Wärme - und Stoffübertragung

, Volume 23, Issue 5, pp 267–273 | Cite as

Non-darcy double-diffusive mixed convection from heated vertical and horizontal plates in saturated porous media

  • M. Kumari
  • H. S. Takhar
  • G. Nath
Article
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Abstract

The non-darcy mixed convection flows from heated vertical and horizontal plates in saturated porous media have been considered using boundary layer approximations. The flows are considered to be driven by multiple buoyancy forces. The similarity solutions for both vertical and horizontal plates have been obtained. The governing equations have been solved numerically using a shooting method. The heat transfer, mass transfer and skin friction are reduced due to inertial forces. Also, they increase with the buoyancy parameter for aiding flow and decrease for the opposing flow. For aiding flow, the heat and mass transfer coefficients are found to approach asymptotically the forced or free convection values as the buoyancy parameter approaches zero or infinity.

Keywords

Heat Transfer Skin Friction Mass Transfer Coefficient Free Convection Buoyancy Force 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Nomenclature

A

constant

C

concentration

Cf

skin friction coefficient

D

binary diffusion coefficient

f

dimensionless stream function

f', G, H

dimensionless velocity, temperature and concentration, respectively

g

acceleration due to gravity

f″w,G′w,H′w

surface skin friction, heat transfer and mass transfer parameters, respectively

GrL

Grashof number

k

thermal conductivity

K

permeability of the porous medium

K*,Le

inertial coefficient and Lewis number, respectively

Nu

Nusselt number

Pr

Prandtl number

Ra

Rayleigh number

ReL,Rex

Reynolds numbers defined with respect toL andx, respectively

Sc, Sh

Schmidt number and Sherwood nufnber, respectively

T

temperature

u, ν

velocity components alongx andy directions, respectively

x, y

distances along and perpendicular to the surface

Greek symbols

α

equivalent thermal diffusivity

β

volumetric coefficient of thermal expansion

β*

volumetric coeffcient of expansion with mass fraction

η

similarity variable

λ1

parameter characterizing the inertial effect

λ2

buoyancy parameter due to thermal diffusion

λ3

ratio of mass diffusion and thermal; diffusion parameters

ϱ, μ, ν

density, dynamic viscosity and kinerfiatic viscosity, respectively

ψ

dimensional stream function

Superscript

l

derivatives with respect toη

Subscripts

w, ∞

conditions at the wall and in the free stream, respectively

x, y

partial derivatives with respect tox andy, respectively

Non-darcy doppelt diffuse Mischkonvektion an beheizten senkrechten und horizontalen Platten in gesättigten porösen Medien

Zusammenfassung

Es wurde “non-darcy” Mischkonvektion an beheizten vertikalen und horizontalen Platten in gesättigten porösen Medien unter Benutzung von angenä herten Grenzschichten betrachtet. Es wurde angenommen, daß die Strömung durch Auftriebskräfte hervorgerufen werden. Für vertikale und horizontale Platten wurden einanderä hnliche Lösungen erzielt. Die beschreibenden Gleichungen wurden numerisch mit einer Shooting-Methode gelöst. Die Wä rme- und Stoffübertragung und die Oberflä chenreibung wurden infolge von Trä gheitskrä ften reduziert. Mit den Auftriebsparametern steigen sie für Gleichstrom an und fallen für Gegenstrom ab. Es wurde festgestellt, daß sich die Wärme- und Stoffübertragungskoeffizienten für Gleichstrom asymptotisch den Werten der erzwungenen oder freien Konvektion annä hern, wenn der Auftriebsparameter gegen null oder unendlich geht.

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Copyright information

© Springer-Verlag 1988

Authors and Affiliations

  • M. Kumari
    • 1
  • H. S. Takhar
    • 1
  • G. Nath
    • 1
  1. 1.Department of Applied MathematicsIndian Institute of ScienceBangaloreIndia

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