Entropy

International Communications in Heat and Mass Transfer 36 (2009) 25–31

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International Communications in Heat and Mass Transfer
j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / i c h m t

A numerical study on entropy generation induced by turbulent forced convection in
curved rectangular ducts with various aspectratios☆
T.H. Ko ⁎, C.P. Wu
Department of Mechanical Engineering, Lunghwa University of Science and Technology, 300, Wan-Shou Rd., Sec. 1, Kueishan, 33306, Taoyuan, Taiwan, ROC

article

info

Available online 7 October 2008
Keywords:
Curved rectangular duct
Turbulent forced convection
Irreversibility
Entropy generation
Minimal entropy generation principle

abstract
The present paperanalyzes the entropy generation induced by turbulent forced convection in a curved
rectangular duct with external heating by numerical methods. The problem is assumed as steady, threedimensional and turbulent. The flow features, including the secondary flow motions, the distribution of local
entropy generation as well as the overall entropy generation in the whole flow fields, are analyzed. For abaseline case with Re = 20,000, external heat flux q⁎ = 0.112 and aspect ratio γ = 1, the results show the
entropy generation induced by the frictional irreversibility concentrates within the regions adjacent to the
duct walls, whereas the entropy generation resulted from the heat transfer irreversibility only significantly
occurs near the outer wall of the duct where the external heat flux imposed.Except the baseline case, two
additional cases with aspect ratio equal to 0.25 and 4 are calculated. Through the comparison of the three
aspect-ratio cases, it is seen that the resultant entropy generations in the flow fields for the three cases are all
dominated by the frictional irreversibilities. Among the three aspect-ratio cases, the resultant entropy
generation is minimal in the γ = 1 case.Accordingly, the case with γ = 1 is concluded to be the optimal aspect
ratio under the current flow condition based on the minimal entropy generation principle.
© 2008 Elsevier Ltd. All rights reserved.

1. Introduction
The modern design concept for a thermal system pursues not only
the enhancement of the heat transfer performance, but also requests the
minimal power requirement.Unfortunately, the enhancement of the
heat transfer performance usually must be achieved at the expense of
the increase of power input. Therefore, the optimal trade-off between
the heat transfer enhancement and the power input requirement
becomes one of the major concerns in the design considerations of a
thermal system. Recently, the optimal analysis of a thermal system has
been proposed from the viewpoint of thermodynamic second law. The
entropy generation has been adopted as a gauge for evaluating the
efficient exergy use in a thermal system. The system with the minimal
entropy generation is considered as the optimal design.
Bejan [1,2] has described the systematic methodology of computing
the entropy generation through heat and fluid flow in several heat
exchangers. Thereafter, abundantresearches discussing the optimal
design of thermal systems based on minimal entropy generation principle
have been proposed [3–13], among which most of the studies were
focused on the laminar flows. Some typical examples include: the optimization for convective heat transfer through a duct with constant heat flux
studied by Nag and Kumar [3]; the irreversibility analysis in various duct
☆Communicated by W.J. Minkowycz.
⁎ Corresponding author.
E-mail address: thko@mail.lhu.edu.tw (T.H. Ko).
0735-1933/$ – see front matter © 2008 Elsevier Ltd. All rights reserved.
doi:10.1016/j.icheatmasstransfer.2008.08.016

geometries with constant wall heat flux and laminar flow performed by
Sahin [4]; the exergoeconomic analysis on the optimal fin geometry in an
electronics cooling system...