In the present study the optimum dimensions of circular rectangular and triangular profile fins with fin-to-fin and fin-to-base radiant interaction are determined. The basic assumptions are one-dimensional heat conduction and black surface radiation. The governing equations are formulated by means of dimensionless variables and solved numerically. The optimum fin dimensions, bore thickness and height, are presented in generalized dimensionless form and explicit correlations are provided for the dimensionless optimum parameters. The results are analyzed and reported in diagrams that give insight to the operational characteristics of the heat rejection mechanism.
Issue Section:
Technical Notes
1.
Sparrow
, E. M.
, Miller
, G. B.
, and Jonsson
, V. K.
, 1962
, “Radiating Effectiveness of Annular-Finned Space Radiators, with Mutual Irradiation Between Radiator Elements
,” ASCE, J. Aerosp. Eng.
, 29
, pp. 1291
–1299
.2.
Chung
, B. T. F.
, and Zhang
, B. X.
, 1991
, “Minimum Mass Longitudinal Fins With Radiation Interaction at the Base
,” J. Franklin Inst.
, 328
(1
), pp. 143
–161
.3.
Chung
, B. T. F.
, and Zhang
, B. X.
, 1991
, “Optimization of Radiating Fin Array Including Mutual Irradiations Between Radiator Elements
,” ASME J. Heat Transfer
, 113
, pp. 814
–822
.4.
Krishnaprakas
, C. K.
, 1997
, “Optimum Design of Radiating Longitudinal Fin Array Extending From a Cylindrical Surface
,” ASME J. Heat Transfer
, 119
, pp. 857
–860
.5.
Schnurr
, E. M.
, and Cothran
, C. A.
, 1974
, “Radiation from an Array of Gray Circular Fins of Trapezoidal Profile
,” AIAA J.
, 12
(11
), pp. 1476
–1480
.6.
Schnurr
, E. M.
, Shapiro
, A. B.
, and Townsend
, M. A.
, 1976
, “Optimization of Radiating Fin Arrays With Respect to Weight
,” ASME J. Heat Transfer
, 98
, pp. 643
–648
.7.
Razelos
, P.
, and Georgiou
, E.
, 1992
, “Two-Dimensional Effects and Design Criteria for Convective Extended Surfaces
,” Heat Transfer Eng.
, 13
(3
), pp. 38
–48
.8.
Razelos
, P.
, and Imre
, K.
, 1980
, “The Optimum Dimensions of Circular Fins With Variable Thermal Parameters
,” ASME J. Heat Transfer
, 102
(2
), pp. 420
–425
.9.
Schittkowski, K., 1986, “NLPQL: A FORTRAN Subroutine Solving Constrained Nonlinear Programming Problems,” Annals of Operations Research, Clyde L. Monma, ed., 5, pp. 485–500.
10.
Razelos
, P.
, 1979
, “The Optimization of Convective Fins With Internal Heat Generation
,” Nucl. Eng. Des.
, 52
(2
), pp. 289
–299
.11.
Modest, M. F., 1993, Radiative Heat Transfer, McGraw-Hill, New York.
12.
Razelos
, P.
, and Krikkis
, R. N.
, 2001
, “Optimum Design of Longitudinal Rectangular Fins with Base to Fin Radiant Interaction
,” Heat Transfer Eng.
, 22
(3
), pp. 3
–17
.13.
Ascher, U. M., Mattheij, R. M. M., and Russel, R. D., 1995, Numerical Solution of Boundary Value Problems for Ordinary Differential Equations, 2nd ed., SIAM, Philadelphia, PA.
14.
Keller, H. B., 1992, Numerical Methods for Two-Point Boundary-Value Problems, Dover, New York.
15.
Hairer, E., Nørsett, S. P., and G., Wanner, 1987, Solving Ordinary Differential Equations I. Nonstiff Problems, Springer-Verlag, New York.
16.
Sparrow
, E. M.
, 1963
, “A New and Simpler Formulation for Radiative Angle Factors
,” ASME J. Heat Transfer
, 85
, pp. 81
–88
.Copyright © 2004
by ASME
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