Civil Engineering Reference
In-Depth Information
Note that the cross-hatched edges are perfectly insulated and it is assumed that
the convection coefficients on all surfaces is the same constant.
Solve Example 7.5 using the two-element model in Figure 7.11b. How do the
results compare to those of the four-element model?
7.21
The rectangular element shown in Figure P7.22 contains a line source of constant
strength
Q
∗
located at the element centroid. Determine
7.22
f
(
e
Q
}
.
{
4
3
(2, 4)
(4, 4)
Q
*
1
2
y
(2, 2)
(4, 2)
x
Figure P7.22
f
(
e
Q
}
Determine the forcing function components of
for the axisymmetric
element of Example 7.10 for the case of uniform internal heat generation
Q
.
{
7.23
A steel pipe (outside diameter of 60 mm and wall thickness of 5 mm) contains
flowing water at constant temperature
80
◦
C
, as shown in Figure P7.24. The
convection coefficient between the water and pipe is 2000 W/m
2
-
◦
C. The pipe
is surrounded by air at 20
◦
C, and the convection at the outer pipe surface is
20 W/m
2
-
◦
C. The thermal conductivity of the pipe material is 60 W/m-
◦
C.
Determine the stiffness matrices and nodal forcing functions for the two
axisymmetric elements shown.
7.24
Flow
1
2
2.5 mm
2.5 mm
z
r
Figure P7.24
