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Radiation effect on mixed convection along a vertical plate with uniform surface temperature

Strahlungseinflüsse auf die Mischkonvektion entlang einer senkrechten Platte mit gleichförmiger Oberflächentemperatur

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Abstract

This paper investigates the effect of radiation on the forced and free convection flow of an optically dense viscous incompressible fluid along a heated vertical flat plate with uniform free stream and uniform surface temperature with Rosseland diffusion approximation. With appropriate transformations, the boundary layer equations governing the flow are reduced to local nonsimilarity equations valid in the forced convection regime as well as in the free convection regime. A group of transformation is, also, introduced to reduce the boundary layer equations to a set of local nonsimilarity equations valid in both the forced and free convection regimes. Solutions of the governing equations are obtained by employing the implicit finite difference methods together with Keller box scheme and are expressed in terms of local shear stress and local rate of heat transfer for a range of values of the pertinent parameters.

Zusammenfassung

In der Arbeit wird der Einfluß der Wärmestrahlung auf die erzwungene und freie Konvektionsströmung eines optisch dichten, zähen, inkompressiblen Fluids entlang einer beheizten, senkrechten Platte mit gleichförmiger Oberflächentemperatur mit Hilfe der Rosseland-Diffusionsnäherung untersucht. Durch geeignete Transformationen lassen sich die den Strömungsvorgang beschreibenden Grenzschichtgleichungen in lokale, Nichtähnlichkeits-Gleichungen überführen, die sowohl im Bereich der Zwangs- wie der Freikonvektion Gültigkeit haben. Durch Anwendung impliziter Finitdifferenzen-Methoden in Verbindung mit dem “Keller-Box” Schema wurden Lösungen der Grundgleichungen gewonnen und in Form lokaler Schubspannungen und Wärmeübergangsintensitäten in einem weiten Bereich der Haupteinflußparameter dokumentiert werden.

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Abbreviations

a :

Rosseland mean absorption coefficient

f :

dimensionless stream function

u :

velocity component in thex-direction

v :

velocity component in they-direction

g :

acceleration of gravity

R d :

conduction-radiation parameter

T :

temperature of fluid

T 0 :

temperature of ambient fluid

T w :

plate temperature

C p :

specific heat at constant pressure

κ :

the coefficient of thermal diffusivity

Pr :

Prandtl number

Q :

nondimensional heat transfer

x :

coordinate measuring distance along plate

y :

coordinate measuring distance normal to plate

α :

effective thermal diffusivity (k/ρC p )

ψ :

stream function

θ :

dimensionless temperature function

θ w :

dimensionless surface temperature

β :

the coefficient of volume expansion

ν :

the kinematic coefficient of viscosity

ϱ :

fluid density

σ :

Stephen-Boltzman constant

σ s :

scattering coefficient

τ w :

nondimensional shear stress

η :

similarity variable

ξ :

scaled streamwise coordinate

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Authors and Affiliations

  1. Department of Mathematics, University of Dhaka, 1000, Dhaka, Bangladesh

    M. A. Hossain

  2. Manchester School of Engineering, University of Manchester, M13 9PL, Manchester, U.K.

    H. S. Takhar (Reader)

Authors
  1. M. A. Hossain
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  2. H. S. Takhar
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Hossain, M.A., Takhar, H.S. Radiation effect on mixed convection along a vertical plate with uniform surface temperature. Heat and Mass Transfer 31, 243–248 (1996). https://doi.org/10.1007/BF02328616

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