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Can the shape influence entropy generation for thermal convection of identical fluid mass with identical heating? A finite element introspection

Leo Lukose (Department of Chemical Engineering, Indian Institute of Technology Madras, Chennai, India)
Tanmay Basak (Department of Chemical Engineering, Indian Institute of Technology Madras, Chennai, India)

International Journal of Numerical Methods for Heat & Fluid Flow

ISSN: 0961-5539

Article publication date: 23 November 2020

Issue publication date: 24 May 2021

141

Abstract

Purpose

This paper aims to investigate the role of shapes of containers (nine different containers) on entropy generation minimization involving identical cross-sectional area (1 sq. unit) in the presence of identical heating (isothermal). The nine containers are categorized into three classes based on their geometric similarities (Class 1: square, tilted square and parallelogram; Class 2: trapezoidal type 1, trapezoidal type 2 and triangular; Class 3: convex, concave and curved triangular).

Design/methodology/approach

Galerkin finite element method is used to solve the governing equations for a representative fluid (engine oil: Pr = 155) at Ra = 103–105. In addition, finite element method is used to solve the streamfunction equation and evaluate the entropy generation terms (Sψ and Sθ). Average Nusselt number ( Nub¯) and average dimensionless spatial temperature ( θ^) are also evaluated via the finite element basis sets.

Findings

Based on larger Nub¯, larger θ^ and optimal Stotal values, containers from each class are preferred as follows: Class 1: parallelogrammic and square, Class 2: trapezoidal type 1 and Class 3: convex (larger θ^, optimum Stotal) and concave (larger Nub¯). Containers with curved walls lead to enhance the thermal performance or efficiency of convection processes.

Practical implications

Comparison of entropy generation, intensity of thermal mixing ( θ^) and average heat transfer rate give a clear picture for choosing the appropriate containers for processing of fluids at various ranges of Ra. The results based on this study may be useful to select a container (belonging to a specific class or containers with curved or plane walls), which can give optimal thermal performance from the given heat input, thereby leading to energy savings.

Originality/value

This study depicts that entropy generation associated with the convection process can be reduced via altering the shapes of containers to improve the thermal performance or efficiency for processing of identical mass with identical heat input. The comparative study of nine containers elucidates that the values of local maxima of Sψ (Sψ,max), Sθ (Sθ,max) and magnitude of Stotal vary with change in shapes of the containers (Classes 1–3) at fixed Pr and Ra. Such a comparative study based on entropy generation minimization on optimal heating during convection of fluid is yet to appear in the literature. The outcome of this study depicts that containers with curved walls are instrumental to optimize entropy generation with reasonable thermal processing rates.

Keywords

Acknowledgements

The authors would like to thank anonymous reviewers for critical comments and suggestions, which improved the quality of the manuscript.

Citation

Lukose, L. and Basak, T. (2021), "Can the shape influence entropy generation for thermal convection of identical fluid mass with identical heating? A finite element introspection", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 31 No. 6, pp. 1749-1789. https://doi.org/10.1108/HFF-05-2020-0257

Publisher

:

Emerald Publishing Limited

Copyright © 2020, Emerald Publishing Limited

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