Abstract
The problem of laminar, natural convection flow over a vertical frustum of a cone is treated in this paper. The thermal boundary condition at the wall include both the constant wall temperature and the constant wall heat flux cases. The governing differential equations are solved by a combination of quasilinearization and finite-difference methods. Numerical solutions are obtained for a range of Prandtl numbers. The solutions are found to approach to the solutions for a full cone if the flow is far downstream or the radius of the cross-section at the leading edge is very small.
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Abbreviations
- f :
-
dependent variable, defined in equation (13) or (25)
- g :
-
dependent variable, defined in equation (13) or (25)
- g e :
-
gravitational acceleration
- h :
-
heat transfer coefficient, or η-grid
- k :
-
heat conductivity, or ξ-grid
- L :
-
characteristic length
- Nu :
-
Nusselt number
- Pr:
-
Prandtl number
- q :
-
heat flux
- r :
-
radial distance from the axis of the cone
- r 0 :
-
radius of the cone
- Re:
-
Reynolds number
- T :
-
temperature
- u, v :
-
velocity components in the x- and y-directions
- x, y :
-
rectangular coordinates
- θ :
-
dimensionless temperature, defined in equation (4)
- β :
-
bulk modulus
- α :
-
cone angle
- ν :
-
dynamic viscosity
- ψ :
-
stream function
- ξ, η :
-
independent variables, defined in equation (13) or equation (25)
- w :
-
condition at the surface
- ∞:
-
condition far from the surface
- r :
-
reference condition
- o :
-
wall condition
References
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Na, T.Y., Chiou, J.P. Laminar natural convection over a frustum of a cone. Appl. Sci. Res. 35, 409–421 (1979). https://doi.org/10.1007/BF00420389
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DOI: https://doi.org/10.1007/BF00420389