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Laminar natural convection over a slender vertical frustrum of a cone with constant wall heat flux

Laminare natürliche Konvektion über einem dünnen, senkrechten Kegelstumpf mit konstantem Wand wär mestrom

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Abstract

The problem of laminar natural convection flow over a slender frustrum of a cone with constant wall heat flux is treated in this paper. The governing differential equations are solved by a combination of quasilinearization and finite-difference methods. Numerical solutions are obtained for Prandtl numbers from 0.1 to 100 for a range of values of transverse curvature parameter. It is found that the effect of transverse curvature is of great significance in such flows.

Zusammenfassung

In dieser Arbeit wird das Problem der laminaren, natürlichen Konvektionsströmung öber einem dünnen Kegelstumpf mit konstantem Wandwärmestrom behandelt. Die maßgeblichen Differentialgleichungen werden mit Hilfe einer Kombination von Quasilinearisierung und Differenzenverfahren gelöst. Numerische Lösungen werden für die Prandtl ' sehen Zahlen zwischen 0. l und 100 innerhalb eines Bereiches von Querkrüm mungswerten erhalten. Es wird gezeigt, daß der Einfluß der Querkrümmung in solchen Strömungen von großer Bedeutung ist.

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Abbreviations

A,B,C:

constants in the transformation, defined in Eq.(14)

f:

dependent variable, defined in Eq. (7)

g:

dependent variable, defined in Eq. (7)

ge :

gravitational acceleration

k:

heat conductivity

kn :

ξ-grid

L:

characteristic length

Nu:

Nusselt number

Pr:

Prandtl number

qw :

wall heat flux

r:

radial distance from the axis of the cone

RTVC :

transverse curvature ratio, defined in Eq.(28)

Re:

Reynolds number

T:

temperature

u,v:

velocity components in the x- and y-directions, respectively

x,y:

rectangular coordinates

θ:

dimensionless temperature, defined in Eq.(4)

β:

bulk modulus

α:

cone angle

ν:

dynamic viscosity

Ψ:

stream function

ξ, η:

transformed independent variables, defined in Eq. (7)

γ:

transverse curvature parameter

References

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Authors and Affiliations

  1. University of Michigan-Dearborn, 48128, Dearborn, Michigan, USA

    T. Y. Na

  2. University of Detroit, 48221, Detroit, Michigan, USA

    J. P. Chiou

Authors
  1. T. Y. Na
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  2. J. P. Chiou
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Na, T.Y., Chiou, J.P. Laminar natural convection over a slender vertical frustrum of a cone with constant wall heat flux. Wärme- und Stoffübertragung 13, 73–78 (1980). https://doi.org/10.1007/BF00997635

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  • DOI: https://doi.org/10.1007/BF00997635

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