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Wärme - und Stoffübertragung

, Volume 23, Issue 4, pp 213–217 | Cite as

Free convection flow over an uniform-heat-flux surface with temperature-dependent viscosity

  • J. -Y. Jang
  • C. -N. Lin
Article

Abstract

The role of temperature-dependent viscosity is studied in laminar free convection flow adjacent to a vertical surface with uniform heat flux. The resulting non-similar equations are solved by using a suitable variable transformation and employing an implicit finite difference method. It is shown that the constant viscosity results evaluated at the ambient fluid temperature underestimate the Nusselt number and overestimate the drag coefficient. The heat transfer predictions for large values of the viscosity parameter may be two times the constant viscosity parameter prediction. The present analysis is in good agreement with the corresponding correlation of previous experimental investigation.

Keywords

Heat Flux Nusselt Number Finite Difference Method Constant Viscosity Ambient Fluid 
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

Cd,x/Cd·L

local drag coefficient average drag coefficient

Cp

specific heat of fluid

f

dimensionless stream function

Grx*

local flux Grashof number

g

acceleration due to gravity

K*

viscosity parameter

k

thermal conductivity of fluid

L

length of surface in flow direction

Nux/NuL

local Nusselt number

P

average Nusselt number

Pr

Prandtl number

q″

heat flux at the wall

T

temperature

Uc

convection velocity

u, v

streamwise and transverse velocity component

x, y

streamwise and transverse coordinate

Greek symbols

β

coefficient of thermal expansion

η

dimensionless transverse coordinate

υ, v

absolute and kinematic viscosity of fluid

v*

viscosity ratio parameter

ξ

dimensionless streamwise coordinate

ϱ

density

φ

dimensionless temperature

ψ

stream function

t

wall shear stress

Subscripts

F

referred to results from Fujii et al. [8]

P

referred to results from the present analysis

w

referred to condition at wall temperature

referred to condition at ambient temperature

Strömung bei freier Konvektion über eine Oberfläche mit einheitlichem Wärmestrom und mit temperaturabhängiger Viskosität

Zusammenfassung

Die Rolle der Temperaturabhängigkeit der Viskosität wird in laminarer Strömung mit freier Konvektion, angrenzend an eine senkrechte Oberfläche mit einheitlichem Wärmestrom, untersucht. Die restlichen Gleichungen werden durch Anwendung einer geeigneten Variablentransformation und einer impliziten Finiten-Differenzen-Methoden gelöst. Es wird gezeigt, daß die Ergebnisse bei konstanter Viskosität, berechnet mit der Temperatur der umgebenden Flüssigkeit, die Nusseltzahl unterschreiten und den Widerstandsbeiwert überschreiten. Die Nusseltzahl bei Wärmeübertragung mit großen Viskositätsparametern ist ungefähr zweimal höher als die bei konstanter Viskosität. Die vorliegende Untersuchung stimmt gut mit vorhergehenden experimentellen Ergebnissen überein.

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References

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Copyright information

© Springer-Verlag 1988

Authors and Affiliations

  • J. -Y. Jang
    • 1
  • C. -N. Lin
    • 1
  1. 1.Department of Mechanical EngineeringNational Cheng-Kung UniversityTainanTaiwan 70101 ROC

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