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Laminar natural convection over a slender vertical frustum of a cone

Laminare natürliche Konvektion an einem dünnen, senkrechten Kegelstumpf

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Abstract

The problem of laminar, natural convection flow over a slender frustum of a cone is treated in this paper. The governing differential equations are solved by a combination of quasi-linearization and finite-difference methods. Numerical solutions are obtained for Pr=0.7 and for a range of values of the transverse curvature parameter. It is shown that the effect of transverse curvature is of great significance in such flows.

Zusammenfassung

In diesem Bericht ist das Problem der laminaren natürlichen Konvektionsströmung an einem dünnen Kegelstumpf behandelt. Die maßgebliche Differentialgleichung ist durch eine Verbindung von Quasilinearisation und Differenzenverfahren gelöst. Eine numerische Lösung für Pr=0.7 wird für verschiedene Werte eines Krümmungsparameters angegeben. Es ist gezeigt, daß in solchen Strömungen dieser Krümmungsparameter eine große Bedeutung besitzt.

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Abbreviations

f:

dependent variable, defined in Eq. (7)

g:

dependent variable, defined in Eq. (7)

ge :

gravitational acceleration

h:

heat transfer coefficient, or η-grid

k:

heat conductivity, or ξ-grid

L:

characteristic length

Nu:

Nusselt number

Pr:

Prandtl number

r:

radial distance from the axis of the cone

R:

transverse curvature effect ratio, defined in Eq. (23)

Re:

Reynold number

T:

temperature

u, v:

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

x, y:

rectangular coordinates

θ:

dimensionless temperature, definedinEq. (4)

β:

bulk modulus

α:

cone angle

ν:

dynamic viscosity

ψ:

stream function

ξ, η:

independent variable, defined in (7)

γ:

transverse curvature parameter

Literature

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Authors and Affiliations

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

    T. Y. Na

  2. University of Detroit, 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 frustum of a cone. Warme- und Stoffubertragung 12, 83–87 (1979). https://doi.org/10.1007/BF01002323

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  • DOI: https://doi.org/10.1007/BF01002323

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