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Research Papers

Geometric Size Optimization of Annular Step Fin Using Multi-Objective Genetic Algorithm

[+] Author and Article Information
Abhijit Deka

Department of Mechanical Engineering,
School of Engineering,
Tezpur University,
Napaam,
Tezpur, Assam 784 028, India
e-mail: adeka13@tezu.ernet.in

Dilip Datta

Department of Mechanical Engineering,
School of Engineering,
Tezpur University,
Napaam,
Tezpur, Assam 784 028, India
e-mails: ddatta@tezu.ernet.in; datta_dilip@rediffmail.com

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF THERMAL SCIENCE AND ENGINEERING APPLICATIONS. Manuscript received April 15, 2016; final manuscript received December 8, 2016; published online March 7, 2017. Assoc. Editor: Sandra Boetcher.

J. Thermal Sci. Eng. Appl 9(2), 021013 (Mar 07, 2017) (9 pages) Paper No: TSEA-16-1095; doi: 10.1115/1.4035838 History: Received April 15, 2016; Revised December 08, 2016

Although an annular stepped fin can produce better cooling effect in comparison to an annular disk fin, it is yet to be studied in detail. In the present work, one-dimensional heat transfer in a two-stepped rectangular cross-sectional annular fin with constant base temperature and variable thermal conductivity is modeled as a multi-objective optimization problem. Taking cross-sectional half-thicknesses and outer radii of the two fin steps as design variables, an attempt is made to obtain the efficient fin geometry primarily by simultaneously maximizing the heat transfer rate and minimizing the fin volume. For further assessment of the fin performance, three more objective functions are studied, which are minimization of the fin surface area and maximization of the fin efficiency and effectiveness. Evaluating the heat transfer rate through the hybrid spline difference method, the well-known multi-objective genetic algorithm, namely, nondominated sorting genetic algorithm II (NSGA-II), is employed for approximating the Pareto-optimal front containing a set of tradeoff solutions in terms of different combinations of the considered five objective functions. The Pareto-optimal sensitivity is also analyzed for studying the influences of the design variables on the objective functions. As an outcome, it can be concluded that the proposed procedure would give an open choice to designers to lead to a practical stepped fin configuration.

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Figures

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Fig. 1

Schematic diagram of a two-stepped rectangular cross-sectional annular fin

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Fig. 2

Pareto fronts of f1 separately paired with f2, f3, f4, and f5: in terms of f1 and f2 (a), f1 and f3 (b), f1 and f4 (c), and f1 andf5(d)

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Fig. 3

Six selective efficient fin geometries corresponding to tradeoff solutions A–F of Fig. 2(a)

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Fig. 4

Three-dimensional representation of fin geometries corresponding to tradeoff solutions C and F of Fig. 2(a): (a) 3D representation of solution C and (b) 3D representation of solution F

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Fig. 5

Pareto front containing the set of tradeoff solutions in terms of f4 and f5

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Fig. 6

Value path plots of the five-dimensional Pareto front with objective values normalized in the range of [0,1]

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Fig. 7

Pareto-optimal sensitivity analysis of the heat transfer rate in terms of the design variables

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