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Research Papers: Natural and Mixed Convection

Dual Solutions for Opposing Mixed Convection in Porous Media

[+] Author and Article Information
Jian-Jun Shu

School of Mechanical
and Aerospace Engineering,
Nanyang Technological University,
50 Nanyang Avenue,
Singapore 639798, Singapore
e-mail: mjjshu@ntu.edu.sg

Qi-Wen Wang

School of Business,
Shanghai DianJi University,
1350 Ganlan Road,
Lingang New City,
Pudong New District,
Shanghai 201306, China

Ioan Pop

Department of Mathematics,
Babeş-Bolyai University,
Cluj-Napoca 400084, Romania

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received May 30, 2016; final manuscript received April 26, 2017; published online June 1, 2017. Assoc. Editor: Peter Vadasz.

J. Heat Transfer 139(10), 102501 (Jun 01, 2017) (4 pages) Paper No: HT-16-1327; doi: 10.1115/1.4036727 History: Received May 30, 2016; Revised April 26, 2017

The problem of steady mixed convection boundary layer flow on a cooled vertical permeable circular cylinder embedded in a fluid-saturated porous medium is studied. Here, we evaluate the flow and heat transfer characteristics numerically for various values of the governing parameters and demonstrate the existence of dual solutions beyond a critical point.

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References

Pop, I. , and Ingham, D. B. , 2001, Convective Heat Transfer: Mathematical and Computational Modelling of Viscous Fluids and Porous Media, Pergamon, Oxford, UK.
Ingham, D. B. , and Pop, I. , 2005, Transport Phenomena in Porous Media, Elsevier Science, Oxford, UK.
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Nield, D. A. , and Bejan, A. , 2013, Convection in Porous Media, 4th ed., Springer, New York.
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Shu, J.-J. , and Pop, I. , 1997, “ Inclined Wall Plumes in Porous Media,” Fluid Dyn. Res., 21(4), pp. 303–317. [CrossRef]
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Shu, J.-J. , and Wilks, G. , 2008, “ Heat Transfer in the Flow of a Cold, Axisymmetric Vertical Liquid Jet Against a Hot, Horizontal Plate,” ASME J. Heat Transfer, 130(1), p. 012202. [CrossRef]
Shu, J.-J. , 2012, “ Laminar Film Condensation Heat Transfer on a Vertical, Non-Isothermal, Semi-Infinite Plate,” Arabian J. Sci. Eng., 37(6), pp. 1711–1721. [CrossRef]
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Merkin, J. H. , 1986, “ On Dual Solutions Occurring in Mixed Convection in a Porous-Medium,” J. Eng. Math., 20(2), pp. 171–179. [CrossRef]
Merkin, J. H. , and Pop, I. , 1987, “ Mixed Convection Boundary-Layer on a Vertical Cylinder Embedded in a Saturated Porous Medium,” Acta Mech., 66(1–4), pp. 251–262. [CrossRef]
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Shu, J.-J. , and Pop, I. , 1998, “ Transient Conjugate Free Convection From a Vertical Flat Plate in a Porous Medium Subjected to a Sudden Change in Surface Heat Flux,” Int. J. Eng. Sci., 36(2), pp. 207–214. [CrossRef]
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Shu, J.-J. , and Wilks, G. , 2013, “ Heat Transfer in the Flow of a Cold, Axisymmetric Jet Over a Hot Sphere,” ASME J. Heat Transfer, 135(3), p. 032201. [CrossRef]
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Rohni, A. M. , Ahmad, S. , Merkin, J. H. , and Pop, I. , 2013, “ Mixed Convection Boundary-Layer Flow Along a Vertical Cylinder Embedded in a Porous Medium Filled by a Nanofluid,” Transp. Porous Media, 96(2), pp. 237–253. [CrossRef]
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Figures

Grahic Jump Location
Fig. 1

Physical model and coordinate system

Grahic Jump Location
Fig. 2

Velocity profile f′ (η) for various σ at λ=−1 and γ=5

Grahic Jump Location
Fig. 3

Reduced skin friction f″(0) with γ for various σ at λ=−1

Grahic Jump Location
Fig. 4

Reduced skin friction f″(0) with σ for various γ at λ=−1

Grahic Jump Location
Fig. 5

Reduced skin friction f″(0) with λ for various γ: (a) σ=−1 and (b) σ=1

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