A variational problem arising in the design of cooling fins
Author:
Earl R. Barnes
Journal:
Quart. Appl. Math. 34 (1976), 1-17
MSC:
Primary 80.49
DOI:
https://doi.org/10.1090/qam/449206
MathSciNet review:
449206
Full-text PDF Free Access
Abstract |
References |
Similar Articles |
Additional Information
Abstract: The efficiency of a cooling fin of given weight is measured by the amount of heat dissipated per unit time by the fin. It is known that the efficiency of a given fin can be altered by changing the shape of the fin. In this paper we determine the shape of the most efficient fin of given weight and length, and thickness $\le H$ and $\ge h$.
E. Schmidt., Die Wärmeübertragung durch Rippen, Zut. d. Ver. Deutch Ing. 70, 885–890 (1926)
- R. J. Duffin, A variational problem relating to cooling fins, J. Math. Mech. 8 (1959), 47–56. MR 0103711, DOI https://doi.org/10.1512/iumj.1959.8.58003
- Jean Céa and Kazimierz Malanowski, An example of a max-min problem in partial differential equations, SIAM J. Control 8 (1970), 305–316. MR 0274915
R. J. Duffin and D. K. McLain, Optimum shape of a cooling fin on a convex cylinder, J. Math. Mech. 17, 769–784 (1968)
J. E. Wilkins, Jr. Minimum mass thin fins and constant temperature gradients, SIAM J. 10, 62–73 (1962)
- Chen-Ya Liu, A variational problem with applications to cooling fins, J. Soc. Indust. Appl. Math. 10 (1962), 19–29. MR 137486
- Chen-Ya Liu, A variational problem relating to cooling fins with heat generation, Quart. Appl. Math. 19 (1961), 245–251. MR 135850, DOI https://doi.org/10.1090/S0033-569X-1961-0135850-9
M. Jacob, Heat transfer, John Wiley and Sons, Inc., New York, 1949, pp. 219–243
S. Saks, Theory of the integral, Hafner, New York, 1937
E. Schmidt., Die Wärmeübertragung durch Rippen, Zut. d. Ver. Deutch Ing. 70, 885–890 (1926)
R. J. Duffin, A variational problem, relating to cooling fins, J. Math. Mech. 8, 47–56 (1959)
J. Cea and K. Malanowski, An example of a max-min problem in partial differential equations, SIAM J. Control 8, 305–316 (1970)
R. J. Duffin and D. K. McLain, Optimum shape of a cooling fin on a convex cylinder, J. Math. Mech. 17, 769–784 (1968)
J. E. Wilkins, Jr. Minimum mass thin fins and constant temperature gradients, SIAM J. 10, 62–73 (1962)
C. Y. Lin, A variational problem with applications to cooling fins, SIAM J. 10, 19–29 (1962)
C. Y. Lin, A variational problem relating to cooling fins with heat generation, Quart. Appl. Math. 19, 245–251 (1962)
M. Jacob, Heat transfer, John Wiley and Sons, Inc., New York, 1949, pp. 219–243
S. Saks, Theory of the integral, Hafner, New York, 1937
Similar Articles
Retrieve articles in Quarterly of Applied Mathematics
with MSC:
80.49
Retrieve articles in all journals
with MSC:
80.49
Additional Information
Article copyright:
© Copyright 1976
American Mathematical Society
