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Research Papers: Heat and Mass Transfer

Homotopy Perturbation Method for the Analysis of Heat Transfer in an Annular Fin With Temperature-Dependent Thermal Conductivity

[+] Author and Article Information
Rishi Roy

Mechanical Engineering Department,
Jadavpur University,
Kolkata 700032, India
e-mail: rishi.arkm@gmail.com

Sujit Ghosal

Mechanical Engineering Department,
Jadavpur University,
Kolkata 700032, India
e-mail: sujit.ghosal@gmail.com

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received March 24, 2015; final manuscript received September 21, 2016; published online October 26, 2016. Assoc. Editor: Alan McGaughey.

J. Heat Transfer 139(2), 022001 (Oct 26, 2016) (8 pages) Paper No: HT-15-1223; doi: 10.1115/1.4034811 History: Received March 24, 2015; Revised September 21, 2016

A recent mathematical technique of homotopy perturbation method (HPM) for solving nonlinear differential equations has been applied in this paper for the analysis of steady-state heat transfer in an annular fin with temperature-dependent thermal conductivity and with the variation of thermogeometric fin parameters. Excellent benchmark agreement indicates that this method is a very simple but powerful technique and practical for solving nonlinear heat transfer equations and does not require large memory space that arises out of discretization of equations in numerical computations, particularly for multidimensional problems. Three conditions of heat transfer, namely, convection, radiation, and combined convection and radiation, are considered. Dimensionless parameters pertinent to design optimization are identified and their effects on fin heat transfer and efficiency are studied. Results indicate that the heat dissipation under combined mode from the fin surface is a convection-dominant phenomenon. However, it is also found that, at relatively high base temperature, radiation heat transfer becomes comparable to pure convection. It is worth noting that, for pure radiation condition, the dimensionless parameter of aspect ratio (AR) of a fin is a more desirable controlling parameter compared to other parameters in augmenting heat transfer rate without much compromise on fin efficiency.

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Figures

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Fig. 1

Geometry of a rectangular profile annular fin

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Fig. 2

Comparison plot of temperature distribution for purely convective heat transfer (β = 0) showing analytical and HPM results

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Fig. 3

Steady-state temperature distribution along the dimensionless fin radius for convection–radiation (ha = 50 W/m2 K and α = ε = 0.8), pure convection (ha = 50 W/ m2 K and α = ε = 0), and pure radiation (ha = 0 and α = ε = 0.8) heat transfer

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Fig. 4

(a) Effect of AR on ɳ and Q* for convection–radiation heat transfer (fLR = 2, Bic = 1.08 × 10−3, and Bir = 2.63 × 10−5), (b) effect of fLR on ɳ and Q* for convection–radiation heat transfer (AR = 10, Bic = 1.08 × 10−3, and Bir = 2.63 × 10−5), (c) effect of Bic on ɳ and Q* for convection–radiation heat transfer (AR = 10, fLR = 2, and Bir = 2.63 × 10−5), and (d) effect of Bir on ɳ and Q* for convection–radiation heat transfer (AR = 10, fLR = 2, and Bic = 1.08 × 10−3)

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Fig. 5

(a) Effect of AR on ɳ and Q* for pure convection heat transfer (fLR = 2 and Bic = 1.08 × 10−3), (b) effect of fLR on ɳ and Q* for pure convection heat transfer (AR = 10 and Bic = 1.08 × 10−3), and (c) effect of Bic on ɳ and Q* for pure convection heat transfer (AR = 10 and fLR = 2)

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Fig. 6

(a) Effect of AR on ɳ and Q* for pure radiation heat transfer (fLR = 2 and Bir = 2.63 × 10−5), (b) effect of fLR on ɳ and Q* for pure radiation heat transfer (AR = 10 and Bir = 2.63 × 10−5), and (c) effect of Bir on ɳ and Q* for pure radiation heat transfer (AR = 10 and fLR = 2)

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Fig. 7

Effect of θb on η and Q* for convection–radiation (AR = 10, fLR = 2, Bic = 1.08 × 10−3, Bir = 2.63 × 10−5, and β = 0), pure convection (AR = 10, fLR = 2, Bic = 1.08 × 10−3, and β = 0), and pure radiation (AR = 10, fLR = 2, Bir = 2.63 × 10−5, and β = 0) heat transfer mechanisms

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