Chapter 6
Fundamentals of Convection
643
The flow of fluid between two large parallel plates is considered. The relations for the maximum
temperature of fluid, the location where it occurs, and heat flux at the upper plate are to be obtained.
Assumptions
1
Steady operating conditions exist.
2
The fluid has constant properties.
3
Body forces such
as gravity are negligible.
Analysis
We take the
xaxis
to be the flow direction, and
y
to be the normal direction.
This is parallel flow
between two plates, and thus
v
= 0. Then the continuity equation reduces to
Continuity
:
0
=
∂
∂
+
∂
∂
y
v
x
u
⎯→
0
=
∂
∂
x
u
⎯→
u = u
(
y
)
Therefore, the
x
component of velocity does not change
in the flow direction (i.e., the velocity profile remains
unchanged). Noting that
u = u
(
y
),
v =
0, and
(flow is maintained by the motion of the
upper plate rather than the pressure gradient), the
x

momentum equation reduces to
0
/
=
∂
∂
x
P
xmomentum
:
x
P
y
u
y
u
v
x
u
u
∂
∂
−
∂
∂
μ
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This note was uploaded on 01/22/2012 for the course PHY 4803 taught by Professor Dr.danielarenas during the Fall '10 term at UNF.
 Fall '10
 Dr.DanielArenas
 Thermodynamics, Convection, Mass, Heat

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