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Technical Briefs

Design and Optimization of Composite Rectangular Fins Using the Relative Inverse Thermal Admittance

[+] Author and Article Information
Juan P. Luna–Abad

Área de Máquinas y Motores Térmicos,
Departamento de Ingeniería Térmica y de Fluidos
Universidad Politécnica de Cartagena,
Edificio de Ingeniería Civil y Oceánica,
Paseo Alfonso XIII, 52,
30203 Cartagena 30203,
Murcia, Spain
e-mail: jp.lunaabad@upct.es,

Francisco Alhama

Departamento de Física Aplicada,
Universidad Politécnica de Cartagena,
Cartagena 30202, Murcia, Spain,
e-mail: paco.alhama@upct.es

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the Journal of Heat Transfer. Manuscript received July 4, 2012; final manuscript received March 7, 2013; published online July 18, 2013. Assoc. Editor: Giulio Lorenzini.

J. Heat Transfer 135(8), 084504 (Jul 18, 2013) (4 pages) Paper No: HT-12-1349; doi: 10.1115/1.4024016 History: Received July 04, 2012; Revised March 07, 2013

The concept of relative inverse admittance applied to composite fins optimization in the case of longitudinal rectangular fins under 2D heat conduction is presented in this work. Here, different values for convective conditions at the fin and composite layer surfaces are used and the influence of the kc/kf ratio and composite thickness in optimum geometry is determined. The optimization process is carried out through universal graphs in which the range of parameters covers most of the practical cases a designer will find. Relative inverse admittance is applied in a general form and emerges as an easily used tool for optimizing composite fins.

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References

Barker, J. J., 1958, “Efficiency of Composite Fins,” Nucl. Sci. Eng., 3, pp. 300–312.
Barrow, H., Mistry, J., and Clayton, D., 1986, “Numerical and Exact Mathematical Analyses of Two Dimensional Rectangular Composite Fins,” Proc. 8th International Heat Transfer Conference, San Francisco, Vol. 2, pp. 367–372.
Tu, P., Inaba, H., Horibe, A., Li, Z., and Haruki, N., 2006, “Fin Efficiency of an Annular Fin Composed of a Substrate Metallic Fin and a Coating Layer,” ASME J. Heat Transfer, 128, pp. 851–854. [CrossRef]
Gorobets, V., 2006, “Thermal Efficiency and the Optimum Sizes of Finned Surfaces with Coating,” Proc. 13th International Heat Transfer Conf., HEX-03, Sydney, Australia.
Gorobets, V., 2008, “Influence of Coating on Thermal Characteristics and Optimum Sizes of Fins,” J. Enhanced Heat Transfer, 15, pp. 65–80. [CrossRef]
Cortés, C., Díez, L. I., and Campo, A., 2008, “Efficiency of Composite Fins of Variable Thickness,” Int. J. Heat Mass Transfer, 51, pp. 2153–2166. [CrossRef]
González-Fernández, C. F., 2002, Heat Transfer and the Network Simulation Method and Network Simulation Method, HornoJ., ed., Research Signpost, Kerala, India, Chap. 2.
Alarcón, M., Alhama, F., and González-Fernámdez, C. F., 2003, “A Revision of the Classical Performance Extended SurfacesAssessment: Proposed New Coefficients,” ASME J. Heat Transfer, 125(6), pp. 1187–1191. [CrossRef]
Luna–Abad, J. P., Alhama, F., and Campo, A., 2010, “Optimization of Longitudinal Rectangular Fins Through the Concept of Relative Inverse Admittance,” Heat Transfer Eng., 31(5), pp. 395–401. [CrossRef]
Luna–Abad, J. P., and Alhama, F., 2010, “Optimization of Longitudinal Rectangular Fins with Asymmetrical Boundary Conditions,” Proc. 14th International Heat Transfer Conference, (ASME), Washington, DC.
Luna–Abad, J. P., 2010, “Caracterización, Optimización y Diseño de Algunos Tipos de Aletas a través del Concepto de Admitancia Térmica Inversa Relativa,” Ph.D. thesis, Universidad Politécnica de Cartagena, Cartagena, Spain.
PSPICE 6.0, 1994, MicroSim Corp., Irvine, CA.

Figures

Grahic Jump Location
Fig. 3

Optimum fin thickness versus fin volume. kc/kf = 100/1 (a) for h/kf = 0.1 m−1, curve (1): ec = 0.2 mm, curve (2): ec = 0.5 mm, curve (3): ec = 1 mm, (b) for h/kf = 1 m−1, curve (1): ec = 0.2 mm, curve (2): ec = 0.5 mm, curve (3): ec = 1 mm, (c) for h/kf = 10 m−1, curve (1): ec = 0.2 mm, curve (2): ec = 0.5 mm, curve (3): ec = 1 mm

Grahic Jump Location
Fig. 2

Optimum fin thickness versus fin core volume. kc/kf = 1/100 (a) for h/kf = 0.1 m−1, curve (1): ec = 0.1 mm, curve (2): ec = 0.2 mm, curve (3): ec = 0.5 mm, curve (4): ec = 1 mm. (b) for h/kf = 1 m−1, curve (1): ec = 0.1 mm, curve (2): ec = 0.2 mm, curve (3): ec = 0.5 mm, curve (4): ec = 1 mm. (c) for h/kf = 10 m−1, curve (1): ec = 0.1 mm, curve (2): ec = 0.2 mm, curve (3): ec = 0.5 mm, curve (4): ec = 1 mm

Grahic Jump Location
Fig. 1

Composite fin. Geometrical and thermal parameters.

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