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On problem of transient coupled thermoelasticity of an annular fin

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Abstract

In this paper, the radial deformation and the corresponding stresses in a homogeneous annular fin for an isotropic material has been investigated. A numerical technique is proposed to obtain the solution of the transient coupled thermoelasticity in an annular fin cylinder with it’s base suddenly subject to a heat flux of a decayed exponential function of time. The system of fundamental equations is solved by using an implicit finite-difference method. The present method is a second-order accurate in time and space and unconditionally stable. A numerical method is used to calculate the temperature, displacement and the components of stresses with time t and through the radial of the annular fin cylinder. The results indicate that the effect of coupled thermoelasticity on temperature, stresses and displacement is very pronounced. Comparison is made with the results predicted by the theory of thermoelasticity in the absence of coupled thermoelasticity.

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Abbreviations

a,b :

Inner and outer radii of the fin.

c :

Specific heat of material of the fin.

E :

Young’s modulus of material of the fin.

G :

Dimensionless parameter.

h :

Heat transfer coefficient.

k :

Is the coefficient of the thermal conductivity.

M :

Dimensionless outer radius.

q a :

Heat flux from the base of the fin.

r,R :

Dimension and dimensionless radial coordinate.

τ,t :

Dimension and dimensionless time.

u,U :

Dimension and dimensionless radial component of displacement.

β :

Linear thermal expansion coefficient of material of the fin.

θ,T,T ∞ :

Dimension, dimensionless and ambient temperature.

δ :

Thickness of the fin.

η :

It is a parameter of the thermo mechanical coupling.

ξ :

Exponent of the decayed heat flux.

ρ :

Density of material of the fin.

σ rr ,σ RR :

Dimension and dimensionless radial stress.

σ θθ ,σ ΘΘ :

Dimension and dimensionless circumferential stress.

υ :

Poisson’s ratio of material of the fin.

Ω:

Dimensionless exponent of the decayed heat flux.

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Authors and Affiliations

  1. Math. Dept., Faculty of Science, Taif University, Taif, Saudi Arabia

    A. M. Abd-Alla & S. M. Abo-Dahab

  2. Math. Dept., Faculty of Science, King Abdul Aziz University, Jeddah, Saudi Arabia

    S. R. Mahmoud

  3. Math. Dept., Faculty of Science, Sohag, Egypt

    A. M. Abd-Alla & S. R. Mahmoud

  4. Math. Dept., Faculty of Science, SVU, Qena, 83523, Egypt

    S. M. Abo-Dahab

Authors
  1. A. M. Abd-Alla
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  2. S. R. Mahmoud
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  3. S. M. Abo-Dahab
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Correspondence to S. M. Abo-Dahab.

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Abd-Alla, A.M., Mahmoud, S.R. & Abo-Dahab, S.M. On problem of transient coupled thermoelasticity of an annular fin. Meccanica 47, 1295–1306 (2012). https://doi.org/10.1007/s11012-011-9513-2

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  • DOI: https://doi.org/10.1007/s11012-011-9513-2

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