This paper analyzes steady-state heat conduction in a triangular-profile fin using a relatively new, exact series method of solution known as the differential transform method. This method converges with only six terms or less for the cases considered. Its advantage is that, unlike many popular methods, it is an exact method and yet it does not require the use of Bessel or other special functions.

Issue Section:
Technical Notes
Keywords:
Computational, Finned Surfaces , Heat Transfer, Temperature, Heat Conduction, heat conduction, boundary-value problems, transforms, convergence of numerical methods
Topics:
Boundary-value problems, Fins, Heat conduction, Temperature, Heat transfer
1.
Zhou, J. K., 1986, Differential Transformation and its Application for Electrical Circuits (in Chinese), Huazhong University Press, Wuhan, P. R. China.
2.
Chen
,
C. K.
, and
Ho
,
S. H.
,
1996
, “
Application of Differential Transformation to Eigenvalue Problems
,”
Appl. Math. Comput.
,
79
, pp.
173
–
188
.
3.
Malik
,
M.
, and
Dang
,
H. H.
,
1998
, “
Vibration of Continuous Systems by Differential Transformation
,”
Appl. Math. Comput.
,
96
, pp.
17
–
26
.
4.
Yu
,
L. T.
, and
Chen
,
C. K.
,
1999
, “
Optimization of Circular Fins with Variable Thermal Parameters
,”
J. Franklin Inst.
,
336B
, pp.
77
–
95
.
5.
Arpaci, V. S., 1966, Conduction Heat Transfer, Addison-Wesley, Reading, MA, p. 150.
6.
Bert
,
C. W.
,
1986
, “
Improved Approximate Methods for Analyzing Steady Heat Conduction
,”
Commun. Appl. Numer. Methods
,
2
, pp.
587
–
592
.
Copyright © 2002
 by ASME
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