Summary
The paper deals with a similarity analysis of free convection about a wedge and a cone which are subjected to mixed thermal boundary conditions. The governing equations and the boundary conditions are reduced to a boundary value problem involving a non-negative parameterm which assumes the values 0,1 and ∞ for the cases of prescribed temperature, prescribed heat flux and radiation boundary condition. A numerical solution has been computed for the case of radiation boundary condition. The results for constant temperature and constant heat flux available in literature are deduced with the aid of a simple transformation. Critical cases have been found for which the solution is same for all values ofm.
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Abbreviations
- a 0,a 1,a 2 :
-
coefficients defined in Eq. (5)
- A :
-
transition parameter used in Eq. (16)
- c :
-
coefficient ofC in Eq. (7)
- C :
-
function ofx defined in Eq. (7)
- f :
-
dimensionless stream function
- g :
-
acceleration due to gravity
- g 1 :
-
=g cos γ
- G :
-
function ofx defined in Eq. (7)
- m :
-
constant defined in Eq. (12)
- n :
-
= 0 for wedge = 1 for cone
- PHF:
-
prescribed heat flux
- Pr:
-
Prandtl number
- PT:
-
prescribed temperature
- r :
-
=x sin γ
- RBC:
-
radiation boundary condition
- T :
-
temperature
- T e :
-
ambient temperature
- u :
-
velocity component inx-direction
- v :
-
velocity component iny-direction
- x :
-
distance from the vertex measured along the surface
- y :
-
distance normal to the surface
- β:
-
coefficient of thermal expansion
- η:
-
dimensionless similarity variable
- θ:
-
dimensionless temperature
- λ:
-
exponent inC in Eq. (7)
- ν:
-
kinematic viscosity
- γ:
-
semivertical angle
- ψ:
-
stream function
References
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Ramanaiah, G., Malarvizhi, G. Free convection about a wedge and a cone subjected to mixed thermal boundary conditions. Acta Mechanica 93, 119–123 (1992). https://doi.org/10.1007/BF01182577
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DOI: https://doi.org/10.1007/BF01182577