A PREDICTION OF EFFECTIVE THERMAL CONDUCTIVITY · PDF filea prediction of effective thermal...

International Journal Of Recent Advances in Engineering & Technology (IJRAET)

ISSN (Online): 2347-2812, Volume-1, Issue -3, 2013

1

A PREDICTION OF EFFECTIVE THERMAL CONDUCTIVITY OF

POLYESTER COMPOSITES FILLED WITH MICRO-SIZED RICE

HUSK PARTICLES

1Kush Kumar Dewangan,

2Ankur Panwar,

3Neeraj Kumar Sharma

Gurgoan College of Engineering, Gurgoan , India

Email : 1kush.mech@gmail.com1,

2ankurpgce@gmail.com,

3neerajkumar007007@gmail.com

Abstract—This paper describes the preparation of a new

class of polyester composites filled with rice husk, which is

an agro waste as well as a potential natural reinforcing

element. A numerical simulation of the heat-transfer

process within polyester matrix composites filled with

micro-sized rice husk particles is proposed in this paper. A

commercially available finite-element package ANSYS is

used for this numerical analysis. Three-dimensional

spheres-in-cube, cubes-in-cube and ellipsoids-in-cube

lattice array models are constructed to simulate the micro -

structure of composite materials with rice husk content

ranging from about 1 to 11 vol.% and the effective thermal

conductivities of the composites are estimated. Results

show that the effective thermal conductivity (Keff) of the

composites decreases with increase in the volume fraction

of the rice husk fillers. Finally, the simulations are

compared with measured Keff values obtained from other

established correlations such as Rule of Mixture (ROM),

Maxwell’s model and Lewis & Nielsen. This study reveals

that the incorporation of rice husk particles results in

reduction of thermal conductivity of polyester resin

thereby increasing its insulation capability. It is found that

with incorporation of about 11 vol. % of raw rice husk in

the polyester resin reduces its thermal conductivity by

approximately 15 %.

Index Terms—FEM Simulation, Polymer Composites, Rice

Husk Particles, Thermal Conductivity

I. INTRODUCTION

Recently, polymer based composite have more attracted

due to their outstanding properties such as, corrosion

resistance, low coefficient, wear resistance, thermal

conductivity etc. New generation electronic devices

require small size of packages and higher power along

with the high thermal conductivity of polymer

composite. Low thermal conductive polymer is also

demanded. Recently polymer is used as various

insulating purpose. That require new composite with

relatively low thermal conductivity. Thermal

conductivity of polymer may be improved or reduced by

using a low thermal conductivity or high thermal

conductive filler material.

Various type of Natural fillers such as jute, pineapple,

rice husk , hemp, curaua ,wood have been successfully

used to improve the mechanical properties of

thermoplastic composites [1-3]. The first approach on

the use of rice husk ash as a reinforcing filler in

polymers to produce composite is reported by Haxo and

Mehta [4]. Recently, Garcia et al. [5] have analyzed the

use of rice husk as reinforcing material for recovery of

tire rubber powder using the sintering method.

Mechanical properties and thermal stability of rice husk

ash filled epoxy foams, they used at 22.7 wt % of rice

husk ash, the particle average size of WRHA and BRHA

were 2.5 and 2.9 mm respectively was studied by Stefani

et al. [6] The mechanical properties of the epoxy foams

improve especially with the incorporation of WRHA.

Premalal et al. [7] studied on Comparison of the

mechanical properties of rice husk powder filled

polypropylene composites with talc filled polypropylene

composites; it was found that talc composites are easier

to process than RHP filled composites. However, talc

composites exhibit higher yield strength, Young‟s

modulus, flexural modulus and impact resistance. It was

found that RHP composites show higher elongation at

break compared to talc composites.

In recent study Griesinger, Hurler, and Pietralla [8]

found that the thermal conductivity of low-density PE

was seen to increase from 0.35 for an isotropic sample,

to the value of 50W/mK for a sample with an orientation

ratio of 50. This value of thermal conductivity is in the

range of thermal conductivity for steel. The thermal

conductivity of magnetite filled metal-oxide particle

International Journal Of Recent Advances in Engineering & Technology (IJRAET)

ISSN (Online): 2347-2812, Volume-1, Issue -3, 2013

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filler (magnetite, Fe3O4) polymers increases from 0.22

to 0.93 W/(m K) for a filler content of 44 vol% of

magnetite, whereas the electrical resistivity decreases

more than seven orders of magnitude from an insulator

(0% of magnetite) to 10 kV m (47 vol% of magnetite).

Maxwell [9] proposed an equation to calculate the

effective thermal conductivity of Composites, when the

particles are well-dispersed and have no interaction one

with the others. Tsao [10] predicts an equation for the

thermal conductivity of a two-phase solid mixture by

using the additivity of conductance in parallel. Cheng

and Vachon [11] modified Tsao‟s model without

knowing the distribution of the discontinuous phase in

the continuous phase. A semi theoretical model by

Lewis and Nielsen [12] predicts the elastic module of

composites and then the thermal conductivity.

Veyret et al. [13] they proposed on a numerical

approach to predict the effective thermal conductivity of

granular of fibrous reinforced composite and compared

with theoretical and experimental results. Kumlutas¸ and

Tavman [14]they used a finite element model to obtain

the effective thermal conductivity of HDPE composites

as filler content up to 16% volume, as Shape of particle

sphere and cubes, further compared the effective

conductivity with empirical and experimental results.

Nayak et al. [15] they studied the thermal conductivity

of epoxy composites using a 3D finite and element

model of Sphere in cube in lattice array distribution.

Among all these study expect Nayak et al. [15] are used

organic filler (pine wood dust) which is eco-friendly and

bio-degradable. The objective of this paper is to develop

a high thermal insulating polymer composite, contenting

micro-sized Rice husk. Numerical approach was used to

determine the effective thermal conductivity of particle

composite in 3D models. FEM was performed to

understand the relationship between the effective

thermal conductivity of polymer composite at different

filler shape and different volume fraction. FEA is based

on steady-state, heat conduction. Further, the effective

thermal conductivity of Rice husk particles filled in

polymer composite is calculated numerically as a

function of filler concentration and the result obtained

from this investigation are compared with the other

theoretical and empirical models and also with

experimental results.

II. MATHEMATICAL ANALYSIS AND

THEORETICAL CONSIDERATION

In this section discussed several models for Thermal

conductivity of the two-phase system is predicted by

various methods, most of them are given more near to

experimental value.Among the models proposed the

thermal conductivity of composite has depend in the

dispersed region. In previous report, thermal conduction

model proposed by Maxell, Cheng and Vachon,

Ziebland, Lewis and Nielsen were discussed. Thermal

conduction model proposed by Agari and Uno was

discussed about the region of more than 30–vol %

content of filler particles.

First simplest model for two-component composite in

that material would be arranged in parallel or series with

respect to heat flow. This gives the effective thermal

conductivity of composite in either upper or lower

bounds. For parallel conduction model

(1- )c m fk ø k øk (1)

Where k: thermal conductivity, c: composite, m: matrix,

f: filler,ø :volume fraction of filler.

And for series conduction model:

1 (1- )

c m f

ø ø

k k k

(2)

The effective thermal conductivity of composite is given

by when considered geometric mean model:

1.f

mck k k

(3)

The correlations presented by Eqs. (1), (2) and (3) are

derived on the basis of the Rules-of- mixture. Tsao [10]

derived an equation relating the two-phase solid mixture

thermal conductivity to the conductivity of the

individual components and to two parameters which

describe the spatial distribution of the two phases. By

assuming a parabolic distribution of the discontinuous

phase in the continuous phase. Further the model of the

Tsao [10] is modified by the cheng and vachon [11] this

model that did not required data for additional

parameter. Assuming a parabolic distribution of the

discontinuous phase volume fraction cheng and vachon

[11] proposed a new model which is applicable for

spherical particle as well as foe fiber filled composite

mf kk

1

1 1

2

2

mmfm

mf

mfmmf

ck

B

kkBk

kkCBtan

kkBkkkCk

(4)

If mf kk

1 1

kc C k k k B k km m mf f

International Journal Of Recent Advances in Engineering & Technology (IJRAET)

ISSN (Online): 2347-2812, Volume-1, Issue -3, 2013

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12

2

Bk B k k C k km m mf f B

InB kmk B k k C k km m mf f

(5)

Where for both equation

3 / 2B 4 2 / (3 )C

By the using potential theory. Maxwell [9] obtained an

exact solution for the conductivity of randomly

distributed and non-intersecting homogenous spheres in

a homogenous medium.

fmmf

fmmf

mckkkk

kkkkkk

2

22 (6)

Halpin [16] equation is modified by the Lewis and

Nielsen [12].to includes the effect of the shape of the

particles and the orientation or type of packing for a

two-phase system, and they have got:

B

ABkk mc

1

1 (7)

Akk

kkB

mf

mf

1 (8)

2

11

m

m (9)

The values of A and

m for many geometric shapes and

orientation are given in Tables I and II.

Table I Value of A for various systems [12]

Type of dispersed

phase

Direction of

heat flow

A

Cubes Any 2

Spheres Any 1.5

Aggregates of spheres Any (2.5/ m) -1

Randomly oriented

rods Aspect ratio=2

Any 1.58

Randomly oriented

rods Aspect ratio=4

Any 2.08

Randomly oriented

rods Aspect ratio=6

Any 2.8

Randomly oriented

rods Aspect ratio=10

Any 4.93

Randomly oriented

rods Aspect ratio=15

Any 8.38

Uniaxially oriented

fibers

Parallel to

fibers

2L/D

Uniaxially oriented

fibers

Perpendicula

r to fibers

0.5

Table II Value of m for various systems [12]

Shape of

particle

Type of

packing m

Spheres Hexagonal

close

0.7405

Spheres Face centered

cubic

0.7405

Spheres Body centered

cubic

0.60

Spheres Simple cubic 0.524

Spheres Random close 0.637

Rods and fibers Uniaxial

hexagonal close

0.907

Rods and fibers Uniaxial simple

cubic

0.785

Rods and fibers Uniaxial

random

0.82

Rods and fibers Three

dimensional

random

0.52

III. EXPERIMENTAL STUDY

A. Composite Fabrication

Polyesteris used as matrix material in a liquid form, with

low thermal conductivity 0.345W/mk at room

temperature and density 1.35gm/cc. The organic bio-

based filler material rice husk is used in a powder form.

Particle approximately as shape like sphere and sized in

the range of 80-100 microns for rice husk. Solid density

of the rice husk is about 0.4 to 0.7 gm/cc and its thermal

conductivity 0.0359 w/mk. The dough (Polyester filled

with RHs) is then slowly decanted into the glass tubes,

coated beforehand with wax and uniform thin film of

silicone-releasing agent. The composites are cast by

conventional hand-lay-up technique in cup so as to get

plate

Specimens (dia. 40 mm, height 5 mm).

International Journal Of Recent Advances in Engineering & Technology (IJRAET)

ISSN (Online): 2347-2812, Volume-1, Issue -3, 2013

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Table III Preparation of particulate filled composites by

hand- lay-up technique.

Sample Composition

1 Polyester +1.88vol%(0.765 wt% ) filler

2 Polyester +4.18 vol%(1.702wt% )filler

3 Polyester +6.54vol%(2.664 wt% )filler

4 Polyester +9.16vol%(3.731 wt% )filler

5 Polyester +11.30vol%(4.603wt% )filler

Composite samples of five different compositions, as

listed in Table 3are made. The mean particle size of rice

husk used in samples 1 (1.88vol.%), 2 (4.18 vol.%), 3

(6.54 vol.%),4(9.16 vol.%) and 5(11.3 vol.%) is 100

micron. The castings are left to cure at room temperature

for about 24 h after which the cup is broken and samples

are released. Specimens of suitable dimension are cut

using a diamond cutter for further physical

characterization and thermal conductivity test

B. Operating Principle of Unithermtm

Model 2022

The measurement of thermal conductivity of various

materials Unitherm™ Model 2022 is used. These

include polymers, ceramics, composites, glasses,

rubbers, some metals, and other materials oflow to

medium thermal conductivity. For this measurement a

relatively small test sample is required. In this test non-

solids, such as pastes or liquids, can be tested using

special containers. Thin films can also be tested

accurately using a multi-layer technique. The tests are in

accordance with ASTM E-1530 Standard.

The process for determine the measure effective thermal

conductivity of composite material is held under a

uniform compressive load between two polished

surfaces, each controlled at a different temperature. The

lower surface is part of a calibrated heat flow transducer.

The heat flows from the upper surface, through the

sample, to the lower surface, establishing an axial

temperature gradient in the stack. After reaching thermal

equilibrium, the temperature difference across the

sample is measured along with the output from the heat

flow transducer. These values and the sample thickness

are then used to calculate the thermal conductivity. The

temperature drop through the sample is measured with

temperature sensors in the highly conductive metal

surface layers on either side of the sample. For one-

dimensional heat conduction equation by Fourier‟s Low

at the steady state condition given as Eq. (10).

1 2-T TQ KA

x

(10)

Where Q is the heat flux (W), K is the thermal

conductivity (W/m K), A is the cross-sectional area

(m2), T1-T2 is the difference in temperature (K), x is the

thickness of the sample (m).

The thermal resistance of a sample can be given as

xR

KA

(11)

where R is the resistance of the sample between hot and

cold surfaces (m2 K/W).Unitherm™ 2022 measures

thermal conductivity of solid material by determine the

thermal resistance between the upper and lower

surfaces. It‟s have a heat flux transducer that measures

the Q value and the temperature difference can be

obtained between the upper plate and lower plate. Thus

the thermal resistance can be calculated between the

upper and lower surfaces. Further, the thermal

conductivity of the samples can be calculated using Eq.

(11).

IV. NUMERICAL ANALYSIS

To predict the effective thermal conductivity of the

composite the finite element method (FEM) is more

efficient. Thermal analysis of heat transfer was carried

out using the finite element software of the program

ANSYS.The finite element method (FEM), originally

introduced by Turner et al. [17], is a powerful

computational technique for approximate solutions to a

variety of „„real-world” engineering The FEM is a

numerical procedure that can be used to obtain solutions

to a large class of engineering problems involving stress

analysis, heat transfer, fluid flow etc. ANSYS is general-

purpose finite- element modeling package for

numerically solving a wide variety of mechanical

problems that include static/dynamic, structural analysis

(both linear and nonlinear), heat transfer, and fluid

problems, as well as acoustic and electromagnetic

problems.

Numerical Modeling of the Problem

Basic step used for determine the thermal conductivity

of the composite the finite element method (ANSYS) is

modeling, material properties, element type, meshing

and boundary condition. Among these one of most

important step is element type and meshing that affect

the result very much. In Three-dimensional numerical

analysis solid98, solid87 and solid70 are used. Three-

dimensional numerical analysis was carried out for the

conductive heat transfer in the composite material. In

which matrix phase is taken as a cube and dispread

phase is as micro-sized particle in different shape like

sphere, cube and ellipsoid, which is in the form of lattice

array. Three dimensional-models have been used to

simulate the micro-structure of composite material for

various filler concentration1.41 vol.% to 11.3 vol% are

shown in figure (2).

In the numerical analysis of the heat conduction

problem, the temperatures at the nodes along the

International Journal Of Recent Advances in Engineering & Technology (IJRAET)

ISSN (Online): 2347-2812, Volume-1, Issue -3, 2013

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surfaces ABCD is prescribed as T1 (=100˚C) and the

convective heat transfer coefficient of ambient is

prescribed as 2.5 W/m2 K at ambient temperature of

27˚C. The heat flow direction and the boundary

conditions are shown in Fig. 1. The other surfaces

(ABFE, AEDH, BCGF, and CDHG) parallel to the

direction of the heat flow are all assumed adiabatic. The

temperatures at the nodes in the interior region and on

the adiabatic boundaries are unknown. These

temperatures are obtained with the help of finite-element

program package ANSYS. In this analysis of the ideal

case it will be assumed that the composites are

macroscopically homogeneous, locally both the matrix

and filler are homogeneous and isotropic, the thermal

contact resistance between the filler and the matrix is

negligible, the composite lamina is free of voids and the

filler are arranged in a square periodic array/uniformly

distributed in matrix. Temperature profile obtains from

FEM for composites with cubes, spheres and ellipsoids

particle concentration of 11.3 vol% are shown in Fig 3-

5.

Fig.1Boundary conditions

Fig.2 Geometric model of Rice husk particle (cubes) in

polyester (cube) at 11.3vol%

Fig.3Temperature profile for composite with cube

particle concentration of 11.3 vol%

Fig. 4.Temperature profile for composite with sphere

particle concentration of 11.3vol%

Fig.5 Temperature profile for composite with ellipsoid

(aspect ratio1:0.7) particle concentration of 11.3 vol%

International Journal Of Recent Advances in Engineering & Technology (IJRAET)

ISSN (Online): 2347-2812, Volume-1, Issue -3, 2013

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Table IV Effective Thermal conductivity values of composites obtained from different FEM models

Sample Filler content

(vol. %)

Effective thermal conductivity of the composite (W/mK)

FEM model

cubes-in cube

FEM model Ellipsoids -in

cube Aspect ratio (1:0.7)

FEM model

Spheres -in-cube

Experimental

value

1 0 0.345 0.345 0.345 0.345

2 1.8 0.336 0.331 0.331 0.334

3 4.18 0.327 0.324 0.316 0.325

4 6.54 0.317 0.313 0.309 0.316

5 9.16 0.308 0.304 0.300 0.306

6 11.3 0.297 0.293 0.296 0.299

V. RESULT AND DISCUSSION

In real materials, particle filled polyester composites

contain countless filler particles, because of the small

micron-scale filler. Note that the size of individual

particles remains unchanged. The distance between

particles will also decrease as the volume fraction of

fillers increases, Models with different volume fraction

content different no of filler particle ranging from 36

to 216. Basic step used for determine the thermal

conductivity of the composite the finite element

method (ANSYS) is modeling, selection of material

properties, element type, meshing and boundary

condition. Among these one of most important step

areselection of element type and meshing result. As

different filler shape like cubes, spheres and ellipsoids

effects on the effective thermal conductivity was

estimate by Finite element method are in table IV

shown in fig.6 with comparing experimental results.

The percentage errors associated with each particle

shape for individual composites are given as Table V.

It is further noted that while the particle cube give

more near to experimental value.

In percent study, a numerical and empirical approach

is used to obtain the effective Thermal conductivity of

the polyester composite material filled with micro-

sized RHs particle. The values of effective thermal

conductivities of the particulate filled polyester

composites with varied proportions of micro-sized

RHs particle obtained using Maxwell‟s correlation,

Rules-of-mixture model, Lewis and Nielsen (A=3

Fig. 6Thermal conductivity of polyester composites as

a function of filler content with different filler shape

International Journal Of Recent Advances in Engineering & Technology (IJRAET)

ISSN (Online): 2347-2812, Volume-1, Issue -3, 2013

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Table V Percentage errors of keff obtain from different

Sampl

e

Particulat

e content

Vo1%

Percentag

e error

with

respected

to

measured

value

FEM

model

cubes–in-

cube

FEM

model

Ellipsoids

–in-cube

Aspect

ratio

(1:0.7)

FEM

model

Spheres

–

in-cube

1 1.88 0.59 0.89 0.89

2 4.18 0.61 0.30 1.84

3 6.54 0.31 0.94 2.25

4 9.16 0.65 0.65 1.96

5 11.3 0.66 2.00 0.67

Filler shape with respected to the measured value

and m=0.637), Cheng and Vachon model and those

obtained from FEM analysis are presented in Table VI

and fig. 7. It presents a comparison among the results

obtained using these models with regard to the values

of effective conductivity obtained experimentally. It is

further noted that while the FEM and Maxwell‟s

model overestimate the value of thermal conductivity

the Rules-of-mixture and Lewis & Nielsen model

underestimates the value with respect to the

experimental value.

It leads to a conclusion that for a particulate filled

composite of this kind the FEM model as cube particle

shape can very well be used for predictive purpose in

determining the effective thermal conductivity for a

wide range of particle concentration of polyester

composite.

Table VI Thermal conductivity values of composites obtained from different methods

VI. CONCLUSION Rice husk reinforced polyester composites were

successfully prepared. Effective thermal conductivities

of the particulate filled polyester composites with

micro-sized RHs particle is increases with as the filler

content. From several experimental and computational

findings presented above, following conclusions can

be drawn:

Sample Particulat

e content

(vol. %)

Effective thermal conductivity of the composites (W/mK)

ROM model Lewis and

Nielsen

model

Maxwell‟s

model

FEM model

cubes–in-cube

Experimental

value

1 0 0.345 0.345 0.345 0.345 0.345

2 1.88 0.296 0.331 0.339 0.336 0.334

3 4.18 0.253 0.324 0.334 0.327 0.325

4 6.54 0.220 0.313 0.327 0.317 0.316

5 9.16 0.192 0.304 0.316 0.308 0.306

6 11.3 0.174 0.293 0.308 0.297 0.299

International Journal Of Recent Advances in Engineering & Technology (IJRAET)

ISSN (Online): 2347-2812, Volume-1, Issue -3, 2013

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(a)Finite element method (FEM) can be gainfully

employed for determination of effective thermal

conductivity of these composites with different amount

of Rice husk content.

(b)The values of effective thermal conductivity

obtained for various composite models from FEM are

in reasonable agreement with the experimental values

for a wide range of filler contents from 1.88vol% to

11.3 vol. %.

(c)The values of thermal conductivity obtained from

FEM (cubes-in-cube arrangement) are found to be

more accurate (close to experimental values) than the

calculated values from existing theoretical models

such as Rule of mixture, Maxwell‟s equation, Lewis

and Nielsen‟s model and FEM spheres-in-cube model

and Ellipsoid-in-cube model(aspect ratio 1:0.7 ).

(d)Incorporation of micro-sized Rice-Husk results in

significant improvement of thermal insulation for

polyester resin .With addition of 1.88 vol. % of Rice

Husk the thermal insulation of polyester improves by

about 3.18 % and with addition of 11.3 vol. % of Rice

Husk the improvement is about 13.33 %.

(e) With increased thermal insulation, this new class of

Rice husk filled polyester composites can be used for

applications such as electronic packages,

encapsulations, die (chip) attachments, thermal grease,

thermal interface material and electrical cable

insulation.

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