Chapter 6
Fundamentals of Convection
637
Parallel flow of oil between two plates is considered. The velocity and temperature distributions, the
maximum temperature, and the heat flux are to be determined.
Assumptions
1
Steady operating conditions exist.
2
Oil is an incompressible substance with constant
properties.
3
Body forces such as gravity are negligible.
4
The plates are large so that there is no variation
in
z
direction.
Properties
The properties of oil at the average temperature of (40+15)/2 = 27.5
°
C are (Table A13):
k
= 0.145 W/mK
and
μ
= 0.580 kg/ms = 0.580 Ns/m
2
Analysis
(
a
) 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
)
12 m/s
Oil
L
=0.7 mm
T
2
=40
°
C
T
1
=25
°
C
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
0
/
=
∂
∂
x
P
(flow is maintained
by the motion of the upper plate rather than the pressure
gradient), the
x
momentum equation (Eq. 628) reduces to
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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