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An analysis on forced convection in a channel filled with a Brinkman-Darcy porous medium: Exact and approximate solutions

Analyse von Zwangskonvektion in einem mit porösem Brinkman-Darcy-Medium gefüllten Kanal

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Abstract

An analysis was made to investigate non-Darcian fully developed flow and heat transfer in a porous channel bounded by two parallel walls subjected to uniform heat flux. The Brinkmanextended Darcy model was employed to study the effect of the boundary viscous frictional drag on hydrodynamic and heat transfer characteristics. An exact expression has been derived for the Nusselt number under the uniform wall heat flux condition. Approximate results were also obtained by exploiting a momentum integral relation and an auxiliary relation implicit in the Brinkmanextended Darcy model. Excellent agreement was confirmed between the approximate and exact solutions even in details of velocity and temperature profiles.

Zusammenfassung

Diese Studie untersucht voll entwickelte „Non-Darcy“-Strömung und Wärmetransport in einem porösen Kanal, der durch zwei parallele Wände gebildet und einem einheitlichen Wärmestrom ausgesetzt wird. Das erweiterte „Brinkman-Darcy-Modell” wurde angewandt, um den Effekt des viskosen Reibungswiderstands der Wände auf die hydrodynamischen Charakteristiken und die Wärmeübertragung zu untersuchen. Ein exakter Ausdruck wurde für die Nusselt-Zahl unter einheitlichem Wandwärmestrom abgeleitet. Annähernde Ergebnisse wurden durch die Auswertung einer Impuls-Integral-Beziehung und einer im erweiterten „Brinkman-Darcy-Modell“ implizierten Hilfsfunktion erhalten. Ausgezeichnete Übereinstimmung zwischen den genäherten und den exakten Lösungen konnten sogar in den Geschwindigkeits- und Temperaturprofilen festgestellt werden.

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Abbreviations

C f :

drag coefficient

f :

velocity profile function

h :

half channel height

K :

permeability

Nu :

Nusselt number

p :

pressure

Re :

Reynolds number

q w :

wall heat flux

T :

temperature

u :

flow velocity

x :

coordinate in the flow direction

y :

coordinate normal to the channel wall

α :

porous media shape parameter

ɛ :

porosity

η :

dimensionless coordinate,y/h

θ :

temperature profile function

μ :

fluid viscosity

ζ :

velocity profile shape factor

ϱ :

fluid density

B :

bulk mean

c :

channel center-line

w :

wall

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Authors and Affiliations

  1. Dept. of Energy and Mechanical Engineering, Shizuoka University, 3-5-1 Johoku, 432, Hamamatsu, Japan

    A. Nakayama Ph. D., H. Koyama Dr. Eng. & F. Kuwahara

Authors
  1. A. Nakayama Ph. D.
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  2. H. Koyama Dr. Eng.
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  3. F. Kuwahara
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Nakayama, A., Koyama, H. & Kuwahara, F. An analysis on forced convection in a channel filled with a Brinkman-Darcy porous medium: Exact and approximate solutions. Wärme- und Stoffübertragung 23, 291–295 (1988). https://doi.org/10.1007/BF01001055

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