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Research Papers: Natural and Mixed Convection

Mixed Convection Stagnation-Point Flow Past a Vertical Flat Plate With a Second Order Slip

[+] Author and Article Information
Alin V. Roşca

Faculty of Economics and Business
Administration,
Babeş-Bolyai University,
Cluj-Napoca 400084, Romania
e-mail: alin.rosca@econ.ubbcluj.ro

Ioan Pop

Department of Mathematics,
Babeş-Bolyai University,
Cluj-Napoca 400084, 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, 2013; final manuscript received May 13, 2013; published online October 21, 2013. Assoc. Editor: Giulio Lorenzini.

J. Heat Transfer 136(1), 012501 (Oct 21, 2013) (8 pages) Paper No: HT-13-1031; doi: 10.1115/1.4024588 History: Received January 21, 2013; Revised May 13, 2013

An exact similarity solution of the steady mixed convection flow of a viscous and incompressible fluid in the vicinity of two-dimensional stagnation-point with a second-order slip condition has been investigated. Using appropriate similarity variable, the Navier–Stokes equations coupled with the energy equation governing the flow and heat transfer are reduced to a system of nonlinear ordinary (similarity) equations, which are well-posed. These equations are solved numerically in the buoyancy assisting and opposing flow regions. It is found that a reverse flow region develops in the buoyancy opposing flow case, and dual (upper and lower branch) solutions are found to exist in the case of opposing flow region for a certain range of the negative values of the mixed convection parameter. A stability analysis has been performed, which shows that the upper branch solutions are stable and physically realizable in practice, while the lower branch solutions are not stable and, therefore, not physically realizable in practice. The numerical results have been compared with those reported in the literature, the agreement being excellent.

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Figures

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Fig. 1

Physical model and coordinate system

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Fig. 2

Variation of f"(0) with λ when a = 0 and b = 0

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Fig. 3

Variation of f"(0) with λ for several values of a when b = 0

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Fig. 4

Variation of f"(0) with λ for several values of b when a = 0

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Fig. 5

Variation of -θ'(0) with λ when a = 0 and b = 0

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Fig. 6

Variation of -θ'(0) with λ for several values of a when b = 0

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Fig. 7

Variation of -θ'(0) with λ for several values of b when a = 0

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Fig. 8

Dimensionless velocity f'(η) profiles for several values of λ(<0) when a = 0 and b = 0

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Fig. 9

Dimensionless temperature θ(η) profiles for several values of λ(<0) when a = 0 and b = 0

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Fig. 10

Dimensionless velocity f'(η) profiles for several values of a when b = 0 and λ = -1

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Fig. 11

Dimensionless temperature θ(η) profiles for several values of a when b = 0 and λ = -1

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Fig. 12

Dimensionless velocity f'(η) profiles for several values of b when a = 0 and λ = -0.5

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Fig. 13

Dimensionless temperature θ(η) profiles for several values of b when a = 0 and λ = -0.5

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Fig. 14

Dimensionless velocity f'(η) profiles for several values of λ when a = 1 and b = -1

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Fig. 15

Dimensionless temperature θ(η) profiles for several values of λ when a = 1 and b = -1

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Fig. 16

Streamlines for the first solution branch for λ = -1.3 (solid line) and λ = -1.5 (dotted line) when a = 1 and b = -1

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Fig. 17

Streamlines for the second solution branch for λ = -1.3 (left) and λ = -1.5 (right) when a = 1 and b = -1

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