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Stagnation Flow on a Heated Vertical Plate With Surface Slip

[+] Author and Article Information
C. Y. Wang

Department of Mathematics,
Michigan State University,
East Lansing, MI 48824

Chiu-On Ng

Department of Mechanical Engineering,
The University of Hong Kong,
Pokfulam Road, Hong Kong
e-mail: cong@hku.hk

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received December 18, 2012; final manuscript received February 14, 2013; published online June 6, 2013. Assoc. Editor: Andrey Kuznetsov.

J. Heat Transfer 135(7), 074505 (Jun 06, 2013) (8 pages) Paper No: HT-12-1664; doi: 10.1115/1.4023750 History: Received December 18, 2012; Revised February 14, 2013

Two problems of stagnation flow on a uniformly heated surface with slip and temperature jump are solved in this paper with an exact similarity method. In the first problem, an axially symmetric stagnation flow impinging on a uniformly heated vertical flat surface is considered, and in the second problem, an inclined, two-dimensional stagnation flow impinging on the vertical surface is examined. It is shown that the surface slip can have a significant effect on the flow and the heat transfer in the two problems.

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Figures

Grahic Jump Location
Fig. 1

Two stagnation flows impinging on a uniformly heated vertical flat surface in the z = 0 plane (a) an axially symmetric stagnation flow, where the x-axis is vertically upward (b) an inclined, two-dimensional stagnation flow, where the x-axis is at an angle α from the vertical. The z-axis is normal to the plane in either case.

Grahic Jump Location
Fig. 2

(a) Similarity function ϕ′(ζ). Dashed curve: no-slip λ = 0, γ = 0, solid curve: λ = 0.1, γ = 0.2, dashed-dotted curve: λ = 5, γ = 2. (b) Similarity function H(ζ), P = 0.7. Dashed curve: no-slip λ = 0, γ = 0, solid curve: λ = 0.1, γ = 0.2, dashed-dotted curve: λ = 5, γ = 2. (c) Similarity function H(ζ), P = 7. Dashed curve: no-slip λ = 0, γ = 0, solid curve: λ = 0.1, γ = 0.2, dashed-dotted curve: λ = 5, γ = 2. (d) Similarity function M(ζ), P = 0.7. Dashed curve: no-slip λ = 0, γ = 0, solid curve: λ = 0.1, γ = 0.2, dashed-dotted curve: λ = 5, γ = 2. (e) Similarity function M(ζ), P = 7. Dashed curve: no-slip λ = 0, γ = 0, solid curve: λ = 0.1, γ = 0.2, dashed-dotted curve: λ = 5, γ = 2.

Grahic Jump Location
Fig. 3

(a) Streamlines in the plane y = 0 for no-slip (λ = 0, γ = 0) and G = 2. (b) Streamlines in the plane y = 0 for λ = 0.1, γ = 0.2, and G = 2. (c) Streamlines in the plane y = 0 for λ = 5, γ = 0.2, and G = 2.

Grahic Jump Location
Fig. 4

(a) Streamlines in the plane y = 0 for no-slip (λ = 0, γ = 0) and G = 5. (b) Streamlines in the plane y = 0 for λ = 0.1, γ = 0.2, and G = 5. (c) Streamlines in the plane y = 0 for λ = 5, γ = 0.2, and G = 2.

Grahic Jump Location
Fig. 5

(a) Inclined 2D stagnation similarity function M(ζ), P = 0.7. Dashed curve: no-slip λ = 0, γ = 0, solid curve: λ = 0.1, γ = 0.2, dashed-dotted curve: λ = 5, γ = 2. (b) Inclined 2D stagnation similarity function M(ζ), P = 7. Dashed curve: no-slip λ = 0, γ = 0, solid curve: λ = 0.1, γ = 0.2, dashed-dotted curve: λ = 5, γ = 2. (c) Inclined 2D stagnation similarity function N(ζ), P = 0.7. Dashed curve: no-slip λ = 0, γ = 0, Solid curve: λ = 0.1, γ = 0.2, dashed-dotted curve: λ = 5, γ = 2. (d) Inclined 2D stagnation similarity function N(ζ), P = 7. Dashed curve: no-slip λ = 0, πγ = 0, solid curve: λ = 0.1, γ = 0.2, dashed-dotted curve: λ = 5, γ = 2.

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