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
References
Cheng, P.: Heat transfer in geothermal systems. Advances in Heat transfer 14 (1978) 1–105
Brinkman, H. C.: A calculation of the viscous force exerted by a flowing fluid on a dense swarm of particles. Appl. Scient. Res. A1 (1948) p. 81
Chan, B. K. C.; Ivey, C. M.; Barry, J. M.: Natural convection in enclosed porous media with rectangular boundaries. J. Heat Transfer 92 (1970) 21–27
Tong, R. W.; Subramanian, E.: A boundary-layer analysis for natural convection in vertical porous enclosures — Use of the Brinkman-extended Darcy model. Int. J. Heat Mass Transfer 28 (1985) 563–571
Lauriat, G.; Prasad, V.: Natural convection in a vertical porous cavity: A numerical study for Brinkman-extepded Darcy formulation, natural convection in porous media (ed. by Prasad, V. and Hussain, N. A.). New York: ASME 1986, pp. 13–22
Sen, A. K.: Natural convection in a shallow porous cavity — the Brinkman model. Int. J. Heat Mass Transfer 30 (1987) 855–868
Vasseur, P.; Robillard, L.: The Brinkman model for boundary layer regime in a rectangular cavity with uniform heat flux from the side. Int. J. Heat Mass Transfer 30 (1987) 717–727
Koh, J. C. Y.; Colony, R.: Analysis of cooling effectiveness for porous material in a coolant passage. J. Heat Transfer 96 (1974) 324–330
Kaviany, M.: Laminar flow through a porous channel bounded by isothermal parallel plates. Int. J. Heat Mass Transfer 28 (1985) 841–858
Nakayama, A.; Koyama, H.: Free convective heat transfer over a nonisothermal body of arbitrary shape embedded in a fluidsaturated porous medium. J. Heat Transfer 109 (1987) 125–130
Cheng, P.: Convective heat transfer in porous layers by integral methods. Letters in Heat Mass Transfer 5 (1987) 243–252
Nakayama, A.; Koyama, H.: Effect of thermal stratification on free convection within a porous medium. J. Thermophysics and Heat Transfer 1 (1987) 282–285
Nakayama, A.; Koyama, H.: An integral method for combined free and forced convection within a fluid saturated porous medium. Appl. Scient. Res. 44 (1987) 333–340
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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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DOI: https://doi.org/10.1007/BF01001055