Civil Engineering Reference
In-Depth Information
at constant mass flow rate
m
.
The convection coefficient between the stainless
steel pipe wall and the polymer is
h
. Polymer specific heat
c
is also taken to be
constant. Is this a one-dimensional problem? How would you solve this problem
using the finite element method?
An office heater (often incorrectly called a
radiator,
since the heat transfer mode
is convection) is composed of a central pipe containing heated water at constant
temperature, as depicted in Figure P7.18. Several two-dimensional heat transfer
fins are attached to the pipe as shown. The fins are equally spaced along the
length of the pipe. Each fin has thickness of 0.125 in. and overall dimensions
4in
.
×
4in
.
Convection from the edges of the fins can be neglected. Consider the
pipe as a point source
Q
∗
=
600
Btu/hr-ft
2
and determine the net heat transfer to
the ambient air at 20
◦
C, if the convection coefficient is
h
=
300
Btu/(hr-ft
2
-
◦
F).
Use four finite elements with linear interpolation functions (consider symmetry
conditions here).
7.18
Figure P7.18
One who seriously considers the symmetry conditions of Problem 7.18 would
realize that quarter symmetry exists and four elements represent 16 elements in
the full problem domain. What are the boundary conditions for the symmetric
model?
7.19
The rectangular fins shown in Figure P7.20 are mounted on a centrally located
pipe carrying hot water. Temperature at the contact surface between fin and
pipe is a constant
T
1
. For each case depicted, determine the applicable symmetry
conditions and the boundary conditions applicable to a finite element model.
7.20
T
1
T
a
T
a
T
a
T
a
T
a
T
2
T
2
(b)
T
a
T
1
(a)
(c)
(d)
Figure P7.20
