9.
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 parameter
m 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 of
m.Notation
a
0,
a
1,
a
2
coefficients defined in Eq. (5)
-
A
transition parameter used in Eq. (16)
-
c
coefficient of
C in Eq. (7)
-
C
function of
x defined in Eq. (7)
-
f
dimensionless stream function
-
g
acceleration due to gravity
-
g
1
=
g cos
-
G
function of
x 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
- RBC
radiation boundary condition
-
T
temperature
-
T
e
ambient temperature
-
u
velocity component in
x-direction
-
v
velocity component in
y-direction
-
x
distance from the vertex measured along the surface
-
y
distance normal to the surface
-
coefficient of thermal expansion
-
dimensionless similarity variable
-
dimensionless temperature
-
exponent in
C in Eq. (7)
-
kinematic viscosity
-
semivertical angle
-
stream function
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