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Inertia effects on mixed convection for vertical plates with variable wall temperature in saturated porous media

Der Einfluß von Trägheitseffekten auf die Mischkonvektion an vertikalen Platten veränderlicher Wandtemperatur in vollständig getränkten porösen Medien

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Abstract

Mixed convection in a porous medium from a vertical plate with variable wall temperature is investigated. The entire mixed convection regime is divided into two regions and two sets of transformations are used. The first region is for the forced convection dominated regime (FCDR) and the other one is for the natural convection dominated regime (NCDR). The dimensionless parameterK′ U ∞/ν is found to characterize the effect of inertia resistance in the first region and the dimensionless parameter (K′ U ∞/ν (Ra x /Pe x ) is found to characterize the effect of inertia resistance in the second region. The solution of the first region is carried out from ξ f =0.0 to ξ f =1.0, and the solution of the second region is carried out from ξ n =0.0 to ξ n =1.0. Velocity and temperature profiles are calculated at different values of the governing parameters. Local Nusslet number variation for the entire mixed convection regime is also calculated and presented.

Zusammenfassung

Es wird die Mischkonvektion an einer, in ein poröses Medium eingebetteten vertikalen Platte veränderlicher Wandtemperatur untersucht. Das gesamte Mischkonvektionsgebiet ist dabei in zwei Bereiche unterteilt und es kommen zwei Transformationsätze zur Anwendung. Der erste Bereich umfaßt das durch Zwangskonvektion regierte Gebiet (FCDR), der andere das durch freie Konvektion dominierte (NCDR). Nach Befund charakterisiert der dimensionslose ParameterK′ U ∞/ν den Einfluß des Trägheitswiderstandes im ersten Bereich und der dimensionslose Parameter (K′ U ∞)/ν · (Ra x /Pe x ) jenes im zweiten. Die Lösung im ersten Bereich wird für ξ f =0,0 bis 1,0 ermittelt und die Lösung im zweiten für ξ n =0,0 bis 1,0. Geschwindigkeits- und Temperaturprofile wurden für verschiedene Werte der Einflußparameter errechnet. Der Verlauf der lokalen Nusselt-Zahl ist für das gesamte Mischkonvektionsgebiet dargestellt.

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Abbreviations

f,F :

dimensionless stream function

G :

parameter of inertia effect on natural convection dominated regime, (K′ u ∞/ν)Ra x /Pe x

h(x):

local heat transfer coefficient

\(\bar h\) :

average heat transfer coefficient, (1/L) ∫ L0 h(x) dx

k :

thermal conductivity

K :

permeability coefficient of the porous medium

K′:

coefficient of Forchheimer's equation

L :

length of the plate

Nu x :

local Nusselt number,hx/k

\(\bar Nu\) :

average Nusselt number,\(\bar hL/k\)

Pe x :

local Peclet number,u ∞ x/α

q w :

local surface heat flux

R :

parameter of inertial effect on forced convection dominated regime,K′ u ∞/ν

Ra x :

modified local Rayleigh number,gβ[T w (x)−T ∞]Kx/(vα)

T :

temperature

T ∞ :

free stream temperature

T w :

wall temperature

u, v :

velocity components inx- andy-direction

u ∞ :

free stream velocity

x,y :

axial and normal coordinates

α :

effective thermal diffusivity of saturated porous medium

β :

volumetric coefficient of thermal expansion

δ :

boundary layer thickness

η f ,η n :

pseudo-similarity variables

φ, ϕ :

dimensionless temperatures

μ :

dynamic viscosity

v :

kinematic viscosity

ξ f :

nonsimilarity parameter for the forced convection dominated regime

ξ n :

nonsimilarity parameter for the free convection dominated regime

ρ :

fluid density

τ w :

local wall shear stress

ψ :

stream function

f :

forced convection dominated condition

n :

natural convection dominated condition

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Authors and Affiliations

  1. Mechanical Engineering Department, Jordan University of Science and Technology, P.O. Box, 3030, Irbid, Jordan

    Z. H. Kodah

  2. Mechanical Engineering Department, The University of Jordan, Amman, Jordan

    H. M. Duwairi

Authors
  1. Z. H. Kodah
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  2. H. M. Duwairi
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Kodah, Z.H., Duwairi, H.M. Inertia effects on mixed convection for vertical plates with variable wall temperature in saturated porous media. Heat and Mass Transfer 31, 333–338 (1996). https://doi.org/10.1007/BF02184047

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