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Technical Brief

Notes on Steady Natural Convection Heat Transfer by Double Diffusion From a Heated Cylinder Buried in a Saturated Porous Media

[+] Author and Article Information
Carlos Alberto Chaves

Department of Mechanical Engineering,
University of Taubate,
Taubate, SP 12060-440, Brazil
e-mail: carlosachaves@yahoo.com.br

Wendell de Queiroz Lamas

Department of Basic Sciences and Environment,
School of Engineering at Lorena,
University of Sao Paulo,
Lorena, SP 12602-810, Brazil
e-mail: wendell.lamas@usp.br

Luiz Eduardo Nicolini do Patrocinio Nunes

Department of Mechanical Engineering,
University of Taubate,
Taubate, SP 12060-440, Brazil
e-mail: luiz.nunes@unitau.com.br

Jose Rui Camargo

Department of Mechanical Engineering,
University of Taubate,
Taubate, SP 12060-440, Brazil
e-mail: rui@unitau.br

Francisco Jose Grandinetti

Department of Mechanical Engineering,
University of Taubate,
Taubate, SP 12060-440, Brazil
e-mail: grandi@unitau.br

1Present address: Rua Daniel Danelli, s/n, Jardim Morumbi, Taubate, SP 12060-440, Brazil.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received May 1, 2014; final manuscript received February 12, 2015; published online March 24, 2015. Assoc. Editor: Jose L. Lage.

J. Heat Transfer 137(7), 074501 (Jul 01, 2015) (7 pages) Paper No: HT-14-1283; doi: 10.1115/1.4029878 History: Received May 01, 2014; Revised February 12, 2015; Online March 24, 2015

This paper aims to present numerical solutions for the problem of steady natural convection heat transfer by double diffusion from a heated cylinder buried in a saturated porous media exposed to constant uniform temperature and concentration in the cylinder and in the media surface. A square finite domain 3 × 3 and acceptance criterion converged solution with an absolute error under 1 × 10−3 were considered to obtain results presented. The Patankar's power law for approaching of variables calculated T, C, and ϕ also was adopted. In order of method validation, an investigation of mesh points number as function of Ra, Le, and N was done. A finite volume scheme has been used to predict the flow, temperature, and concentration distributions at any space from a heat cylinder buried into a fluid-saturated porous medium for a bipolar coordinates system. Examples presented show that the differences in the flow distribution caused not only when Rayleigh number range is considered but also when Lewis number range is considered. Further, increase in the Rayleigh number has a significant influence in the flow distribution when the concentration distribution is considered. Steady natural convection heat transfer by double diffusion from a heated cylinder buried in a saturated porous medium is studied numerically using the finite volume method. To model fluid flow inside the porous medium, the Darcy equation is used. Numerical results are obtained in the form of streamlines, isotherms, and isoconcentrations. The Rayleigh number values range from 0 to 1000, the Lewis number values range from 0 to 100, and the buoyancy ratio number is equal to zero. Calculated values of average heat transfer rates agree reasonably well with values reported in the literature.

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References

Figures

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Fig. 1

Bipolar coordinates system

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Fig. 2

Typical cell of the volume control method

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Fig. 3

Influence of Ra on Nu in the cylinder and in the wall for BN = 0 and Le = 1

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Fig. 4

Influence of Le and Ra on Sherwood in the wall (BN = 0): (a) Sh up to 6 and (b) Sh up to 35

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Fig. 5

Influence of Ra on the distribution of local Nu (BN = 0): (a) in the cylinder and (b) in the wall

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Fig. 6

Influence of Ra on local Sherwood distribution in the cylinder for: (a) Le = 0.1 and BN = 0; (b) Le = 10 and BN = 0; and (c) Le = 100 and BN = 0

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Fig. 7

Influence of Le on local Sherwood distribution in the cylinder for: (a) Ra = 1 and BN = 0; (b) Ra = 100 and BN = 0; and (c) Ra = 1000 and BN = 0

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