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Technical Brief

Mixed Convection Boundary Layer Flow Near the Lower Stagnation Point of a Cylinder Embedded in a Porous Medium Using a Thermal Nonequilibrium Model

[+] Author and Article Information
Haliza Rosali

Department of Mathematics,
Faculty of Science,
Universiti Putra Malaysia,
Serdang, Selangor 43400, Malaysia
e-mail: liza_r@upm.edu.my

Anuar Ishak

School of Mathematical Sciences,
Faculty of Science and Technology,
Universiti Kebangsaan Malaysia,
Bangi, Selangor 43600, Malaysia
e-mail: anuar_mi@ukm.edu.my

Ioan Pop

Department of Mathematics,
Babeş-Bolyai University,
CP 253, Cluj-Napoca 400082, Romania
e-mail: popm.ioan@yahoo.co.uk

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received January 21, 2015; final manuscript received March 9, 2016; published online April 26, 2016. Assoc. Editor: Andrey Kuznetsov.

J. Heat Transfer 138(8), 084501 (Apr 26, 2016) (7 pages) Paper No: HT-15-1055; doi: 10.1115/1.4033164 History: Received January 21, 2015; Revised March 09, 2016

The present paper analyzes the problem of two-dimensional mixed convection boundary layer flow near the lower stagnation point of a cylinder embedded in a porous medium. It is assumed that the Darcy's law holds and that the solid and fluid phases of the medium are not in thermal equilibrium. Using an appropriate similarity transformation, the governing system of partial differential equations are transformed into a system of ordinary differential equations, before being solved numerically by a finite-difference method. We investigate the dependence of the Nusselt number on the solid–fluid parameters, thermal conductivity ratio and the mixed convection parameter. The results indicate that dual solutions exist for buoyancy opposing flow, while for the assisting flow, the solution is unique.

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Figures

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Fig. 1

Two-dimensional physical model and coordinate system

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Fig. 9

Temperature profiles for fluid and solid phases when γ=0.5 and λ=1 (assisting flow)

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Fig. 10

Temperature profiles for fluid and solid phases when γ=1

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Fig. 8

Temperature profiles for solid phase when γ=0.5 and λ=−1.2 (opposing flow)

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Fig. 7

Temperature profiles for fluid phase when γ=0.5 and λ=−1.2 (opposing flow)

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Fig. 6

Solid phase Nusselt number for various values of γ when H = 5

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Fig. 5

Fluid phase Nusselt number for various values of γ when H = 5

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Fig. 4

The rates of surface heat transfer for both the solid and fluid phases for various values of H when γ=0.5

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Fig. 3

Solid phase Nusselt number for various values of H when γ=0.5

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Fig. 2

Fluid phase Nusselt number for various values of H, when γ=0.5

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Fig. 11

Temperature profiles for fluid and solid phases when γ=1 (case of λ→0)

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