The performance of tree-like fins with varying bifurcation angle, surface emissivity, material, width-to-thickness ratio, and base heat rate was examined. Overall system performance was examined computationally. The computational results have been validated, verified, and cast in terms of commonly defined dimensionless parameters. Tree-like fins were found to be more effective and more efficient than the rectangular fins. Fin efficiency and effectiveness were found to increase with increasing bifurcation angles while base temperatures were found to decrease with increasing bifurcation angles. As expected, base temperatures were highest for the largest width-to-thickness ratios and smallest for materials with relatively higher thermal conductivities.
Issue Section:
Radiative Heat Transfer
References
1.
Schmidt
, E.
, 1926
, “Die Warmeubertragung Durch Rippen
,” Z. Ver. Dtsch. Ing.
, 70
, pp. 885
–889
.2.
Duffin
, R. J.
, 1962
, “A Variational Problem Relating to Cooling Fins
,” J. Math. Mech.
, 8
, pp. 47
–56
.3.
Liu
, C.
, 1962
, “A Variational Problem With Applications to Cooling Fins
,” J. Soc. Ind. Appl. Mech.
, 10
(1
), pp. 19
–29
.10.1137/01100024.
Mackay
, D. B.
, and Leventhal
, E. L.
, 1960
, “Radiant Heat Transfer From a Flat Plate Uniformly Heated Along the Edge
,” AIChE 4th National Heat Transfer Conference
, New York
.5.
Wilkins
, J. E.
, 1960
, “Minimum-Mass Thin Fins which Transfer Heat Only by Radiation to Surroundings at Absolute Zero
,” J. Soc. Ind. Appl. Math.
, 8
(4
), pp. 630
–639
.10.1137/01080476.
Bartas
, J. G.
, and Sellers
, W. H.
, 1960
, “Radiation Fin Effectiveness
,” ASME J. Heat Transfer
, 82C
, pp. 73
–75
.10.1115/1.36798827.
Sparrow
, E. M.
, and Eckert
, E. R. G.
, 1962
, “Radiant Interaction Between Fin and Base Surfaces
,” ASME J. Heat Transfer
, 84
(1
), pp. 12
–18
.10.1115/1.36842818.
Callinan
, J. P.
, and Berggren
, W. P.
, 1959
, “Some Radiator Design Criteria for Space Vehicles
,” ASME J. Heat Transfer
, 81C
, pp. 237
–238
.9.
Aziz
, A.
, and Kraus
, A. D.
, 1996
, “Optimum Design of Radiating and Convecting-Radiating Fins
,” Heat Transfer Eng.
, 17
(3
), pp. 44
–78
.10.1080/0145763960893988010.
Naumann
, R. J.
, 2004
, “Optimizing the Design of Space Radiators
,” Int. J. Thermophys.
, 25
(6
), pp. 1929
–1941
.10.1007/s10765-004-7747-011.
Schnurr
, N. M.
, Shapiro
, A. B.
, and Townsend
, M. A.
, 1976
, “Optimization of Radiating Fin Arrays With Respect to Weight
,” ASME J. Heat Transfer
, 98
(4
), pp. 643
–648
.10.1115/1.345061312.
Krikkis
, R. N.
, and Razelos
, P.
, 2002
, “Optimum Design of Spacecraft Radiators With Longitudinal Rectangular and Triangular Fins
,” ASME J. Heat Transfer
, 124
(5
), pp. 805
–812
.10.1115/1.149735913.
Kumar
, S. S.
, Nayak
, N.
, and Venkateshan
, S. P.
, 1993
, “Optimum Finned Space Radiators
,” Int. J. Heat Fluid Flow
, 14
(2
), pp. 191
–200
.10.1016/0142-727X(93)90028-L14.
Khor
, Y. K.
, Hung
, Y. M.
, and Lim
, B. K.
, 2010
, “On the Role of Radiation View Factor in Thermal Performance of Straight-Fin Heat Sinks
,” Int. Commun. Heat Mass Transfer
, 37
(8
), pp. 1087
–1095
.10.1016/j.icheatmasstransfer.2010.06.01215.
Shabany
, Y.
, 2008
, “Radiation Heat Transfer From Plate-Fin Heat Sinks
,” Semiconductor Thermal Measurement and Management Symposium
, pp. 132
–136
.16.
Ellison
, G. N.
, 1979
, “Generalized Computations of the Gray Body Shape Factor for Thermal Radiation From a Rectangular U-Channel
,” IEEE Trans. Compon., Hybrids Manuf. Technol.
, 2
(4
), pp. 517
–522
.10.1109/TCHMT.1979.113549217.
Razelos
, P.
, and Krikkis
, R. N.
, 2001
, “Optimum Design of Longitudinal Rectangular Fins With Base-to-Fin Radiant Interaction
,” Heat Transfer Eng.
, 22
(4
), pp. 3
–17
.10.1080/01457630175021576018.
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
.10.1016/0016-0032(91)90011-Q19.
Chung
, B. T. F.
, and Zhang
, B. X.
, 1991
, “Optimization of Radiating Fin Array Including Mutual Irradiation Between Radiator Elements
,” ASME J. Heat Transfer
, 133
(4
), pp. 814
–822
.10.1115/1.291120820.
Krishnaprakas
, C. K.
, and Narayana
, K. B.
, 2003
, “Heat Transfer Analysis of Mutually Irradiating Fins
,” Int. J. Heat Mass Transfer
, 46
(5
), pp. 761
–769
.10.1016/S0017-9310(02)00356-321.
Thompson
, D'A. W.
, 1942
, On Growth and Form
, Cambridge University Press
, Cambridge, UK
.22.
Mandelbrot
, B. B.
, 1982
, The Fractal Geometry of Nature
, Freeman
, New York
.23.
Barnsley
, M.
, 1988
, Fractals Everywhere
, Academic Press
, San Diego
.24.
Murray
, C. D.
, 1926
, “The Physiological Principle of Minimum Work. I. The Vascular System and the Cost of Blood Volume
,” J. Physiol.
, 12
(3
), pp. 207
–214
.25.
Cohn
, D. L.
, 1954
, “Optimal Systems: The Vascular System
,” Bull. Math. Biophys.
, 16
, pp. 59
–74
.10.1007/BF0248181326.
Calamas
, D.
, and Baker
, J.
, 2013
, “Performance of a Biologically-Inspired Heat Exchanger With Hierarchical Bifurcating Flow Passages
,” J. Thermophys. Heat Transfer
, 27
(1
), pp. 80
–90
.10.2514/1.T395027.
Van Der Vyver
, H.
, 2003
, “Validation of a CFD Model of a Three-Dimensional Tube-In-Tube Heat Exchanger
,” Proceedings of Third International Conference on CFD in the Minerals and Process Industries, CSIRO, Melbourne, Australia
, pp. 235
–240
.28.
Meyer
, J.
, and Van Der Vyver
, H.
, 2005
, “Heat Transfer Characteristics of a Quadratic Koch Island Fractal Heat Exchanger
,” Heat Transfer Eng.
, 26
(9
), pp. 22
–29
.10.1080/0145763050020563829.
Lee
, D. J.
, and Lin
, W. W.
, 1995
, “Second Law Analysis on Fractal-Like Fin Under Cross Flow
,” AIChe J.
, 41
(10
), pp. 2314
–2317
.10.1002/aic.69041101530.
Xu
, P.
, Yu
, B.
, Yun
, M.
, and Zou
, M.
, 2006
, “Heat Conduction in Fractal Tree-Like Branched Networks
,” Int. J. Heat Mass Transfer
, 49
, pp. 3746
–3751
.10.1016/j.ijheatmasstransfer.2006.01.03331.
Bejan
, A.
, 2000
, Shape and Structure, From Engineering to Nature
, Cambridge University Press
, Cambridge, UK
.32.
Bejan
, A.
, 1997
, “Constructal-Theory Network of Conducting Paths for Cooling a Heat Generating Volume
,” Int. J. Heat Mass Transfer
, 40
(4
), pp. 799
–816
.10.1016/0017-9310(96)00175-533.
Bejan
, A.
, and Lorente
, S.
, 2010
, “The Constructal Law of Design and Evolution in Nature
,” Philos. Trans. R. Soc. London, Ser. B
, 365
(1545
), pp. 1335
–1347
.10.1098/rstb.2009.030234.
Bejan
, A.
, and Lorente
, S.
, 2006
, “Constructal Theory of Generation of Configuration in Nature and Engineering
,” J. Appl. Phys.
, 100(4)
, p. 041301
.10.1063/1.222189635.
Bejan
, A.
, and Errera
, M. R.
, 2000
, “Convective Trees of Fluid Channels for Volumetric Cooling
,” Int. J. Heat Mass Transfer
, 43
, pp. 3105
–3118
.10.1016/S0017-9310(99)00353-136.
Bejan
, A.
, and Dan
, N.
, 1999
, “Two Constructal Routes to Minimal Heat Flow Resistance via Greater Internal Complexity
,” ASME J. Heat Transfer
, 121
(1
), pp. 6
–14
.10.1115/1.282596837.
Bejan
, A.
, Lorente
, S.
, and Lee
, J.
, 2008
, “Unifying Constructal Theory of Tree Roots, Canopies and Forests
,” J. Theor. Biol.
, 254
(3
), pp. 529
–540
.10.1016/j.jtbi.2008.06.02638.
Rocha
, L. A. O.
, Lorenzini
, E.
, and Biserni
, C.
, 2005
, “Geometric Optimization of Shapes on the Basis of Bejan's Constructal Theory
,” Int. Commun. Heat Mass Transfer
, 32
(10
), pp. 1281
–1288
.10.1016/j.icheatmasstransfer.2005.07.01039.
Bejan
, A.
, 2002
, “Dendritic Constructal Heat Exchanger With Small-Scale Crossflows and Larger-Scales Counterflows
,” Int. J. Heat Mass Transfer
, 45
(23
), pp. 4607
–4620
.10.1016/S0017-9310(02)00165-540.
da Silva
, A. K.
, Lorente
, S.
, and Bejan
, A.
, 2004
, “Constructal Multi-Scale Tree-Shaped Heat Exchangers
,” J. Appl. Phys.
, 96
(3
), pp. 1709
–1718
.10.1063/1.176608941.
Zimparov
, V. D.
, da Silva
, A. K.
, and Bejan
, A.
, 2006
, “Constructal Tree-Shaped Parallel Flow Heat Exchangers
,” Int. J. Heat Mass Transfer
, 49
, pp. 4558
–4566
.10.1016/j.ijheatmasstransfer.2006.04.03542.
Alebrahim
, A.
, and Bejan
, A.
, 1999
, “Constructal Trees of Circular Fins for Conductive and Convective Heat Transfer
,” Int. J. Heat Mass Transfer
, 42
, pp. 3585
–3597
.10.1016/S0017-9310(99)00021-643.
Bejan
, A.
, Almogbel
, M.
, 2000
, “Constructal T-Shaped Fins
,” Int. J. Heat Mass Transfer
, 43
, pp. 2101
–2115
.10.1016/S0017-9310(99)00283-544.
Almogbel
, M.
, and Bejan
, A.
, 2000
, “Cylindrical Trees of Pin Fins
,” Int. J. Heat Mass Transfer
, 43
, pp. 4285
–4297
.10.1016/S0017-9310(00)00049-145.
Almogbel
, A.
, Bejan
, A.
, 2001
, “Constructal Optimization of Nonuniformly Distributed Tree-Shaped Flow Structures for Conduction
,” Int. J. Heat Mass Transfer
, 44
, pp. 4185
–4195
.10.1016/S0017-9310(01)00080-146.
Kuddusi
, L.
, and Egrican
, N.
, 2008
, “A Critical Review of Constructal Theory
,” Energy Convers. Manage.
, 49
(5
), pp. 1283
–1294
.10.1016/j.enconman.2007.05.02347.
Ghodoossi
, L.
, 2004
, “Conceptual Study on Constructal Theory
,” Energy Convers. Manage.
, 45
(9-10
), pp. 1379
–1395
.10.1016/j.enconman.2003.09.00248.
Plawsky
, J. L.
, 1993
, “Transport in Branched Systems I: Steady-State Response
,” Chem. Eng. Commun.
, 123
, pp. 71
–86
.10.1080/0098644930893616649.
Plawsky
, J. L.
, 1993
, “Transport in Branched Systems II: Transient Response
,” Chem. Eng. Commun.
, 123
, pp. 87
–109
.10.1080/0098644930893616750.
Glowinski
, R.
and Le Tallec
, P.
, 1989
, “Augmented Lagrangian Methods and Operator-Splitting Methods in Nonlinear Mechanics
,” SIAM, Philadelphia.51.
Marchuk
, G. I.
, 1982
, Methods of Numerical Mathematics
, Springer-Verlag
, Berlin
.52.
Samarskii
, A. A.
, 1989
, Theory of Difference Schemes
, Nauka
, Moscow
.53.
Kern
, D. Q.
, and Kraus
, A. D.
, 1972
, Extended Surface Heat Transfer
, McGraw-Hill
, New York
, pp. 203
–211
.54.
Fox
, R. W.
, and McDonald
, A. T.
, 1992
, Introduction to Fluid Mechanics
, 4th ed., John Wiley & Sons
, New York
.Copyright © 2013 by ASME
You do not currently have access to this content.
