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Efficiency and optimisation of fin with temperature-dependent thermal conductivity: a simplified solution

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Abstract

An analytical simplified solution is proposed for temperature distribution and fin efficiency, when thermal conductivity is temperature dependent. An optimal linearization technique is used to solve the nonlinear equation. Based on classical solution, some accurate results are obtained and presented with thermal conductivity parameter and fin parameter. Arithmetic mean temperature is less precise than an equivalent thermal conductivity. Optimal thickness for rectangular fin is derived.

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Abbreviations

a :

cross-sectional area

Bi :

Biot number Bi = αw/2λ 0

F :

factor

L :

fin length

m :

fin parameter \({m\, = \,{\sqrt \frac{2\alpha}{\lambda_{0}w}}}\)

q :

heat flux dissipated

S :

fin profile

T :

temperature

w :

fin thickness

x :

axial distance measured from fin base

α :

convection heat transfer coefficient

ε :

thermal conductivity parameter

η :

fin efficiency

θ :

dimensionless temperature θ = T/T 0

χ :

function

λ :

thermal conductivity λ =  λ0(1 + ɛθ)

λ + :

equivalent thermal conductivity

λ 0 :

constant thermal conductivity

λ m :

mean arithmetic thermal conductivity

opt:

optimal

0:

base of the fin

1:

classical with λ 0

2:

proposed with λ +

3:

classical with λ m

4:

Aziz’s solution

*:

unit width

+:

fin parameter

*:

corrected optimal width

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Author information

Authors and Affiliations

  1. BP 164, Médéa, 26000, Algeria

    M. N. Bouaziz

  2. BP 108, Médéa, 26000, Algeria

    S. Hanini

Authors
  1. M. N. Bouaziz
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  2. S. Hanini
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Correspondence to M. N. Bouaziz.

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Bouaziz, M.N., Hanini, S. Efficiency and optimisation of fin with temperature-dependent thermal conductivity: a simplified solution. Heat Mass Transfer 44, 1–9 (2007). https://doi.org/10.1007/s00231-006-0225-4

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  • DOI: https://doi.org/10.1007/s00231-006-0225-4

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