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Investigation of Two-Dimensional Unsteady Stagnation-Point Flow and Heat Transfer Impinging on an Accelerated Flat Plate

[+] Author and Article Information
Ali Shokrgozar Abbassi

Asghar Baradaran Rahimi1

 Faculty of Engineering,Ferdowsi University of Mashhad, Mashhad 91775-1111, Iranrahimiab@yahoo.com

1

Corresponding author.

J. Heat Transfer 134(6), 064501 (Apr 26, 2012) (5 pages) doi:10.1115/1.4005742 History: Received August 26, 2010; Revised November 17, 2011; Published April 26, 2012; Online April 26, 2012

General formulation and solution of Navier–Stokes and energy equations are sought in the study of two-dimensional unsteady stagnation-point flow and heat transfer impinging on a flat plate when the plate is moving with variable velocity and acceleration toward main stream or away from it. As an application, among others, this accelerated plate can be assumed as a solidification front which is being formed with variable velocity. An external fluid, along z-direction, with strain rate a impinges on this flat plate and produces an unsteady two-dimensional flow in which the plate moves along z-direction with variable velocity and acceleration in general. A reduction of Navier–Stokes and energy equations is obtained by use of appropriate similarity transformations. Velocity and pressure profiles, boundary layer thickness, and surface stress-tensors along with temperature profiles are presented for different examples of impinging fluid strain rate, selected values of plate velocity, and Prandtl number parameter.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 1

Schematic problem graph

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Figure 2

Velocity in x-direction at selected values of ξ for different time values and exponential plate velocity function

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Figure 3

Velocity in x-direction at selected values of ξ for different time values and polynomial plate velocity function

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Figure 4

Boundary layer thickness at different time values and sinusoidal plate velocity function

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Figure 5

Velocity in w-direction at selected values of ξ for different time values and exponential plate velocity function

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Figure 6

Shear-stress at different time values and all values of ξ for sinusoidal plate velocity function

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Figure 7

Pressure variation in boundary layer at certain time and different values of ξ for exponential plate velocity function

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Figure 8

Pressure variation in boundary layer at ξ=0.1 and different values of time for exponential plate velocity function

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Figure 9

Thermal boundary layer profile for Pr=0.1 and different time values for exponential plate velocity function

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Figure 10

Thermal boundary layer profile for Pr=1.0 and different time values at ξ=0.1,2.2 for exponential plate velocity function

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Figure 11

Thermal boundary layer thickness for different values of time and for all values of Prandtl number and exponential plate velocity function

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Figure 12

Thermal boundary layer profile for Pr=1.0 and different time values for polynomial plate velocity function

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