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Steady laminar flow past a heated horizontal plate embedded in a saturated porous medium

Stetige laminare Strömung über eine in einem gesättigten porösen Medium eingebettete horizontale Platte

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Abstract

In this paper we study the boundary layer equations for steady laminar flow past a heated horizontal plate embedded in a saturated porous medium by adopting the formulation of Chandrasekhara [3], Kolar and Sastri [7]. The velocity distribution and temperature distribution are determined by using the implicit Crank-Nicolson-Predictor-Corrector method of finite difference scheme [7] and [1]. With the help of a compute the distributions are estimated at both (i+1/2)th and (i+1)th levels and they are presented in tabular form. The curves for these distributions are plotted. We calculate the shear stress and skin friction at the wall and observe that the skin-friction directly depends upon the dimensions of the plate and inversely depends upon the Reynolds numberRe. The heat flux and the Nusselt number are evaluated. Further we observe that the Nusselt number depends upon the length of the porous plate.

Zusammenfassung

Diese Untersuchung befaßt sich mit den Grenzschichtgleichungen für eine stetige laminare Strömung über eine beheizte Platte, die in ein gesättigtes poröses Medium eingebettet ist, mittels des Formalismus von Chandrasekhara [3], Kolar und Sastri [7]. Die Geschwindigkeits- und Temperaturverteilung wurden unter Benutzung der impliziten Crank-Nicolson-Korrekturmethode des Finiten-Elemente-Schemas bestimmt. Die (i+1/2). und die (i+1). Ebene der Verteilungen wurden mit Computer-Hilfe berechnet und in Tabellenform dargestellt. Die Graphen der Temperatur- und Geschwindigkeitsverteilung wurden ausgeplottet. Die Schubspannungen und die Oberflächenreibung an der Wand wurden berechnet und es konnte festgestellt werden, daß die Oberflächenreibung direkt von der Größe der Platte abhängt und umgekehrt proportional der Reynolds-ZahlRe ist. Der Wärmestrom und die Nusselt-Zahl wurden bestimmt. Weiterhin konnte festgestellt werden, daß die Nusselt-Zahl von der Länge der porösen Platte abhängt.

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Abbreviations

C p :

specific heat of the convective fluid

D :

skin friction

k :

permeability of the porous medium

k f :

thermal conductivity of the fluid

k m :

the coefficient of thermal conductivity of the porous medium

k s :

the conductivity of the solid matrix

N(x):

Nusselt number

q(x):

specific heat flux

Re :

local Reynolds number

T :

temperature

T 0 :

temperature of the free stream

T w :

temperature of the plate

u :

velocity in thex-direction

u 0 :

velocity of the free stream

V :

velocity iny-direction

x :

coordinate axis along the plate

y :

coordinate axis normal to the plate

α :

thermal diffusivity

δ :

thickness of the velocity boundary layers in thex direction

Δ :

thickness of the velocity boundary layer in they-direction

ε :

the porosity of the medium

η :

dimensionless variable

ν :

kinematic viscosity of the fluid

ϱ :

density of the fluid

Γ :

shear stress

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Authors and Affiliations

  1. Iranian Research Org. for Science and Technology, Mashad Center, P.O. Box, 91735-139, Mashad, Iran

    R. Javdani Yekta

  2. Department of Mathematics, Shivaji University, 416004, Kolhapur, India

    B. B. Waghmode

Authors
  1. R. Javdani Yekta
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  2. B. B. Waghmode
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Yekta, R.J., Waghmode, B.B. Steady laminar flow past a heated horizontal plate embedded in a saturated porous medium. Wärme- und Stoffübertragung 25, 167–177 (1990). https://doi.org/10.1007/BF01590148

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  • DOI: https://doi.org/10.1007/BF01590148

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