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Research Papers: Forced Convection

Unsteady Two-Dimensional Stagnation-Point Flow and Heat Transfer of a Viscous, Compressible Fluid on an Accelerated Flat Plate

[+] Author and Article Information
H. R. Mozayyeni

Faculty of Engineering, Ferdowsi
University of Mashhad,
Mashhad 91775-1111, Iran

Asghar B. Rahimi

Professor
Faculty of Engineering, Ferdowsi
University of Mashhad,
Mashhad 91775-1111, Iran
e-mail: rahimiab@yahoo.com
and rahimiab@um.ac.ir

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received March 28, 2013; final manuscript received October 14, 2013; published online January 9, 2014. Assoc. Editor: Ali Ebadian.

J. Heat Transfer 136(4), 041701 (Jan 09, 2014) (9 pages) Paper No: HT-13-1167; doi: 10.1115/1.4026008 History: Received March 28, 2013; Revised October 14, 2013

The general formulation and exact solution of the Navier–Stokes and energy equations regarding the problem of steady and unsteady two-dimensional stagnation-point flow and heat transfer is investigated in the vicinity of a flat plate. The plate is moving at time-dependent or constant velocity towards the main low Mach number free stream or away from it. The main stream impinges along z-direction on the flat plate with strain rate a and produces two-dimensional flow. The fluid is assumed to be viscous and compressible. The density of the fluid is affected by the existing temperature difference between the plate and potential far field flow. Suitably introduced similarity transformations are used to reduce the governing equations to a coupled system of ordinary differential equations. Finite Difference Scheme is used to solve these non-linear ordinary differential equations. The obtained results are presented over a wide range of parameters characterizing the problem. It is revealed that the significance of the increase of thermal expansion coefficient, β, and wall temperature on velocity and temperature distributions is much more noticeable for a plate moving away from impinging flow. Moreover, negligible shear stress and heat transfer is reported between the plate and fluid viscous layer close to the plate for a wide range of β coefficient when the plate moves away from incoming far field flow.

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References

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Figures

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Fig. 1

Configuration of the problem

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Fig. 2

Comparison of f′ profiles between the present work and Ref. [13] when S˙˜=-10

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Fig. 3

Effects of β coefficient on f′ profiles for different values of plate velocity when Tw = 100  °C, Pr = 0.7

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Fig. 4

Effects of wall temperature on f′ profiles for different values of plate velocity when β = 0.003, Pr = 0.7

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Fig. 5

Effects of β coefficient on w-component distributions for different values of plate velocity when Tw = 100  °C, Pr = 0.7

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Fig. 6

Effects of β coefficient on θ profiles for different values of plate velocity when Tw = 100  °C, Pr = 0.7

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Fig. 7

Effects of wall temperature on θ profiles for different values of plate velocity when β = 0.003, Pr = 0.7

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Fig. 8

Effects of Pr No. on θ profiles for different values of plate velocity when Tw = 100  °C, β = 0.003

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Fig. 9

Dimensionless pressure distributions for different values of wall temperature and dimensionless plate velocity when β = 0.003, Pr = 0.7

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Fig. 10

Effects of β variations on dimensionless heat transfer coefficient for different values of plate velocity when Tw = 100  °C, Pr = 0.7

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Fig. 11

Effects of β variations on shear stress for different values of constant plate velocity when Tw = 100  °C, Pr = 0.7

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Fig. 12

Effects of β parameter on f′ profiles at different times when Tw = 125  °C, Pr = 0.7

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Fig. 13

Effects of Wall Temperature on f′ profiles at different times when β = 0.003, Pr = 0.7

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Fig. 14

Effects of β parameter on distributions of dimensionless w-component of velocity at different times when Tw = 125  °C, Pr = 0.7

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Fig. 15

Effects of β parameter on θ profiles at different times when Tw = 125  °C, Pr = 0.7

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Fig. 16

Effects of Wall Temperature on θ profiles at different times when β = 0.003, Pr = 0.7

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Fig. 17

Distributions of dimensionless heat transfer coefficient in unsteady procedure for different values of wall temperature when β = 0.003, Pr = 0.7

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Fig. 18

Effects of Pr on dimensionless Pressure distributions at different times when Tw = 125  °C, β = 0.003

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Fig. 19

Effects of Pr on θ profiles at different times when Tw = 125  °C, β = 0.003

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