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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

Figures

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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. 2

Three-dimensional stream surface and velocity profiles

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Fig. 1

Schematic of the problem

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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. 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. 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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