Civil Engineering Reference
In-Depth Information
Therefore,
a
0
=
1
a
1
=
4
2
−
3
1
−
3
a
2
=
3
Using the temperature results of Example 7.1 for the aluminum element, we have
1
−
2
+
2
4
2
1
=
T
1
=
95
.
14
2
=
T
2
=
90
.
14
3
=
T
3
=
85
.
14
a
2
=
2(95
.
14)
−
4(90
.
14)
+
2(85
.
14)
=
0
For element 2, representing the copper portion of the bar, the same result is obtained.
7.3 ONE-DIMENSIONAL CONDUCTION
WITH CONVECTION
One-dimensional heat conduction, in which no heat flows from the surface of the
body under consideration (as in Figure 5.8), is not commonly encountered. A
more practical situation exists when the body is surrounded by a fluid medium
and heat flow occurs from the surface to the fluid via
convection
. Figure 7.2a
shows a solid body, which we use to develop a one-dimensional model of heat
transfer including both conduction and convection. Note that the representation
is the same as in Figure 5.8 with the very important exception that the assump-
tion of an insulated surface is removed. Instead, the body is assumed to be sur-
rounded by a fluid medium to which heat is transferred by convection. If the fluid
is in motion as a result of some external influence (a fan or pump, for example),
the convective heat transfer is referred to as
forced convection
. On the other
hand, if motion of the fluid exists only as a result of the heat transfer taking place,
we have
natural convection
. Figure 7.2b depicts a control volume of differential
length, which is assumed to have a constant cross-sectional area and uniform
T
Convection
q
h
q
in
Q
U
d
q
x
d
x
q
x
q
x
d
x
q
out
d
x
(a)
(b)
Figure 7.2
One-dimensional conduction with surface convection.
(a) General model. (b) Differential element as a control volume.
