Wärme - und Stoffübertragung

, Volume 20, Issue 1, pp 33–37 | Cite as

Non-darcy natural convection on a vertical cylinder in a saturated porous medium

  • M. Kumari
  • Ioan Pop
  • G. Nath
Article

Abstract

The steady free convection boundary layer flow of non-Darcy fluid along an isothermal vertical cylinder embedded in a saturated porous medium using the Ergun model has been studied. The partial differential equations governing the flow have been solved numerically using an implicit finite-difference scheme developed by Keller. It is found that the heat transfer is strongly affected by the modified Grashof number which characterizes the non-Darcy fluid, and the curvature parameter. Also the heat transfer is found to be more than that of the flat plate.

Keywords

Heat Transfer Free Convection Convection Boundary Layer Boundary Layer Flow Saturated Porous Medium 

Nomenclature

f

transformed stream function

g

acceleration due to gravity

Gr*

modified Grashof number

km

thermal conductivity of the porous medium

K

permeability of the saturated porous medium

K*

inertial coefficient in the Ergun model

L

length of the cylinder

p

static pressure

q

local heat transfer rate per unit area

Q

total surface heat transfer rate

r

radi coordinate

r0

radius of cylinder

Rax

modified local Rayleigh number

T

temperature

u, v

velocity components in thex- andr-directions, respectively

x

axial coordinate

Greek Symbols

α

equivalent thermal diffusivity

β

coefficient of thermal expansion

η

pseudo-similarity variable

θ

dimensionless temperature

μ

viscosity of convective fluid

v

kinematic viscosity of convective fluid

ϱ

density of convective fluid

ξ

stretched streamwise coordinate

ξL

constant

ψ

streamfunction

Subscripts

r, x

denote derivatives with respect tor andx, respectively

w

refers to wall conditions

refers to free stream conditions

Superscript

'

denotes derivatives with respect toη

Nicht-Darcysche freie Konvektion an einem vertikalen Zylinder in einem gesättigten, porösen Medium

Zusammenfassung

Es wird die Grenzschichtströmung bei stationärer, freier Konvektion eines nicht-Darcyschen Fluids entlang eines isothermen, vertikalen Zylinders, der in ein gesättigtes, poröses Medium eingelagert ist, mit dem Ergun-Modell behandelt. Die partiellen Differentialgleichungen, welche die Strömung beschreiben, wurden numerisch unter Verwendung eines von Keller entwickelten, impliziten Finiten-Differenzen-Schemas gelöst. Es zeigte sich, daß der Wärmeübergang stark von der modifizierten Grashof-Zahl beeinflußt wird, welche das nicht-Darcysche Fluid und den Krümmungsparameter charakterisiert. Der Wärmeübergang am Zylinder ist höher als an einer ebenen Platte.

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References

  1. 1.
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  2. 2.
    Kumari, M.; Pop, I.; Nath, G.: Finite-difference and improved perturbation solutions for free convection on a vertical cylinder embedded in a porous medium. To be publishedGoogle Scholar
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Copyright information

© Springer-Verlag 1986

Authors and Affiliations

  • M. Kumari
    • 1
  • Ioan Pop
    • 2
  • G. Nath
    • 3
  1. 1.Department of Applied MathematicsIndian Institute of ScienceBangaloreIndia
  2. 2.Faculty of MathematicsUniversity of ClujClujRomania
  3. 3.Department of Applied MathematicsIndian Institute of ScienceBangaloreIndia

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