Free convective transpiration over a vertical plate: a numerical study

doi:10.1007/BF01650468

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Free convective transpiration over a vertical plate: a numerical study

Journal Article•DOI•

Free convective transpiration over a vertical plate: a numerical study

A. K. Kolar¹, V. M. K. Sastri¹•Institutions (1)

Indian Institute of Technology Madras¹

01 Nov 1988-Vol. 23, Iss: 6, pp 327-336

TL;DR: In this article, a simple finite difference scheme has been successfully employed to solve the nonlinear coupled partial differential equations, with nonhomogeneous boundary condition, which describe the free convection at a vertical plate with transpiration.

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Abstract: A rarely adopted simple finite difference scheme has been successfully employed to solve the nonlinear coupled partial differential equations, with nonhomogeneous boundary condition, which describe the free convection at a vertical plate with transpiration. The solution is obtained for a Prandtl number of 0.72, in the blowing parameter range of — 1.9 < Cx < 1.9. The effects of suction and blowing on heat transfer and skin friction are discussed. It is concluded that the boundary layer has a better memory of the upstream suction distribution than of the upstream blowing distribution.

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Combined heat and mass transfer effects on mhd free convection flow past an oscillating plate embedded in porous medium

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R. C. Chaudhary, Arpita Jain, Received November

01 Jan 2007

TL;DR: In this paper, the authors studied the MHD flow past an infinite vertical oscillating plate through a porous medium, taking account of the presence of free convection and mass transfer.

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Abstract: The objective of this paper is to study the MHD flow past an infinite vertical oscillating plate through porous medium, taking account of the presence of free convection and mass transfer. The governing equations are solved in closed form by Laplace-transform technique. The results are obtained for velocity, temperature, concentration, Nusselt number and skin-friction. The effects of various material parameters are discussed on flow variables and presented by graphs.

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74 citations

Cites background from "Free convective transpiration over ..."

...Vedhanayagam et al. [1], Martynenko et al. [2], Kolar et al. [ 3 ], Ramanaiah et al....
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Journal Article•DOI•

The effects of thermal radiation and viscous dissipation on MHD heat and mass diffusion flow past an oscillating vertical plate embedded in a porous medium with variable surface conditions

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P. M. Kishore, V. Rajesh, S. Vijayakumar Verma

01 Jan 2012-Theoretical and Applied Mechanics

TL;DR: In this paper, the authors studied the hydromagnetic flow of a viscous incompressible fluid past an oscillating vertical plate embedded in a porous medium with radiation, viscous dissipation and variable heat and mass diffusion.

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Abstract: This investigation is undertaken to study the hydromagnetic flow of a viscous incompressible fluid past an oscillating vertical plate embedded in a porous medium with radiation, viscous dissipation and variable heat and mass diffusion. Governing equations are solved by unconditionally stable explicit finite difference method of DuFort – Frankel’s type for concentration, temperature, vertical velocity field and skin - friction and they are presented graphically for different values of physical parameters involved. It is observed that plate oscillation, variable mass diffusion, radiation, viscous dissipation and porous medium affect the flow pattern significantly.

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35 citations

Cites methods from "Free convective transpiration over ..."

...Free convection at a vertical plate with transpiration was investigated by Kolar and Sastri [4]....
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Journal Article•DOI•

MHD heat and mass diffusion flow by natural convection past a surface embedded in a porous medium

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R. C. Chaudhary¹, Arpita Jain¹•Institutions (1)

University of Rajasthan¹

01 Jan 2009-Theoretical and Applied Mechanics

TL;DR: In this article, an analytical study of the transient hydromagnetic natural convection flow past a vertical plate embedded in a porous medium is presented, taking account of the presence of mass diffusion and fluctuating temperature about time at the plate.

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Abstract: This paper presents an analytical study of the transient hydromagnetic natural convection flow past a vertical plate embedded in a porous medium, taking account of the presence of mass diffusion and fluctuating temperature about time at the plate. The governing equations are solved in closed form by the Laplace-transform technique. The results are obtained for temperature, velocity, penetration distance, Nusselt number and skin-friction. The effects of various parameters are discussed on the flow variables and presented by graphs.

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17 citations

Journal Article•

Unsteady mhd free convection flow and mass transfer near a moving vertical plate in the presence of thermal radiation

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Shaik. Abzal, G. V. Ramana Reddy, S. Vijaya Kumar Varma

01 Jan 2011-International Journal of Mathematical Archive

TL;DR: In this article, the problem of unsteady MHD free convection flow and mass transfer near a moving vertical plate in the presence of thermal radiation has been examined in detail.

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Abstract: The problem of unsteady MHD free convection flow and mass transfer near a moving vertical plate in the presence of thermal radiation has been examined in detail in this paper. The governing boundary layer equations of the flow field are solved by a closed analytical form. A parametric study is performed to illustrate the influence of radiation parameter, magnetic parameter, Grashof number, Prandtl number on the velocity, temperature, concentration and skin-friction. The results are discussed graphically and qualitatively. The numerical results reveal that the radiation induces a rise in both the velocity and temperature, and a decrease in the concentration. The model finds applications in solar energy collection systems, geophysics and astrophysics, aero space and also in the design of high temperature chemical process systems.

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15 citations

Cites background from "Free convective transpiration over ..."

...Vijaya Kumar Varma/ Unsteady mhd free convection flow and mass transfer near a moving vertical plate in the presence of thermal radiation / IJMA- 2(7), July-2011, Page: 1046-1053...
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...With the help of Eqn (6), the governing Eqns (1) - (3) reduce to: 2 2 1u u Gr Gc M u t y K θ φ ∂ ∂ = + + − + ∂ ∂ (7) 2 2 1 Pr Pr F t y θ θ θ ∂ ∂ = − ∂ ∂ (8) 2 2 1 t Sc y φ φ∂ ∂ = ∂ ∂ (9) The corresponding initial and boundary conditions in non-dimension form are: 0,u = 0,θ = 0ϕ = 0, 0y t∀ > ≤ ( ),u f t= ,1=θ 1=φ at 0=y , 0t > (10) 0=u , 0=θ , 0=φ as ∞→y The system Eqns (7) - (9) subject to the boundary conditions (10), includes the effect of free convection and mass transfer on the flows near a moving isothermal vertical plate....
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...A, and Wilson M, Natural convection flow from a vertical permeable flat plate with variable surface temperature and species concentration, Engineering Computations, 17(7), pp....
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...2 1 u u Gr Gc M u t y K θ φ ∂ ∂ = + + − + ∂ ∂ (7)...
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...The system Eqns (7) - (9) subject to the boundary conditions (10), includes the effect of free convection and mass transfer on the flows near a moving isothermal vertical plate....
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Journal Article•DOI•

Magnetohydrodynamics Free Convection Flow of a Radiating and Chemically Reacting Fluid Past an Impulsively Moving Plate With Ramped Wall Temperature

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Kalidas Das¹•Institutions (1)

Kalyani Government Engineering College¹

01 Nov 2012-Journal of Applied Mechanics

14 citations

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References

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An analysis of laminar free-convection flow and heat transfer about a flat plate parallel to the direction of the generating body force

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Simon Ostrach

01 Jan 1953

TL;DR: In this article, the free-convection flow and heat transfer about a flat plate parallel to the direction of the body force are formally analyzed and the type of flow is found to be dependent on the Grashof number alone.

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Abstract: The free-convection flow and heat transfer (generated by a body force) about a flat plate parallel to the direction of the body force are formally analyzed and the type of flow is found to be dependent on the Grashof number alone. For large Grashof numbers (which are of interest in aeronautics), the flow is of the boundary-layer type and the problem is reduced in a formal manner, which is analogous to Prandtl's forced-flow boundary-layer theory, to the simultaneous solution of two ordinary differential equations subject to the proper boundary conditions. Velocity and temperature distributions for Prandtl numbers of 0.01, 0.72, 0.733, 1, 1, 10, 100, and 1000 are computed, and it is shown that velocities and Nusselt numbers of the order of magnitude of those encountered in forced-convection flows may be obtained in free-convection flows. The theoretical and experimental velocity and temperature distributions are in good agreement. A flow and a heat-transfer parameter, from which the important physical quantities such as shear stress and heat-transfer rate can be computed, are derived as functions of Prandtl number alone.

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552 citations

Book•

Numerical methods in engineering

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Mario G. Salvadori, M. L. Baron, D. C. Drucker¹•Institutions (1)

Brown University¹

01 Jan 1955

TL;DR: Sommaire as discussed by the authors discusses the practical solution of algebraic and transcendental equations, finite differences and their applications, numerical integration of initial value problems, and numerical intergation of ordinary boundary value problems.

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Abstract: Sommaire : Chap. I - The practical solution of algebraic and transcendental equations. Chap. II - Finite differences and their applications. Chap. III - The numerical integration of initial value problems. Chap. IV - The numerical intergation of ordinary boundary value problems. Chap. V - The numerical solution of partial differential equations

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405 citations

Journal Article•DOI•

Free convection with blowing and suction

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John H. Merkin¹•Institutions (1)

University of Leeds¹

01 May 1972-International Journal of Heat and Mass Transfer

TL;DR: In this article, the effects of uniform blowing and suction on the free convection boundary layer on a vertical plate are considered, and a numerical solution of the full boundary layer equations is obtained in both cases.

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84 citations

"Free convective transpiration over ..." refers background or methods or result in this paper

...From the survey of literature, it is seen that only [ 8 ] and [10] are finite difference studies....
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...A step by step numerical solution was obtained by Merkin [ 8 ] by solving the third order momentum equation simultaneously with the second order energy equation....
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...It would probably remedy the situation to a little extent if the coupled equations are both of second order, rather than one being a third order equation, as it is in [ 8 ]....
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...The value of the blowing parameter for zero heat transfer seems to be near about 3. Merkin [ 8 ] has shown that for large suction rates, the temperature and velocity profiles become independent of x. Parikh et al. [10] obtained a value of - 1.39 for the slope of the asymptotic profile which agreed with their numerical solution within 2 percent....
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Journal Article•DOI•

Free Convection With Blowing or Suction

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Ephraim M Sparrow¹, R. D. Cess²•Institutions (2)

University of Minnesota¹, Westinghouse Electric²

01 Aug 1961-Journal of Heat Transfer-transactions of The Asme

72 citations

Journal Article•DOI•

The Effect of Mass Transfer on Free Convection

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R. Eichhorn¹•Institutions (1)

Princeton University¹

01 Aug 1960-Journal of Heat Transfer-transactions of The Asme

TL;DR: In this paper, the constant property laminar boundary layer equations with free convection and mass transfer were considered and solutions to the equations in the form of skin fi- iction and heat-transfer parameters were presented for the constant wall temperature case for a fluid with Pr = 0.73.

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Abstract: Consideration is given to the constant property laminar boundary layer equations with free convection and mass transfer. Similar solutions are possible for blowing rate distributions varying as the distance from the leading edge raised to the power (n -- 1)/4 where n is the exponent in a power law surface temperature distribution. Solutions to the equations in the form of skin fi- iction and heat-transfer parameters, and velocity and temperature profiles are presented for the constant wall temperature case for a fluid with Pr = 0.73. The cases considered range from strong suction to strong blowing. Mass transfer has a pronounced effect on the heat transfer but only a slight effect on the skin friction. In light of the solutions presented, these effects are shown to be physically rational. (auth)

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66 citations