A problem in cooling fin design
Authors:
L. E. Bobisud and J. E. Calvert
Journal:
Quart. Appl. Math. 57 (1999), 369-380
MSC:
Primary 34B15; Secondary 80A20
DOI:
https://doi.org/10.1090/qam/1686195
MathSciNet review:
MR1686195
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Abstract: We consider two related one-dimensional steady-state problems of heat conduction/radiation in a cooling fin. In both problems the solution consists of the value of a parameter (length of the fin) and a monotone temperature distribution in the fin. Three boundary conditions are accordingly imposed: temperature at both ends of the fin and heat flux at one end. We show that these problems have solutions only for data satisfying certain constraints, and we obtain sufficient conditions for existence. Good estimates for the required fin length are also provided.
A. J. Chapman, Heat Transfer, 2nd ed., Macmillan, New York, 1967
- Andrzej Granas, Ronald Guenther, and John Lee, Nonlinear boundary value problems for ordinary differential equations, Dissertationes Math. (Rozprawy Mat.) 244 (1985), 128. MR 808227
- A. Granas, R. B. Guenther, and J. W. Lee, Some general existence principles in the Carathéodory theory of nonlinear differential systems, J. Math. Pures Appl. (9) 70 (1991), no. 2, 153–196. MR 1103033
A. J. Chapman, Heat Transfer, 2nd ed., Macmillan, New York, 1967
A. Granas, R. B. Guenther, and J. W. Lee, Nonlinear boundary value problems for ordinary differential equations, Dissertationes Mathematicae 244, 1–128 (1985)
A. Granas, R. B. Guenther, and J. W. Lee, Some general existence principles in the Carathéodory theory of nonlinear differential systems, J. Math. Pures et Appl. 70, 153–196 (1991)
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Article copyright:
© Copyright 1999
American Mathematical Society
