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Research Papers: Micro/Nanoscale Heat Transfer

# Effective Thermal Conductivities of a Novel Fuzzy Fiber-Reinforced Composite Containing Wavy Carbon Nanotubes

[+] Author and Article Information
S. I. Kundalwal, R. Suresh Kumar

Department of Mechanical Engineering,
Indian Institute of Technology,
Kharagpur 721302, India

M. C. Ray

Department of Mechanical Engineering,
Indian Institute of Technology,
Kharagpur 721302, India
e-mail: mcray@mech.iitkgp.ernet.in

1Present address: Mechanics and Aerospace Design Laboratory, Department of Mechanical and Industrial Engineering, University of Toronto, Toronto, ON M5S 3G8, Canada.

2Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received December 13, 2013; final manuscript received September 19, 2014; published online November 5, 2014. Assoc. Editor: Wilson K. S. Chiu.

J. Heat Transfer 137(1), 012401 (Nov 05, 2014) (12 pages) Paper No: HT-13-1642; doi: 10.1115/1.4028762 History: Received December 13, 2013; Revised September 19, 2014

## Abstract

This article deals with the investigation of the effect of carbon nanotube (CNT) waviness on the effective thermal conductivities of a novel fuzzy fiber-reinforced composite (FFRC). The distinctive feature of the construction of this novel FFRC is that wavy CNTs are radially grown on the circumferential surfaces of the carbon fibers. Effective thermal conductivities of the FFRC are determined by developing the method of cells (MOCs) approach in conjunction with the effective medium (EM) approach. The effect of CNT waviness is studied when wavy CNTs are coplanar with either of the two mutually orthogonal planes of the carbon fiber. The present study reveals that (i) if CNT waviness is parallel to the carbon fiber axis then the axial ($K1$) and the transverse ($K2$) thermal conductivities of the FFRC are improved by 86% and 640%, respectively, over those of the base composite when the CNT volume faction present in the FFRC is 16.5% and the temperature is 400 K, (ii) the effective value of $K1$ of the FFRC containing wavy CNTs being coplanar with the carbon fiber axis is enhanced by 75% over that of containing straight CNTs for the fixed CNT volume faction when the temperature is 400 K, and (iii) the CNT/polymer matrix interfacial thermal resistance does not affect the effective thermal conductivities of the FFRC. The present work also reveals that for a particular value of the CNT volume fraction, optimum values of the CNT waviness parameters, such as the amplitude and the wave frequency of the CNT for improving the effective thermal conductivities of the FFRC can be estimated.

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## Figures

Fig. 6

RVE of the unwound PMNC material containing a CNT wave coplanar with either the longitudinal plane (that is, 1–3 planes) or the transverse plane (that is, 2–3 planes) of the carbon fiber

Fig. 5

Transverse cross sections of the CFF with unwound and wound PMNC

Fig. 4

Transverse and longitudinal cross sections of the CFF in which wavy CNTs are coplanar with either the 2–3 or the 1–3 planes; (a) CNT waviness is coplanar with the 2–3 planes and (b) CNT waviness is coplanar with the 1–3 planes (from Ref. [24])

Fig. 3

(a) Fuzzy fiber coated with wavy CNTs being coplanar with the transverse (2–3) planes of the carbon fiber and (b) fuzzy fiber coated with wavy CNTs being coplanar with the longitudinal (1–3) planes of the carbon fiber

Fig. 2

Schematic diagram of a lamina made of the FFRC containing wavy CNTs (from Ref. [24])

Fig. 1

(a) Scanning electron microscopy image of vertically aligned curved CNTs (from Ref. [22]) and (b) scanning electron microscopy image of aligned CNTs grown on the alumina fiber (from Ref. [23])

Fig. 8

Comparisons of the effective (a) axial (KA) and (b) transverse (KT) thermal conductivities of aligned CNT-polymer nanocomposite estimated by the MOC and EM approaches with those of the experimental data [12]; for the comparison purpose, the thermal conductivities of the multi-walled CNT (Kn) and the polymer material (Kp) are taken as 22.1 W/mK and 0.26 W/mK, respectively, as considered by Marconnet et al. [12]; triangles represent the experimental data for the thermal conductivities, dotted lines represent best fits obtained from the EM approach for the experimental results considering an alignment factor (AF) of CNTs as 0.77 observed from the scanning electron microscopy, solid lines and cross signs represent the thermal conductivities predicted by the EM and MOC approaches, respectively, when the value of alignment factor for the reinforced CNTs is 1

Fig. 7

Repeating unit cell of the unwound PMNC material with four subcells (β, γ = 1,2)

Fig. 12

Variation of the effective axial thermal conductivities (K1) of the FFRC containing either straight CNTs or wavy CNTs being coplanar with the carbon fiber axis (that is, 1–3 planes) against the temperature when the CNT volume fraction is constant (Rk=20 × 10-8 m2K/W)

Fig. 13

Variation of the effective transverse thermal conductivities (K2) of the FFRC containing either straight CNTs or wavy CNTs being coplanar with the carbon fiber axis (that is, 1–3 planes) against the temperature when the CNT volume fraction is constant (Rk=20 × 10-8 m2K/W)

Fig. 9

Variations of the thermal conductivities of the constituent phases of the FFRC against the temperature (from Refs. [3,38,39]); (a) thermal conductivity of the armchair (10,10) CNT (Kn), (b) thermal conductivity of the carbon fiber (Kf), and (c) thermal conductivity of the polymer material (Kp)

Fig. 10

Variation of the effective (a) axial (K1) and (b) transverse (K2) thermal conductivities of the FFRC against the temperature (Rk = 0); dashed lines represent data for the base composite (that is, without CNTs), squares represent data for the FFRC containing straight CNTs, dotted lines represent data for the FFRC containing wavy CNTs being coplanar with the axis of carbon fiber (that is, 1–3 plane), plus signs represent data for the FFRC containing wavy CNTs being coplanar with the transverse plane of carbon fiber (that is, 2–3 plane)

Fig. 11

RVE of the unwound PMNC material containing a CNT wave having the length, Lnr=LN, coplanar with the longitudinal plane (that is, 1–3 planes) of the carbon fiber

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