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Natural convection in porous media above a near horizontal uniform heat flux surface

Freie Konvektion in einem porösen Medium oberhalb einer nahezu horizontalen Fläche mit gleichmäßiger Wärmestromdichte

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Abstract

The boundary layer in free convection above a uniformly heated semi-infinite flat plate, which is inclined at a small angle to the horizontal in porous media is discussed. For positive inclinations of the plate, series solutions, one valid near the leading edge and the other at large distances from it, are obtained. When the inclination is negative, a series solution valid near the leading edge is again obtained. A step-by-step numerical technique, based on a scheme by Keller, is used to complete the solution in the region where neither series is adequate. For the negative inclinations of the plate, the boundary layer separates and a region of reverse flow develops.

Zusammenfassung

Hier wird die Grenzschicht bei freier Konvektion in einem porösem Medium oberhalb einer gleichmäßig beheizten, halbunendlichen flachen Platte, die mit einem kleinen Winkel gegen die Horizontale geneigt ist, untersucht. Für positive Neigungen der Platte sind zwei Reihenlösungen, eine gültig für den Anlaufbereich und die andere für einen großen Abstand davon, emittelt worden. Eine gültige Reihenlösung für eine negative Neigung in der Nähe des Anlaufbereiches ist ebenfalls bestimmt worden.

Es ist ein schrittweises numerisches Verfahren, das auf der Methode von Keller basiert, benützt worden, um das Ergebnis im Bereich, in welchem keine Reihenansätze existieren, zu vervollständigen. Für negative Neigungen der Platte zerteilt sich die Grenzschicht und es entwickelt sich ein Bereich von Rückströmung.

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Abbreviations

g :

acceleration due to gravity

k :

effective thermal diffusivity

K :

permeability of the porous medium

L :

length scale

q :

heat transfer

Ra :

Rayleigh number

T :

temperature

x,y :

Cartesian coordinates along and normal to the plate

u,v :

velocity components alongx andy axes, respectively

α :

thermal diffusivity of the porous medium

β :

coefficient of thermal expansion

γ :

angle of inclination of the plate to the horizontal

η,\(\bar \eta\) :

similarity variables

θ :

dimensionless temperature

λ :

eigenconstant

μ :

dynamic viscosity

ϱ :

density

ψ :

dimensionless stream function

′:

differentiation with respect to η or\(\bar \eta\)

−:

dimensional variables

∼:

dimensionless variables

w :

condition at the plate

∞:

condition in the free stream

References

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Kumari, M., Pop, I. & Nath, G. Natural convection in porous media above a near horizontal uniform heat flux surface. Wärme- und Stoffübertragung 25, 155–159 (1990). https://doi.org/10.1007/BF01590146

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  • DOI: https://doi.org/10.1007/BF01590146

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