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Non-Fourier Thermoelastic Analysis of an Annular Fin with Variable Convection Heat Transfer Coefficient

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Abstract

This paper numerically investigates the hyperbolic thermoelastic problem of an annular fin. The ambient convection heat transfer coefficient of the fin is assumed to be spatially varying. The major difficulty in dealing with such problems is the suppression of numerical oscillations in the vicinity of a jump discontinuity. An efficient numerical scheme involving hybrid application of Laplace transform and control volume method in conjunction with hyperbolic shape functions is used to solve the linear hyperbolic heat conduction equation. The transformed nodal temperatures are inverted to the physical quantities by using numerical inversion of the Laplace transform. Then the stress distributions in the annular fin are calculated subsequently. The results in the illustrated examples show that the application of hyperbolic shape functions can successfully suppress the numerical oscillations in the vicinity of jump discontinuities.

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Abbreviations

c :

Heat capacity (J· kg−1· K−1)

E :

Elastic modulus (MPa)

g :

Volumetric energy source (W· m−3)

H :

Dimensionless convection heat transfer coefficient function

h :

Convection heat transfer coefficient (W· m−2· K−1)

k :

Thermal conductivity (W· m−1· K−1)

l :

Dimensionless distance between two nodes

q :

Heat flux (W· m−2)

r :

Radial coordinate (m)

r 1 :

Base radius of the annular fin (m)

r 2 :

Tip radius of the annular fin (m)

s :

Laplace transform parameter

T :

Temperature (K)

T b :

Fin base temperature (K)

T ∞ :

Ambient temperature (K)

t :

Time coordinate (s)

u :

Radial displacement component (m)

w :

Propagation speed of thermal wave (m· s−1)

α :

Thermal diffusivity (m2· s−1)

β :

Dimensionless relaxation time, \({\alpha \tau /r_{1}^{2}}\)

γ :

Constant

δ :

Fin thickness (m)

λ :

(β s2 + s)1/2

ν :

Poisson’s ratio

\({\xi}\) :

γ (β s + 1)

ρ :

Density (kg· m−3)

σ r :

Radial stress component (MPa)

σ θ :

Tangential stress component (MPa)

τ :

Relaxation time (s)

ω :

Thermal expansion coefficient (K−1)

*:

Dimensionless quantity

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Authors and Affiliations

  1. Clean Energy Center, Department of Mechanical Engineering, Kun Shan University, No. 949, Da Wan Rd., Yung-Kang, Tainan, 710-03, Taiwan, ROC

    Haw-Long Lee, Win-Jin Chang, Wen-Lih Chen & Yu-Ching Yang

Authors
  1. Haw-Long Lee
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  2. Win-Jin Chang
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  3. Wen-Lih Chen
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  4. Yu-Ching Yang
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Correspondence to Yu-Ching Yang.

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Lee, HL., Chang, WJ., Chen, WL. et al. Non-Fourier Thermoelastic Analysis of an Annular Fin with Variable Convection Heat Transfer Coefficient. Int J Thermophys 33, 1068–1081 (2012). https://doi.org/10.1007/s10765-012-1220-2

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  • DOI: https://doi.org/10.1007/s10765-012-1220-2

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