Why does the convection coefficient decay in the laminar region?
Why does it increase
significantly with transition to turbulence, despite the increase in the boundary layer
thickness?
Why does the convection coefficient decay in the turbulent region?

Boundary Layer
Equations
The Boundary Layer Equations
•
Consider concurrent velocity and thermal boundary layer development for
steady,
two-dimensional, incompressible flow
with
constant fluid properties
and
negligible body forces
.
(
29
,
,
p
c
k
μ
•
Apply
conservation of mass
,
Newton’s 2
nd
Law of Motion
and
conservation of energy
to a differential control volume and invoke the
boundary layer approximations
.
Velocity Boundary Layer:
Thermal Boundary Layer:

Boundary Layer Equations (cont.)
•
Conservation of Mass:
In the context of flow through a differential control volume, what is the physical
significance of the foregoing terms, if each is multiplied by the mass density of
the fluid?
•
Newton’s Second Law of Motion:
What is the physical significance of each term in the foregoing equation?

Boundary Layer Equations
(cont.)
What is the physical significance of each term in the foregoing equation?
What is the second term on the right-hand side called and under what conditions
may it be neglected?
•
Conservation of Energy:

Similarity Considerations
Boundary Layer Similarity
•
As applied to the boundary layers, the principle of
similarity
is based on
determining
similarity parameters
that facilitate application of results obtained
for a surface experiencing one set of conditions to geometrically similar surfaces
experiencing different conditions.
(Recall how introduction of the similarity
parameters
Bi
and
Fo
permitted generalization of results for transient, one-
dimensional condition).
•
Dependent boundary layer variables
of interest are:
•
For a prescribed geometry, the corresponding
independent variables
are:
Geometrical
:
Size (
L
),
Location (
x,y
)
Hydrodynamic
:
Velocity (
V
)
Fluid Properties:

Similarity
Considerations (cont.)
•
Key similarity parameters may be inferred by non-dimensionalizing the momentum
and energy equations.
•
Recast the boundary layer equations by introducing dimensionless forms of the
independent and dependent variables.