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Research Papers: Forced Convection

Three-Dimensional Stagnation Flow and Heat Transfer of a Viscous, Compressible Fluid on a Flat Plate

[+] Author and Article Information
Asghar B. Rahimi

Professor
e-mail: rahimiab@yahoo.com
Faculty of Engineering,
Ferdowsi University of Mashhad,
P.O. Box No. 91775-1111,
Mashhad, Iran

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the Journal of Heat Transfer. Manuscript received August 29, 2012; final manuscript received April 15, 2013; published online August 19, 2013. Assoc. Editor: Ali Ebadian.

J. Heat Transfer 135(10), 101702 (Aug 19, 2013) (12 pages) Paper No: HT-12-1469; doi: 10.1115/1.4024386 History: Received August 29, 2012; Revised April 15, 2013

The steady-state three-dimensional flow and heat transfer of a viscous, compressible fluid in the vicinity of stagnation point region on a flat plate with constant wall temperature is investigated by similarity solution approach, taking into account the variation of density of the fluid with respect to temperature. The free stream, along z-direction, impinges on the flat plate to produce a flow with different velocity components. An exact solution of the problem is obtained for the three dimensional case by the reduction of the Navier–Stokes and energy equations using appropriate similarity transformations introduced for the first time. The nonlinear ordinary differential equations are solved numerically using a finite difference scheme. Computations have been conducted for different values of the parameters characterizing the problem. The obtained results show that increasing the value of compressibility factor and wall temperature both cause the value of the velocity components and temperature gradients and pressure gradients in the vicinity of the plate to increase.

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References

Howarth, L., 1951, “The Boundary Layer in Three-Dimensional Flow—Part II: The Flow Near a Stagnation Point,” Philos. Mag., 42(7), pp. 1433–1440.
Wang, C. Y., 1973, “Axisymmetric Stagnation Flow Towards a Moving Plate,” AIChE J., 19, pp. 1080–1081. [CrossRef]
Kumari, M., and Nath, G., 1978, “Unsteady Laminar Compressible Boundary-Layer Flow at a Three-Dimensional Stagnation Point,” J. Fluid Mech., 87, pp. 705–717. [CrossRef]
Vasantha, R., and Nath, G., 1989, “Semi-Similar Solutions of the Unsteady Compressible Second-Order Boundary Layer Flow at the Stagnation Point,” Int. J. Heat Mass Transfer, 32, pp. 435–444. [CrossRef]
Chiriac, V. A., and Ortega, A., 2002, “A Numerical Study of the Unsteady Flow and Heat Transfer in a Transitional Confined Slot Jet Impinging on an Isothermal Surface,” Int. J. Heat Mass Transfer, 45, pp. 1237–1248. [CrossRef]
Saleh, R., and Rahimi, A. B., 2004, “Axisymmetric Stagnation-Point Flow and Heat Transfer of a Viscous Fluid on a Moving Cylinder With Time-Dependent Axial Velocity and Uniform Transpiration,” ASME J. Fluids Eng., 126, pp. 997–1005. [CrossRef]
Rahimi, A. B., and Saleh, R., 2007, “Axisymmetric Stagnation-Point Flow and Heat Transfer of a Viscous Fluid on a Rotating Cylinder With Time-Dependent Angular Velocity and Uniform Transpiration,” ASME J. Fluids Eng., 129, pp. 107–115. [CrossRef]
Rahimi, A. B., and Saleh, R., 2008, “Similarity Solution of Un-Axisymmetric Heat Transfer in Stagnation-Point Flow on a Cylinder With Simultaneous Axial and Rotational Movements,” ASME J. Heat Transfer, 130, p. 054502. [CrossRef]
Baris, S., 2003, “Steady Three-Dimensional Flow of a Second Grade Fluid Towards a Stagnation Point at a Moving Flat Plate,” Turk. J. Eng. Environ. Sci., 27, pp. 21–29.
Zuccher, S., Tumin, A., and Reshotko, E., 2006, “Parabolic Approach to Optimal Perturbations in Compressible Boundary Layers,” J. Fluid Mech., 556, pp. 189–216. [CrossRef]
Rahimi, A. B., and Esmaeilpour, M., 2011, “Axisymmetric Stagnation Flow Obliquely Impinging on a Moving Circular Cylinder With Uniform Transpiration,” Int. J. Numer. Methods Fluids, 65, pp. 1084–1095. [CrossRef]
Abbasi, A. S., and Rahimi, A. B., 2009, “Non-Axisymmetric Three-Dimensional Stagnation-Point Flow and Heat Transfer on a Flat Plate,” ASME J. Fluids Eng., 131, p. 074501. [CrossRef]
Abbasi, A. S., and Rahimi, A. B., 2009, “Three-Dimensional Stagnation Flow and Heat Transfer on a Flat Plate With Transpiration,” J. Thermophys. Heat Transfer, 23, pp. 513–521. [CrossRef]
Abbasi, A. S., Rahimi, A. B., and Niazman, H., 2011, “Exact Solution of Three-Dimensional Unsteady Stagnation Flow on a Heated Plate,” J. Thermodyn. Heat Transfer, 25, pp. 55–58. [CrossRef]
Abbasi, A. S., and Rahimi, A. B., 2012, “Investigation of Two-Dimensional Unsteady Stagnation-Point Flow and Heat Transfer Impinging on an Accelerated Flat Plate,” ASME J. Heat Transfer, 134, p. 064501. [CrossRef]
Mohammadiun, H., and Rahimi, A. B., 2012, “Axisymmetric Stagnation-Point Flow and Heat Transfer of a Viscous, Compressible Fluid on a Cylinder With Constant Wall Temperature,” J. Thermophys. Heat Transfer, 26(3), pp. 494–502.

Figures

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Fig. 1

Schematic of the problem

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Fig. 2

Three-dimensional stream surface and velocity profiles

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Fig. 3

Comparison of f′ and f′ + g′ profiles with Ref. [12] for λ = 0.1

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Fig. 4

Comparison of f, g, and -(λ+1)f+g profiles with Ref. [12] when λ = 0.5

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Fig. 5

Effect of the variation of β parameter on f′ profiles for (a) an axisymmetric flow and (b) λ = 0.2 when Tw = 200 °C,Pr = 0.7

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Fig. 6

Effect of the variation of β parameter on f′ + g′ profiles for (a) an axisymmetric flow and (b) λ = 0.2 when Tw = 200 °C,Pr = 0.7

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Fig. 7

Effect of the variation of β parameter on ((λ+1)f+g)/c(η) profiles for (a) an axisymmetric flow and (b) λ = 0.2 when Tw = 200 °C,Pr = 0.7

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Fig. 8

Effect of the variation of β parameter on θ profiles for (a) an axisymmetric flow and (b) λ = 0.2 when Tw = 200 °C,Pr = 0.7

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Fig. 9

Effect of the variation of β parameter on dimensionless pressure profiles for (a) an axisymmetric flow and (b) λ = 0.2 when Tw = 200 °C,Pr = 0.7

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Fig. 10

Effect of wall temperature variations on f′ profiles for (a) an axisymmetric flow and (b) λ = 0.2 when β = 0.003,Pr = 0.7

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Fig. 11

Effect of wall temperature variations on f′ + g′ profiles for (a) an axisymmetric flow and (b) λ = 0.2 when β = 0.003,Pr = 0.7

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Fig. 12

Effect of wall temperature variations on ((λ+1)f+g)/c(η) profiles for (a) an axisymmetric flow and (b) λ = 0.2 when β = 0.003,Pr = 0.7

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Fig. 13

Effect of wall temperature variations on θ profiles for (a) an axisymmetric flow and (b) λ = 0.2 when β = 0.003,Pr = 0.7

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Fig. 14

Effect of wall temperature variations on dimensionless pressure profiles for (a) an axisymmetric flow and (b) λ = 0.2 when β = 0.003,Pr = 0.7

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Fig. 15

Effect of the variation of λ parameter on dimensionless velocity profiles in (a) x and (b) z directions when Tw = 200 °C,Pr = 0.7,β = 0.003

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Fig. 16

Effect of the variation of λ parameter on dimensionless (a) pressure and (b) temperature profiles when Tw = 200 °C,Pr = 0.7,β = 0.003

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Fig. 17

Effect of Pr No. on dimensionless temperature profiles for (a) λ = 1.0 and (b) λ = 0.5 when Tw = 200 °C,β = 0.003

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Fig. 18

Variation of dimensionless heat transfer coefficient versus β coefficient for different values of λ parameter when Tw = 185 °C,Pr = 0.7

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