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Heat transfer analysis of composite slabs using meshless element Free Galerkin method

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Abstract

This paper deals with three dimensional heat transfer analysis of composite slabs using meshless element free Galerkin method. The element free Galerkin method (EFG) method utilizes moving least square (MLS) approximants to approximate the unknown function of temperature Tx). These approximants are constructed by using a weight function, a basis function and a set of coefficients that depends on position. Penalty and Lagrange multiplier techniques have been used to enforce the essential boundary conditions. MATLAB codes have been developed to obtain the EFG results. Two new basis functions namely trigonometric and polynomial have been proposed. A comparison has been made among the results obtained using existing (linear) and proposed (trigonometric and polynomial) basis functions for three dimensional heat transfer in composite slabs. The effect of penalty parameter on EFG results has also been discussed. The results obtained by EFG method are compared with those obtained by finite element method

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Abbreviations

a j x):

non constant coefficients

c :

specific heat of the material

c xI , c yI , c zI  :

distances to the nearest neighbors in x, y and z directions

d max :

scaling parameter

% diff:

percentage difference of EFG results

q̄:

rate of internal heat generation /volume

h :

convective heat transfer coefficient

k :

coefficient of thermal conductivity

LMM:

Lagrange multiplier method

PM:

penalty method

Poly:

polynomial basis function

p j x:

monomial basis function

m :

number of terms in the basis

n :

number of nodes in the domain & of influence

n̄:

number of time steps

n′:

outward normal to the surface

n′′:

x,y & z

r x , r y , r z :

normalized radii along x, y and & z directions

S i :

surfaces of three dimensional models

t :

time

t̄:

∂T{∂t

Trig:

trigonometric basis function

T h x:

moving least square approximant

T S_i :

surface temperature

T ∞ :

surrounding fluid temperature

V :

three dimensional domain (V 1 ∪ V 2)

x I , y I , z I :

coordinates of the I th node

w(x − x I ):

weight function

α:

penalty parameter

λ:

Lagrangian multiplier

Φ I (x):

shape function

ρ:

density of the material

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Authors and Affiliations

  1. Mechanical Engineering Group, Birla Institute of Technology and Science, Pilani, 333031, Rajasthan, India

    I. V. Singh

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Singh, I.V. Heat transfer analysis of composite slabs using meshless element Free Galerkin method. Comput Mech 38, 521–532 (2006). https://doi.org/10.1007/s00466-005-0001-1

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