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Research Papers: Natural and Mixed Convection

Natural Convection and Surface Radiation in a Heated Wall, C-Shaped Fracture

[+] Author and Article Information
Alan Lugarini

Research Center for Rheology and
Non-Newtonian Fluids,
Federal University of Technology—Paraná,
Rua Deputado Heitor Alencar Furtado, 5000,
Curitiba 81280-340, Paraná, Brazil
e-mail: alanlugarinisz@yahoo.com.br

Admilson T. Franco

Research Center for Rheology and
Non-Newtonian Fluids,
Federal University of Technology—Paraná,
Rua Deputado Heitor Alencar Furtado, 5000,
Curitiba 81280-340, Paraná, Brazil
e-mail: admilson@utfpr.edu.br

Silvio L. M. Junqueira

Research Center for Rheology and
Non-Newtonian Fluids,
Federal University of Technology—Paraná,
Rua Deputado Heitor Alencar Furtado, 5000,
Curitiba 81280-340, Paraná, Brazil
e-mail: silvio@utfpr.edu.br

José L. Lage

Fellow ASME
Department of Mechanical Engineering,
Lyle School of Engineering,
Southern Methodist University,
Dallas, TX 75275-0337
e-mail: JLL@lyle.smu.edu

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received July 27, 2017; final manuscript received March 8, 2018; published online May 7, 2018. Assoc. Editor: Zhuomin Zhang.

J. Heat Transfer 140(8), 082501 (May 07, 2018) (9 pages) Paper No: HT-17-1433; doi: 10.1115/1.4039643 History: Received July 27, 2017; Revised March 08, 2018

The present study considers the coupled natural convection and surface radiation process through an open fracture of a solid wall facing a reservoir containing isothermal quiescent fluid (air). The fracture is modeled as a regular, C-shape path through the wall, with the vertical surface being heated and the horizontal ones adiabatic. The solid center section of the fracture is thermally participant inasmuch it can be heated or cooled by the natural convection process and by the radiation effect from the other surfaces of the fracture. The convection-radiation phenomenon is mathematically modeled and numerically simulated in a systematic parametric study of the thermal process as affected by changes in the fracture channel size, via changes in the size of the solid center section 0 < D < 1.0, surface emissivity 0 ≤ ε ≤ 1.0, Rayleigh number 105 ≤ Ra ≤ 108, and Pr = 0.71. Attention is given to the radiation shadowing effect caused by the center section of the fracture and of the interference effect, as the fracture channel changes in size, affecting the natural convection process through the fracture. An analytical prediction of the interference effect and an empirical correlation for predicting the total Nusselt number, both validated against the numerical results, are presented.

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Figures

Grahic Jump Location
Fig. 1

Geometric configuration and boundary conditions imposed along the extended boundaries of the domain

Grahic Jump Location
Fig. 2

Isotherms (left) and streamlines (right) for an enclosure with a centrally located solid conductive block (Ra = 106, ε = 1, D = 0.5, κ = 1): (a) from Ref. [13] and (b) present results

Grahic Jump Location
Fig. 3

Total Nusselt number Nut¯ versus D, for ε = 0 (no radiation), 0.5 and 1.0, and 105 ≤ Ra ≤ 108

Grahic Jump Location
Fig. 4

Isotherms (left) and streamlines (right) for Ra = 107 and D = 0.5 showing the radiation effect: (a) ε = 0, (b) ε = 0.5, and (c) ε = 1

Grahic Jump Location
Fig. 5

Variations of Nuc¯ and Nur¯ as function of D for different ε values and several Ra

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Fig. 6

Isotherms (left) and streamlines (right) for ε = 1 showing the occurrence of boundary layer interference in D = 0.8 for Ra = 105 and in D = 0.9 for Ra = 106

Grahic Jump Location
Fig. 7

Isotherms (left) and streamlines (right) for ε = 1 showing the nonoccurrence of boundary layer interference in D = 0.9 for either Ra = 107 and 108

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Fig. 8

Solid block size increase effects on surface radiation

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Fig. 9

Local radiation Nusselt number variation along the heated wall of the cavity for various D and Ra values (ε = 1)

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