PROBLEM 4S.3
KNOWN:
Structural member with known thermal conductivity subjected to a temperature difference.
FIND:
(a) Temperature at a prescribed point P, (b) Heat transfer per unit length of the strut, (c) Sketch
the 25, 50 and 75
°
C isotherms, and (d) Same analysis on the shape but with adiabaticisothermal
oundary conditions reversed.
b
SCHEMATIC:
ASSUMPTIONS:
(1) Twodimensional conduction, (2) Steadystate conditions, (3) Constant properties.
ANALYSIS:
(a) When constructing the flux plot, note that the line of symmetry which passes through
the point P is an isotherm as shown above.
It follows that
() ( )
()
12
T P
T
T
2
100 0
C 2
50 C
=+
=
+
=
D
D
.
<
(b) The flux plot on the symmetrical section is now constructed to obtain the shape factor from which the
eat rate is determined.
That is, from Equation 4S.6 and 4S.7,
h
qk
STT a
n
dSMN
=−
=
A
.
(1,2)
F
rom the plot of the symmetrical section,
o
S
4.2 4
1.05
==
AA
.
For the full section of the strut,
o
M
M
4.2
but N = 2N
o
= 8.
Hence,
o
S
S
2
0.53
A
and with
qq
′ =
A
, giving
q
75W m K 0.53 100 0
C
3975W m
′
=⋅
×
−
=
D
A
.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '10
 LEE,J.S.
 Heat Transfer, heat rate, flux plot

Click to edit the document details