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Research Papers: Forced Convection

Similarity Solutions of Unsteady Three-Dimensional Stagnation 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-mails: rahimiab@yahoo.com;
rahimiab@um.ac.ir

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received June 17, 2014; final manuscript received December 2, 2015; published online January 20, 2016. Assoc. Editor: Peter Vadasz.

J. Heat Transfer 138(4), 041701 (Jan 20, 2016) (9 pages) Paper No: HT-14-1409; doi: 10.1115/1.4032288 History: Received June 17, 2014; Revised December 02, 2015

The most general form of the problem of stagnation-point flow and heat transfer of a viscous, compressible fluid impinging on a flat plate is solved in this paper. The plate is moving with a constant or time-dependently variable velocity and acceleration toward the impinging flow or away from it. In this study, an external low Mach number flow impinges on the plate, along z-direction, with strain rate a and produces three-dimensional flow. The wall temperature is assumed to be maintained constant, which is different from that of the main stream. The density of the fluid is affected by the temperature difference existing between the plate and the incoming far-field flow. Suitably introduced similarity transformations are used to reduce the unsteady, three-dimensional, Navier–Stokes, and energy equations to a coupled system of nonlinear ordinary differential equations. The fourth-order Runge–Kutta method along with a shooting technique is applied to numerically solve the governing equations. The results are achieved over a wide range of parameters characterizing the problem. It is revealed that the significance of the aspect ratio of the velocity components in x and y directions, λ parameter, is much more noticeable for a plate moving away from impinging flow. Moreover, negligible heat transfer rate is reported between the plate and fluid viscous layer close to the plate when the plate moves away with a high velocity.

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Figures

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Fig. 1

Three-dimensional stagnation flow imposed by a suction force in two opposite directions

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Fig. 2

Schematic of the problem

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Fig. 3

Schematic of the problem

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Fig. 4

Three-dimensional stream surface and velocity profiles

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Fig. 5

Comparison of f′ and f′+g′ profiles between the present work and Ref. [11] for λ=0.1

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Fig. 6

f′ distributions for different values of plate velocity and λ parameter when β=0.003, Tw=125 °C, Pr=0.7

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Fig. 7

f′+g′ distributions for different values of plate velocity and λ parameter when β=0.003, Tw=125 °C, Pr=0.7

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Fig. 8

Distributions of dimensionless w component of velocity for different values of plate velocity and λ parameter when β=0.003, Tw=125 °C, Pr=0.7

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Fig. 9

θ distributions for different values of plate velocity and λ parameter when β=0.003, Tw=125 °C, Pr=0.7

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Fig. 10

Dimensionless pressure distributions for different values of plate velocity and λ parameter when β=0.003, Tw=125 °C, Pr=0.7

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Fig. 11

f′ distributions for the case of S˙̃=−3 for different values of λ and β parameters when Tw=100 °C, Pr=0.7

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Fig. 12

f′ distributions for the case of S˙̃=2 for different values of λ and β parameters when Tw=100 °C, Pr=0.7

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Fig. 13

θ distributions for the case of S˙̃=−3 for different values of λ and Pr numbers when β=0.003, Tw=100 °C

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Fig. 14

θ distributions for the case of S˙̃=2 for different values of λ and Pr numbers when β=0.003, Tw=100 °C

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Fig. 15

Effects of λ parameter on unsteady f′ profiles when β=0.003, Tw=125 °C, Pr=0.7

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Fig. 16

Effects of λ parameter on dimensionless form of unsteady w component when β=0.003, Tw=125 °C, Pr=0.7

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Fig. 17

Effects of λ parameter on unsteady θ profiles when β=0.003, Tw=125 °C, Pr=0.7

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Fig. 18

Distributions of dimensionless heat transfer coefficient in unsteady procedure for different values of λ parameter when β=0.003, Tw=125 °C, Pr=0.7

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