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Green’s function solution for transient heat conduction in annular fin during solidification of phase change material

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Abstract

The Green’s function method is applied for the transient temperature of an annular fin when a phase change material (PCM) solidifies on it. The solidification of the PCMs takes place in a cylindrical shell storage. The thickness of the solid PCM on the fin varies with time and is obtained by the Megerlin method. The models are found with the Bessel equation to form an analytical solution. Three different kinds of boundary conditions are investigated. The comparison between analytical and numerical solutions is given. The results demonstrate that the significant accuracy is obtained for the temperature distribution for the fin in all cases.

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Abbreviations

a :

inner radius of annular fin, m

b :

outer radius of annular fin, m

c :

specific heat, J·kg−1 ·K−1

D :

length of fin, m

E :

change rate of energy stored within per unit area, W·m−2

G :

Green’s function

h :

convective heat transfer coefficient, W·m−2·K−1

k :

thermal conductivity, W·m−1·K−1

L :

latent heat of fusion, J·kg−1

q″:

heat flux, W·m−2

S :

distance of solid-liquid interface in z-direction, m

T :

temperature, °C.

α :

thermal diffusivity, m2·s−1

δ :

Dirac delta function

η :

dimensionless r-coordinate

λ :

half thickness of fin, m

θ :

temperature difference (T f − T m )°C

ρ :

density, kg·m−3

τ :

dimensionless time

f:

fin

s:

solid

w:

wall

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Authors and Affiliations

  1. Faculty of Mechanical Engineering, University of Tabriz, Tabriz, 5166616471, Iran

    A. H. Mosaffa & F. Talati

  2. Faculty of Engineering and Applied Science, University of Ontario Institute of Technology, L1H 7K4, Oshawa, Ontario, Canada

    M. A. Rosen

  3. Department of Mechanical Engineering, Amirkabir University of Technology, Tehran, 159163411, Iran

    H. Basirat-Tabrizi

Authors
  1. A. H. Mosaffa
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  2. F. Talati
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  3. M. A. Rosen
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  4. H. Basirat-Tabrizi
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Correspondence to A. H. Mosaffa.

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Mosaffa, A.H., Talati, F., Rosen, M.A. et al. Green’s function solution for transient heat conduction in annular fin during solidification of phase change material. Appl. Math. Mech.-Engl. Ed. 33, 1265–1274 (2012). https://doi.org/10.1007/s10483-012-1620-x

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  • DOI: https://doi.org/10.1007/s10483-012-1620-x

Key words

Chinese Library Classification

2010 Mathematics Subject Classification

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