 

(GPa ) 
Density 

(g/cm
3
) Material Type 

4.3 0.22 1.3 3450 72.5 2.58 Glass Fiber 
> 2.6 0.33 

 
0.17 70.3-103 2.06-4.41 1.04-1.46 Unsaturated 

Polyester 
 
 

Table 2 

Theoretical Thermal Conductivity For the Parallel and the Perpendicular Arrangement Composite Materials. 

Fiber Volume 

Fraction % 

Theoretical Thermal Conductivity  (Kc) (W/m.
 o

C) The Difference Between Parallel 

and Perpendicular Arrangement Parallel Arrangement Perpendicular Arrangement 

0 0.170 0.170 0.000 

3 0.204 0.175 0.029 

6 0.238 0.179 0.059 

9 0.272 0.184 0.088 

12 0.306 0.190 0.116 

15 0.340 0.195 0.145 

 

 

Table 3  

Properties of the Manufactured Composite Specimens When the Fiber are   Arranged in the Parallel Direction to 

the Heat Flow. 

Properties 
Fiber Volume Fraction 

3% 6% 9% 12% 15% 

ρ(g/cm
3
 ) 1.086 1.32 1.179 1.225 1.271 

Kx(W/m-C
o
) 0.175 0.179 0.184 0.190 0.195 

Ky(W/m-C
o
) 0.175 0.179 0.184 0.190 0.195 

Kz(W/m-C
o
) 0.204 0.238 0.272 0.306 0.340 

 

 

Table 4  

Properties of the Manufactured Composite Specimens When the Fiber are Arranged in the Perpendicular 

Direction to the Heat Flow. 

Properties 
Fiber Volume Fraction 

3% 6% 9% 12% 15% 

ρ (g/cm
3
 ) 1.086 1.32 1.179 1.225 1.271 

Kx(W/m-C
o
) 0.204 0.238 0.272 0.306 0.340 

Ky(W/m-C
o
) 0.204 0.238 0.272 0.306 0.340 

Kz(W/m-C
o
) 0.175 0.179 0.184 0.190 0.195 



Mohammed Sellab Hamza                                      Al-Khwarizmi Engineering Journal, Vol. 4, No. 3, PP 85-97 (2008) 

 

 89 

 

 

 

 

 

 

 

 

 

 

 

 

 

Fig.3. Relationship between the Experimental Wall Surface Temperatures (T1and T2) of the Tested 

Specimens and the Time for the Unsaturated Polyester. 

 

 

Figure (4) shows the relationship between the 

temperature of the wall surface (T1and T2) of the 
tested specimens and the time for the different fiber 

volume fraction (Vf=3%and15%) for experimental 

work when the thermal flow in the parallel direction 
to the glass fibers.  

Figure (5) shows the relationship between the 

temperature of wall surface (T1and T2) and time for 
the different fiber volume fraction (Vf=3%, and15%) 

for experimental work when the thermal flow in the 

perpendicular direction to the direction of the glass 

fibers.  
The figures (4 and 5) indicated that the 

experimental temperatures (T2and T3) reach the 

equilibrium state ( T2=T3 ) at different time. 
The relationship between the theoretical thermal 

conductivity and the fiber volume fraction (Vf) for 

parallel and perpendicular direction of glass fibers is 

presented in figure (6), it can be seen that the results 
of the parallel direction was higher than the results 

when the fiber arranged in the perpendicular direction 

to the heat flow. It can be seen that the difference 
between the parallel and the perpendicular direction 

increases with increasing the fiber volume fraction as 

shown in the table (2). Also it was found that the 
maximum difference between the theoretical results 

of the parallel direction and the perpendicular 

direction was (42.6%) at the fiber volume fracture 

(vf=15%) and the minimum difference was 14.2% at 
fiber volume fracture (vf=3%). The experimental 

results indicated that the maximum percentage of 

improvement of the experimental thermal 

conductivity for parallel arrangement 
was96.9% at the vf=15%, and the maximum 

improvement for perpendicular was 13.77% at 

the vf=15% this difference is due to the 
arrangement and orientation of the glass fibers. 

Figure (7) shows the relationship between 

the theoretical and experimental thermal 
conductivity with different values of volume 

fraction of glass fibers for parallel direction, 

while the relationship for perpendicular 

direction is illustrated in figure (8). The 
relationship between the theoretical and the 

experimental thermal conductivity with the 

different values of the fiber volume fraction 
(3% and 15% ) for parallel and perpendicular 

arrangement is illustrated in figure (9), while 

the same relationship different values of the 

fiber volume fraction (9% and 15% ) is 
illustrated in figure (10). Figures (6, 7, 8, 9 and 

10) indicated that the theoretical thermal 

conductivity is greater than the experimental 
conductivity. The difference between the 

theoretical and the experimental conductivity 

is due to the fact that the theoretical 
conductivity is real values and obtained from 

the equations while the experimental values 

depend on the properties of matrix material , 

fibers, the precision of instrument, reading, and 
environmental condition. From the 

experimental and the theoretical results found 

Time (min.) 

W
a
ll

 S
u
rf

a
c
e
 T

e
m

p
e
ra

tu
re

 (
C

o
) 

0

5

10

15

20

25

30

35

40

45

0 5 10 15 20 25 30 35 40 45 50

Time(min)

T
h

e
 t

e
m

p
e

ra
tu

re
 o

f 
w

a
ll
 s

u
rf

a
c

e
(c

)
T1

T2



Mohammed Sellab Hamza                                      Al-Khwarizmi Engineering Journal, Vol. 4, No. 3, PP 85-97 (2008) 

 

 90 

that for the parallel direction the maximum difference of thermal conductivity between the
theoretical and experimental values was (3.82%) 

at (Vf = 15%) while the minimum value was (2.94 

%) at (Vf = 3 %). For the perpendicular direction 
it was found that the maximum difference of 

thermal conductivity between the theoretical value 

and experimental value was (2.56%) at (Vf =15%) 

while the minimum value was (1.71%) at          
(Vf =3 %). It is clear from the results of the this 

research  that the thermal conductivity increases 

with increasing fiber volume fraction of the glass 

fibers but the percentage of increase for parallel 

direction is more than that for perpendicular 

direction for both theoretical and experimental 
work. All the results of the theoretical and 

experimental results prove that the parallel 

arrangement is the best for application and the 

improvement of the thermal conductivity depend 
on the properties of the matrix and the 

reinforcement material and the orientation of the 

fibers. 
 

 

               

20

25

30

35

40

45

50

55

60

0 5 10 15 20 25 30 35 40 45 50 55 60 65

Y

Y1

 

(a)   

 

 

 

 

 

 

 

 

  

(b) Vf=15% 

 

 

 

 (b)    

Fig.4. Relationship between the Experimental e Wall Surface Temperature (T1and T2) of the Tested 

Specimens and the Time When the Fiber Arranged in the Parallel Direction at: 

 a) Volume Fraction of Fiber 3%   b) Volume Fraction of Fiber 15%. 

 

Vf =3% 

Time (min) 

W
a

ll
 S

u
r
fa

c
e
 T

e
m

p
e
r
a
tu

r
e
 (

C
o
) 

T1 

T2 

Parallel Direction 

20

25

30

35

40

45

50

55

60

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Y

Y1

W
a
ll

 S
u

r
fa

c
e
 T

e
m

p
e
r
a

tu
r
e
 (

C
o
) 

T1 
T2 

Parallel Direction 

Vf =15% 

Time (min) 



Mohammed Sellab Hamza                                      Al-Khwarizmi Engineering Journal, Vol. 4, No. 3, PP 85-97 (2008) 

 

 91 

 

 

 

 

 

(a) Vf=3% 

 

 

 

 

 

 

 

(a) 

 

 

 

 

 

 

 

 

 

 

 

(b)  

Fig.5. Relationship between the Experimental Wall Surface Temperature (T1and T2) of the 

Tested Specimens and the Time When the Fiber Arranged in the Perpendicular Direction 

at:   a) Volume Fraction of Fiber 3%.   b) Volume Fraction of Fiber %15. 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Fig.6. The Relation between the Theoretical Thermal Conductivity and the Fiber 

Volume Fraction (Vf) for Parallel and Perpendicular Direction of Manufactured 

Specimens. 

20

25

30

35

40

45

50

55

0 5 10 15 20 25 30 35 40 45 50 55

Time (min.)

T
e

m
p

e
ra

ti
o

n
 o

f 
W

a
ll
 S

u
rf

a
c

e
 (

C
O

 )

T1

T2

(C
o
) 

W
a
ll

 S
u

r
fa

c
e
 T

e
m

p
e
r
a
tu

r
e
 (

C
o
)  

Vf=3% 

 

20

25

30

35

40

45

50

55

0 5 10 15 20 25 30 35 40 45 50 55 60

Time(min.)

T
e

m
p

e
ra

tu
re

 o
f 

W
a

ll
 S

u
rf

a
c

e
 (

C
O

) T1

T2(
C

o
) 

W
a

ll
 S

u
r
fa

c
e
 T

e
m

p
e
r
a

tu
r
e
 (

C
o
) 

 

Vf=15% 

 

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

T
h

e
r
m

a
l 
C

o
n

d
u

c
ti

v
it

y

Theoretical for Parallel

Theoretical for Perpendicular

      0         3        6          9          2          15     

              Fiber Volume Fraction ( % ) 

  
  

  
  

  
T

h
e
r
m

a
l 

C
o
n

d
u

c
ti

v
it

y
 (

W
/m

.C
o
) 



Mohammed Sellab Hamza                                      Al-Khwarizmi Engineering Journal, Vol. 4, No. 3, PP 85-97 (2008) 

 

 92 

 

 

 

 

 

 

 

 

 

 
 

 

 

 

 

 

 

 

Fig.7. The Relation between the Theoretical and Experimental Thermal Conductivity with the 

Fiber Volume Fraction (Vf) for Parallel Direction of Manufactured Specimens. 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Fig.8. The Relation between the Theoretical and Experimental Thermal Conductivity with the 

Fiber Volume Fraction (Vf) for Perpendicular Direction of Manufactured Specimens. 

 

 

 

 

 

 

 

 

 

 

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

T
h

e
rm

a
l 
C

o
n

d
u

c
ti

v
it

y

Theoretical

Experimental

0            3               6            9           12            15 

                     Fiber Volume Fraction ( % ) 

 T
h

e
r
m

a
l 

C
o
n

d
u

c
ti

v
it

y
 (

W
/m

.C
o
) 

0.15

0.155

0.16

0.165

0.17

0.175

0.18

0.185

0.19

0.195

T
h

e
rm

a
l 
C

o
n

d
u

c
ti

ti
v

it
y

Theoretical

Experimental

  0            3              6            9            12            15    

                    Fiber Volume Fraction ( % ) 

T
h

e
r
m

a
l 

C
o

n
d

u
c
ti

v
it

y
 (

W
/m

.C
o
) 



Mohammed Sellab Hamza                                      Al-Khwarizmi Engineering Journal, Vol. 4, No. 3, PP 85-97 (2008) 

 

 93 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Vf = 3% 

 

 

 

 

 

 

 

 

 

 

 

 

 

Vf = 6% 

Fig.9. The Relation between the Theoretical and Experimental Thermal Conductivity with the 

Different Value of Fiber Volume Fraction (Vf = 3% and 6%) for Parallel and Perpendicular 

Direction of Manufactured Specimens. 

 

 

 

 

 

 

 

 

0.155

0.16

0.165

0.17

0.175

0.18

0.185

0.19

0.195

0.2

0.205

T
h

e
rm

a
l 

C
o

n
d

u
c
ti

v
it

y
 

(W
/m

.C
 )

Theoretical

Experimental

         Parallel Direction          Perpendicular Direction               

T
h

e
r
m

a
l 

C
o
n

d
u

c
ti

v
it

y
 (

W
/m

.C
o
) 

0

0.05

0.1

0.15

0.2

0.25

T
h

e
rm

a
l 
C

o
n

d
u

c
ti

v
it

y
 (

 W
 /
m

.C
o

 )

Theoretical

Experimemtal

Parallel Direction         Perpendicular Direction      

T
h

e
r
m

a
l 

C
o

n
d

u
c
ti

v
it

y
 (

W
/m

.C
o
) 



Mohammed Sellab Hamza                                      Al-Khwarizmi Engineering Journal, Vol. 4, No. 3, PP 85-97 (2008) 

 

 94 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Vf= 9 % 

 

 

 

 

 

 

 

 

 

 

 

 

 

Vf= 15 % 

Fig.10. The Relation between the Theoretical and Experimental Thermal Conductivity with the 

Different Value of Fiber Volume Fraction (Vf = 9% and 15%) for Parallel and Perpendicular 

Direction of Manufactured Specimens. 

 

 

Conclusion 
 
     The main conclusions of this research are:  

1- The thermal conductivity of composite 
materials is increasing with increasing of fiber 
volume fraction (Vf), and for the parallel 

direction was higher than that for the 

perpendicular direction. 

2- The minimum value of experimental thermal 
conductivity for perpendicular   arrangement 

was (0.172 W/m. C) at fiber volume fraction 
(3%) and the percentage of improvement and 
the increasing of the experimental thermal 

conductivity was 13.77% while the maximum 

value of experimental thermal conductivity 

for parallel arrangement was (0.237 W/m. C) 

0

0.05

0.1

0.15

0.2

0.25

0.3

T
h

e
rm

a
l 
C

o
n

d
u

c
ti

v
it

y
 (

W
/m

.C
)

Theoretical

Experimental

           Parallel Direction         Perpendicular Direction      
 

 

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

T
h

e
rm

a
l 
C

o
n

d
u

c
ti

v
it

y
 (

 W
/m

. 
C

 )

Theoretical

Experimental

       Parallel Direction         Perpendicular Direction      
 



Mohammed Sellab Hamza                                      Al-Khwarizmi Engineering Journal, Vol. 4, No. 3, PP 85-97 (2008) 

 

 95 

at fiber volume fraction (15%) and the 
percentage of improvement and the increasing 

of the experimental thermal conductivity was 

96.9%. 
3- For parallel. Arrangement, the maximum 

difference between the experimental and 

theoretical values of the thermal conductivity 

was (3.82%) at fiber volume fraction (15%) 
and the minimum difference was 2.94% at 

fiber volume fraction (3%).   

4- For perpendicular arrangement, the maximum 
difference between experimental and 

theoretical thermal conductivity was 2.56% at 

fiber volume fraction (15%) and the minimum 

difference was 1.71% at fiber volume fraction 
(3%). 

 

 

Notation 
 

d1, d2 , d3 Thickness of the brass disks (m) 

ds Thickness of the composite 

specimen (m) 

e Convection heat transfer 

Coefficient (W/m
2
. C) 

K Thermal conductivity (W/m. C) 

Kc1 Thermal conductivity of the 
composite specimen in the parallel 

direction of the fibers (W/m. C) 

Kc2 Thermal conductivity of the 

composite specimen in the 

perpendicular direction of the fibers 

(W/m. C). 

Kf, Km Thermal conductivity of fibers and 

matrix (W/m. C). 
q Heat flux. 

r Radius of specimen (m). 

T1, T2,T3 Temperature across the copper 

disks (1, 2, 3) (C). 

νc νm, νf Volume of composite, matrix and 
reinforced material (m

3
). 

Vf,Vm Fiber volume fraction of matrix and 

fiber (%). 
dT/dx Temperature gradient (%). 

p Power pass though heating coil 

(watt) 

I Electric current pass though heating 
coil(Ampere) 

V Voltage across the terminal of 

heating coil(volt) 

 

 

 

 

References 
 

[1] Zhan – Sheng Guo, Shanyi Du and Boming 
Zhang, “Temperature Distribution of the 
Thick Thermoset Composite”, Journal of 

Modeling and Simulation in materials Science 

and engineering, Volume 12, issue 3, (China) 
may, (2004). 

[2] Murthy, Dr. A. Rama Krishna and B.V Rama 
Krishna,” Thermal Analysis of Epoxy Based 
Fiber-Reinforced”, IE(I) Journal–MC, Vol.84, 

April, (2004) 

[3] F. Rondeaux, Ph. Bready and J.M. Rey, 
“Thermal Conductivity Measurements of 
Epoxy Systems at Low Temperature”, 

Cryogenic Engineering Conference (CEC), 

(USA), July (2001). 
[4] Raimund Rolfes,” 2D Finite Element 

Formulation for 3D Temperature Analysis of 

Numerical Simulation of Heat Transfer”, 

Journal of numerical simulation of heat 
transfer, Germany, May, (2001). 

[5] Lamees A. Khalaf, "Studying the mechanical 
and physical properties for unsaturated 
polyester reinforced by fiber glass and nylon 

fiber  

composites", M.Sc. Thesis, University of 
Technology, Materials engineering 

Department (2006) Baghdad Iraq. 

[6] M.W. Pilling, B. Yates, M.A. Black, “The 
Thermal Conductivity of Carbon Fiber – 
Reinforced Composites “, Journal of 

Materials Science, Vol.14, (1979). 

[7] Saad M. Elie, "Studied the mechanical 
properties and thermal conductivity for 

polymer composite material reinforced by 

aluminum and aluminum oxide particles", 

M.Sc. thesis, University of Technology, 
Materials engineering Department (2007) 

Baghdad Iraq .  

[8] B.W. James and P. Harrison,” Analysis of the 
Temperature Distribution, Heat Flow and 

Effective Thermal Conductivity of 

Homogenous Composite Materials with 
Anisotropic Thermal Conductivity”, Journal 

of Physics, Vol.D, Applied Physics, issue 9, 

sept. (1992). 

[9] Charles A Sorrell, “Advanced Nanoporous 
Composite Materials for Industrial Heating 

Applications”, Applied Sciences Laboratory, 

Inc., 
http://www.eere.energy.gov/industry/imf/pdfs

/ibni.composite. pdf., (2002) 

[10] W. Bolton,” Engineering Materials 
Technology”, butterworth – Heinemann, 

Third edition, (1998) Great Britain. 

http://www.eere.energy.gov/industry/imf/pdfs/ibni.composite
http://www.eere.energy.gov/industry/imf/pdfs/ibni.composite


Mohammed Sellab Hamza                                      Al-Khwarizmi Engineering Journal, Vol. 4, No. 3, PP 85-97 (2008) 

 

 96 

[11] Oronzio Manca, Biagio Morrone, Giuseppe 
Romano, “Analysis of Thermal Response of 

Composite Materials “, Dipartimento 

Ingegneria Aerospaziale Meccanica, 
ttp://event.ua.pt/ds2005/manca3.pdf., Italy, 

(2005).  

[12] William D. Callister,” Materials Science 
and Engineering An Introduction”, Sixth 
Edition, John Wiley and Sons, Inc., 

(2003).U.S.A .New York.  

[13] Munshid  H. Muhammad, Study of  
Mechanical and Thermal Behaviour of 

Hybrid Composite from Carbon and Kevlar 

Fibers M.Sc. Thesis, University of 
Technology, Al-Rasheed College for 

Engineering and Sciences Applied Science 

Department (1989)Baghdad Iraq .  
[14] Salwin B. Abid Al-Wihid, Study of  

Mechanical properties of Hybrid Composite 

from Carbon and Kevlar Fibers M.Sc. 

thesis, University of Technology, Al-
Rasheed College for Engineering and 

Sciences Applied Science Department 

(1989) Baghdad Iraq. 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 



Mohammed Sellab Hamza                                      Al-Khwarizmi Engineering Journal, Vol. 4, No. 3, PP 85-97 (2008) 

 

 97 

 

 الموصليت الحراريت  دراست تأثير الكسرالحجمي أللياف الزجاج على

للمواد المتراكبت البوليمريت 
              

محمذ صالب حمزة 
 الدامعح الركىىلىخٍح /  قسم هىذسح المىاد

 

 
 

الخالصت 
على الرىطٍلح الحزارٌح  (% 3 %,6 %,9 %,12 %,15)      ذم فً هذا الثحث دراسح ذأثٍز الكسز الحدمً اللٍاف الشخاج وتىسة مخرلفح 

العٍىاخ طىعد فً مدمىعرٍه المدمىعح . حٍث طىعد العٍىاخ مه مادج الثىلً أسرز غٍز المشثع  المقىاج تالٍاف الشخاج. للمادج المرزاكثح

االولى كاود  فٍها الٍاف الشخاج مزذثح تشكل مىاسي لالوسٍاب الحزاري, اما المدمىعح الثاوٍح وضمد ترزذٍة  االلٍاف تشكل عمىدي على 

. االوسٍاب الحزاري

اثثرد الىرائح العملٍح ان الرزذٍة المىاسي لاللٍاف ٌعطً مىطلٍح حزارٌح  . فً فحض العٍىاخ (  Leeś disk)   اسرخذمد طزٌقح قزص لً 

حٍث كان مقذار الشٌادجفً . اعلى مه الرزذٍة العمىدي وان المىطلٍح الحزارٌح للمادج المرزاكثح ذشداد مع سٌادج الكسز الحدمً لاللٍاف

للرزذٍة العمىدي كذلك اثثد الىرائح العملٍح ان اقل %  13.33للرزذٍة المىاسي و % 96.91المىطلٍح الحزارٌح تسثة الرقىٌح تااللٍاف هى 

اما اعلى قٍمح كاود   (Vf=3%)للرزذٍة العمىدي عىذ الكسز الحدمً  (0.172w/m.C)قٍمح للمىطلٍح الحزارٌح كاود 

(0.327W/m.C)  ًللرزذٍة المىاسي عىذ كسز حدم(Vf  =  15%.)