Abstract
The problem of natural convection flow and heat transfer induced by a vertically oriented cone with constant surface temperature is treated in this paper. The cone is assumed to have transverse wavy configurations. The resulting boundary layer flow is described by two coupled parabolic partial differential equations. These equations are solved numerically using the Keller-box method for a sinusoidal wavy cone. The effect of sinusoidal waves on the local Nusselt number is determined and presented on graphs. The local Nusselt number is found to be lower than that of the corresponding flat cone.
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Abbreviations
- a :
-
amplitude of the wavy surface of the cone
- f :
-
reduced stream function, Eq. (23)
- g :
-
acceleration due to gravity
- Gr:
-
Grashof number based onl
- h :
-
reduced temperature function, Eq. (23)
- k :
-
heat conductivity
- l :
-
half-wavelength, or length scale, of the wavy surface of the cone
- n:
-
unit vector normal to the wavy surface of the cone
- Nu:
-
local Nusselt number
- p :
-
pressure
- Pr:
-
Prandtl number
- q :
-
heat flux
- r :
-
local radius of the flat cone
- T :
-
temperature
- u, v :
-
velocity component inx- andy-directions
- u c :
-
reference velocity
- x, y :
-
rectangular coordinates
- Y :
-
boundary layer variable, Eq. (15)
- ρ:
-
density
- ν :
-
kinematic viscosity
- β:
-
bulk modulus
- θ:
-
dimensionless temperature
- η:
-
pseudo-similarity variable, Eq. (23)
- σ:
-
function associated with the wavy surface of the cone
- φ:
-
cone half angle
- ψ:
-
stream function
- x :
-
differentiation with respect tox
- ∞:
-
condition at infinity in they-direction
- ω:
-
condition at the wall
- -:
-
dimensional variables
- ^:
-
transformed variables, Eq. (9), or boundary layer variables, Eq. (15)
- ':
-
differentiation with respect to η
References
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Pop, I., NA, TY. Natural convection from a wavy cone. Appl. Sci. Res. 54, 125–136 (1995). https://doi.org/10.1007/BF00864369
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DOI: https://doi.org/10.1007/BF00864369