Abstract
This paper considers the steady-state free convection flow arising from an infinitely long horizontal line source of heat embedded in the base of a vertical adiabatic surface when the ambient fluid is a non-Newtonian fluid for moderately large values of the generalized Grashof numbers by the method of matched asymptotic expansions. In particular, the second-order corrections to account for the non-boundary layer effects have been predicted. A family of numerical solutions for the power-law fluid behavior indexn ranging from 0.4 to 2.0 and for the Prandtl numberPr=10 and 100 are reported.
Zusammenfassung
Diese Arbeit bezieht sich auf die stationäre Auftriebsströmung über einer langen, horizontalen Linienwärmequelle, die in das untere Ende einer senkrechten, adiabaten Fläche eingebettet ist, wobei für das umgebende Fluid nicht-Newtonsches Verhalten unterstellt wird. Unter Voraussetzung mäßig hoher Werte für die verallgemeinerten Grashof-Zahlen kommt die Methode der angepaßten asymptotischen Entwicklung zur Anwendung. Insbesondere wird belegt, daß Korrekturen zweiter Ordnung zur Berücksichtigung von Nichtgrenzschichteffekten erforderlich sind. Die mitgeteilten Ergebnisse umfassen eine Gruppe von numerischen Lösungen im Bereich 0,4 bis 2,0 für den Exponentenn des Potenzansatzes, mit dem das nicht-Newtonsche Fluidverhalten erfaßt wird und jeweils für die Prandtl-ZahlenPr=10 und 100.
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Abbreviations
- C f :
-
skin friction coefficient
- g :
-
acceleration due to gravity
- Gr :
-
generalized Grashof number
- Gr x :
-
generalized local Grashof number
- J :
-
second invariant of the strain-rate tensor
- K :
-
consistency index
- L :
-
reference length
- n :
-
index of power-law viscosity model
- p :
-
pressure
- Pr :
-
generalized Prandtl number
- I :
-
non-dimensional heat input by the thermal source
- r :
-
radial distance
- T :
-
temperature
- T r :
-
reference temperature
- u, v :
-
velocity components along (x, y)-axis
- x, y :
-
coordinates along and normal to the plate
- y :
-
inner variable
- β :
-
thermal expansion coefficient
- η :
-
similarity variable
- θ :
-
non-dimensional temperature
- ϱ :
-
density
- τ :
-
shear stress
- ϕ :
-
angular distance
- ψ :
-
stream function
- -:
-
dimensionless variables
- ′:
-
differentiation with respect toη
- a :
-
adiabatic
- w :
-
wall condition
- ∞:
-
ambient condition
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Gorla, R.S.R., Pop, I. & Lee, J.K. Convective wall plume in power-law fluid: Second-order correction for the adiabatic wall. Wärme - und Stoffübertragung 27, 473–479 (1992). https://doi.org/10.1007/BF01590048
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DOI: https://doi.org/10.1007/BF01590048