An exact general solution for the temperature distribution and the composite radiation convection heat exchange along a constant cross-sectional area fin

Author:
A. R. Shouman

Journal:
Quart. Appl. Math. **25** (1968), 458-462

DOI:
https://doi.org/10.1090/qam/99882

MathSciNet review:
QAM99882

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Abstract | References | Additional Information

Abstract: An exact general solution is obtained for the nonlinear differential equation governing the one-dimensional steady-state heat exchange by composite radiation and convection along constant area fins with uniform temperature at the base and an arbitrary temperature gradient at the other end. The fin can dissipate or receive energy. The fin is assumed to have constant thermal properties, and the radiant interaction between the fin and the base surfaces is neglected.

**[1]**Max Jakob,*Heat transfer*, Vol. 1, John Wiley and Sons, Inc., 1955, pp. 207-243**[2]**R. L. Chambers and E. V. Somers,*Radiation fin efficiency for one-dimensional heat flow in a circular fin*, Trans. ASME**81**, 327-329 (1959)**[3]**Seymour Lieblein,*Analysis of temperature distribution and radiant heat transfer along a rectangular fin of constant thickness*, NASA Technical Note D-196**[4]**J. G. Bartas and W. H. Sellers,*Radiation fin effectiveness*, Trans. ASME**82**, 73-75 (1960)**[5]**J. P. Callinan and W. P. Berggren,*Some radiator design criteria for space vehicles*, Trans. ASME Series C, Heat Transfer**81**, 237-244 (1959)**[6]**J. Ernest Wilkins Jr.,*Minumum-mass thin fins which transfer heat only by radiation to surroundings at absolute zero*, J. Soc. Indust. Appl. Math.**8**(1960), 630–639. MR**0127186****[7]**Chen-Ya Liu,*On optimum rectangular cooling fins*, Quart. Appl. Math.**19**(1961), 72–75. MR**0121073**, https://doi.org/10.1090/S0033-569X-1961-0121073-2**[8]**D. B. Mackay,*Design of space powerplants*, Prentice-Hall, Inc., Chapter II, 1963**[9]**A. R. Shouman,*An exact solution for the temperature distribution and heat transfer along a constant cross-sectional area fin with finite equivalent surrounding sink temperature*, Proceedings of the 9th Midwestern Mechanics Conference, August 1965**[10]**H. M. Hung and F. C. Appl,*Heat transfer of thin fins with temperature-dependent thermal properties and internal heat generation*, ASME Paper No. 65-WA/HT-50

Additional Information

DOI:
https://doi.org/10.1090/qam/99882

Article copyright:
© Copyright 1968
American Mathematical Society