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Correlation equations for optimum design of annular fins with temperature dependent thermal conductivity

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Abstract

Correlation equations for optimum design of annular fins with temperature-dependent thermal conductivity are obtained in the present work. The nonlinear fin equation which is associated with variable thermal conductivity condition is solved by Adomian decomposition method that provides an analytical solution in the form of an infinite power series. The optimum radii ratio of an annular fin which maximizes the heat transfer rate has been found as a function of Biot number and the fin volume for a given thermal conductivity parameter describing the variation of the thermal conductivity. The fin volume is fixed to obtain the dimensionless geometrical parameters of the fin with maximum heat transfer rate. The data from the present solutions is correlated for a suitable range of Biot number and the fin volume. The simple correlation equations presented in this work can assist for thermal design engineers for optimum design of annular fins with temperature-dependent thermal conductivity.

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Abbreviations

A m :

Adomian polynomials

Bi :

Biot number, hr i/k ∞

Bi T :

transverse Biot number, ht/2k ∞

h :

convection heat transfer coefficient [W/(m2K]

k :

thermal conductivity of the fin material [W/(mK)]

L:

the highest order derivative

L −1 :

inverse operator of L

N :

nonlinear operator

q :

dimensionless heat-transfer rate defined in Eq. 28

Q :

dimensional heat-transfer rate (W)

r :

radial coordinate (m)

r i :

inner radius of the annular fin (m)

r o :

outer radius of the annular fin (m)

R :

remainder of linear operator

t :

thickness of the annular fin (m)

T :

temperature (K)

v :

dimensionless volume of the fin \( {V \mathord{/ {\vphantom {V {( {\pi r_{\text{i}}^{3} })}}} \kern-\nulldelimiterspace} {( {\pi r_{\text{i}}^{3} })}} \)

V :

volume of the fin (m3)

α:

integral constant representing dimensionless temperature at the fin tip

β:

dimensionless parameter describing variation of the thermal conductivity

δ:

dimensionless thickness of the fin, t/r i

λ:

the radii ratio, r o/r i

θ:

dimensionless temperature

ξ:

dimensionless radial coordinate

b:

base

∞:

ambient fluid

*:

optimum

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Authors and Affiliations

  1. Department of Mechanical Engineering, Faculty of Engineering, Ataturk University, 25240, Erzurum, Turkey

    Cihat Arslanturk

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  1. Cihat Arslanturk
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Arslanturk, C. Correlation equations for optimum design of annular fins with temperature dependent thermal conductivity. Heat Mass Transfer 45, 519–525 (2009). https://doi.org/10.1007/s00231-008-0446-9

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  • DOI: https://doi.org/10.1007/s00231-008-0446-9

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