Research Papers: Heat and Mass Transfer

A Novel Numerical Approach for Convective and Radiative Heat Transfer Analysis of Fluid Flow Problems Within Triangular Cavities Using Natural Element Method

[+] Author and Article Information
Ardeshir Moftakhari

Cockrell School of Engineering,
Department of Civil, Architectural and
Environmental Engineering,
University of Texas at Austin,
Austin, TX 78712
e-mail: ardeshir_2010@yahoo.com

Cyrus Aghanajafi

School of Mechanical Engineering,
K. N. Toosi University of Technology,
Tehran 64499, Iran

Ardalan Moftakhari Chaei Ghazvin

Department of Mechanical Engineering,
Chemnitz University of Technology,
Chemnitz 09111, Germany

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received October 6, 2016; final manuscript received February 14, 2017; published online April 11, 2017. Assoc. Editor: Zhixiong Guo.

J. Heat Transfer 139(8), 082002 (Apr 11, 2017) (13 pages) Paper No: HT-16-1634; doi: 10.1115/1.4036057 History: Received October 06, 2016; Revised February 14, 2017

Thermal analysis of fluid flow is always regarded as an important research issue within cavities in order to become familiar with the characteristics of fluid flow phenomenon in enclosures. This research paper investigates the fluid and heat transfer analysis of fluid flow inside a triangular cavity using natural element methodology (NEM). This Galerkin-based methodology has been introduced for a decade and almost demonstrated its efficiency in the numerical heat transfer analysis of problems in most engineering sciences. The fluid flow contains natural convection along with conduction and radiation heat transfer with medium's walls, which have absorbing, emitting, semitransparent, and nonscattering characteristics. The final results investigate the effects of radiative and natural convection heat transfer on the fluid flow pattern as expressed in Rayleigh number, stream function, strength of natural convection regime, etc., which are checked with other similar studies presented in the literature and shows how promising NEM can be as an efficient numerical approach to improve computational precision when dealing with fluid mechanic problems.

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Fig. 1

The Voronoi diagram for node number 5

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Fig. 2

The Delaunay triangulation for seven nodes

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Fig. 3

The second-order Voronoi diagram for point (x)

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Fig. 4

The second-order of the Voronoi diagram

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Fig. 5

The geometry and boundary conditions for the triangular cavity

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Fig. 6

The error function changes per time

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Fig. 7

The geometry and boundary conditions of the study by Lauriat [18]

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Fig. 8

Mean temperature profile on the horizontal line passing from the cavity center (y = H/2): (a) present study versus Lauriat for radiation and (b) present study versus Lauriat versus Basak et al. for only natural convection

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Fig. 9

Stream line contour comparison in the triangular cavity: (a) present study and (b) Basak et al. study [33]

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Fig. 10

Stream line contour comparison in the triangular cavity: (a) Ra=104, (b) Ra=105, and (c) Ra=106

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Fig. 11

Temperature contours of a nonradiative medium for different Rayleigh numbers: (a) Ra=104, (b) Ra=105, and (c) Ra=106

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Fig. 12

Stream line contours of a radiative medium for different Planck numbers: (a) qr=0, (b) NCR = 10, and (c) NCR = 0.4

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Fig. 13

Temperature contours of a radiative medium for different Planck numbers: (a) qr= 0, (b) NCR = 10, and (c) NCR = 0.4

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Fig. 14

The changes in Nusselt number versus Planck number: (a) local Nusselt number for cold walls and (b) local Nusselt number for warm walls

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Fig. 15

Average Nusselt number versus Planck number

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Fig. 16

The changes of average Nusselt number versus dimensionless mean temperature: (a) warm walls and (b) cold walls

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Fig. 17

The effects of variable optical thickness and emissivity on combined convection and radiation captured by NEM: (a) Nusselt number versus variable optical thickness and (b) Nusselt number versus variable emissivity coefficient




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