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Higher-order effects in natural convection flow over uniform flux inclined flat plates in porous media

Einflüsse höherer Ordnung bei freier Konvektion über gleichmäßig beheizten schrägen ebenen Platten in porösen Medien

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Abstract

Higher-order boundary-layer effects for natural convection flow along inclined flat plates (of both positive and negative inclinations) with a uniform heat flux surface condition in a saturated porous medium are studied. Using the method of matched asymptotic expansions the three terms in inner and outer expansions have been obtained. It is shown that the first eigenfunction for this considered problem coincides with 0(ɛ 2)-term in the inner expansion.

Zusammenfassung

Es werden Grenzschichteinflüsse höherer Ordnung für die freie Konvektionsströmung über schrägen ebenen Platten (sowohl für positive als auch für negative Schräge) bei gleichmäßigem Wärmestrom in einem gesättigten porösen Medium untersucht. Mit Hilfe der Methode der angepaßten asymptotischen Entwicklungen werden drei Terme der inneren und äußeren Entwicklung bestimmt. Es wird gezeigt, daß die erste Eigenfunktion für

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Abbreviations

A 0,A 1,A 2,C 1 :

constants

g :

acceleration due to gravidy

k :

thermal conductivity of the saturated porous medium

K :

permeability of the porous medium

N :

constant

Nu x :

local Nusselt number=qx/(T w −T ∞)

q :

heat flux

Ra x :

local Rayleigh number=gβK(T w −T ∞) χ cos θ /(α ν)

T :

temperature

u, v :

velocity components along (x, y)-axes

x, y :

coordinates along and normal to the plate, respectively

α :

≡uivalent thermal diffusivity of the porous medium

β :

coefficient of thermal expansion of the fluid

η :

similarity variable=y(Rax)1/2/n

ν :

kinematic viscosity

ɛ :

expansion parameter, Rax −1/2

φ :

inclination angle

λ n :

eigenvalue

ψ :

stream function

ω :

refers to wall condition

∞:

refers to ambient condition

Reference

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Authors and Affiliations

  1. Department of Applied Mathematical Studies, The University of Leeds, LS2 9JT, Leeds, England

    D. B. Ingham

  2. Faculty of Mathematics, University of Cluj, CP 253, R-3400, Cluj, Romania

    I. Pop

Authors
  1. D. B. Ingham
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  2. I. Pop
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Ingham, D.B., Pop, I. Higher-order effects in natural convection flow over uniform flux inclined flat plates in porous media. Wärme- und Stoffübertragung 22, 239–242 (1988). https://doi.org/10.1007/BF01377247

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  • DOI: https://doi.org/10.1007/BF01377247

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