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Thermal Analysis of CNT-Based Nano-Composites by Element Free Galerkin Method

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Abstract

This paper deals with the thermal analysis of carbon nanotube (CNT) based composites by meshless element free Galerkin method. Cylindrical representative volume element (cylindrical RVE) has been chosen to evaluate the thermal properties of nano-composites using multi-domain and simplified approaches. The values of temperature have been calculated at different points and plotted against RVE length and RVE radius. A sensitivity analysis of RVE as well as CNT dimensions has been carried out in detail. The present computations show that the equivalent thermal conductivity is a function of CNT length, CNT radius, RVE length and RVE radius. Based on present numerical simulations, an approximate formula is proposed to calculate the equivalent thermal conductivity of nano-composites. The results obtained by simplified approach have been found in good agreement with those obtained by multi-domain approach.

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Abbreviations

k m_1 :

thermal conductivity of matrix (W/m K)

k m_2 :

thermal conductivity of carbon nanotube (W/m K)

k e :

equivalent thermal conductivity of composite (W/m K)

L :

length of cylindrical RVE (nm)

L c :

CNT length (nm)

m :

number of terms in the basis

m 1 :

matrix material

m 2 :

carbon nanotube material

n :

number of nodes in the domain of influence

n′:

outward normal to the surface

q :

heat flux (W/m2)

r o :

outer radius of CNT (nm)

R o :

radius of cylindrical RVE (nm)

t :

thickness of CNT (nm)

T C :

constant temperature at CNT surface (K)

\(T^{h}({\mathbf{r}})\) :

MLS approximation function for temperature

w :

weight function used in MLS approximation

\(\bar{w}\) :

weighting function used in weak form

α:

penalty parameter

Γ 3 :

CNT surface

Γ:

boundary of the domain

Ω 1 :

domain for matrix

Ω 2 :

domain for CNT

\(\Phi _{I} ({\mathbf{r}})\) :

shape function

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Authors and Affiliations

  1. Faculty of Engineering, Shinshu University, Nagano, 380-8553, Japan

    I. V. Singh, Masa Tanaka & M. Endo

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  1. I. V. Singh
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  2. Masa Tanaka
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  3. M. Endo
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Correspondence to I. V. Singh.

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Singh, I.V., Tanaka, M. & Endo, M. Thermal Analysis of CNT-Based Nano-Composites by Element Free Galerkin Method. Comput Mech 39, 719–728 (2007). https://doi.org/10.1007/s00466-006-0061-x

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  • DOI: https://doi.org/10.1007/s00466-006-0061-x

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