0
Research Papers: Heat and Mass Transfer

Geometric Mean of Fin Efficiency and Effectiveness: A Parameter to Determine Optimum Length of Open-Cell Metal Foam Used as Extended Heat Transfer Surface

[+] Author and Article Information
Tisha Dixit

Cryogenic Engineering Centre,
Indian Institute of Technology,
Kharagpur 721 302, India
e-mail: tisha8889@iitkgp.ac.in

Indranil Ghosh

Cryogenic Engineering Centre,
Indian Institute of Technology,
Kharagpur 721 302, India
e-mail: indranil@hijli.iitkgp.ernet.in

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received May 3, 2016; final manuscript received January 9, 2017; published online March 28, 2017. Assoc. Editor: Milind A. Jog.

J. Heat Transfer 139(7), 072002 (Mar 28, 2017) (11 pages) Paper No: HT-16-1246; doi: 10.1115/1.4036079 History: Received May 03, 2016; Revised January 09, 2017

High porosity open-cell metal foams have captured the interest of thermal industry due to their high surface area density, low weight, and ability to create tortuous mixing of fluid. In this work, application of metal foams as heat sinks has been explored. The foam has been represented as a simple cubic structure and heat transfer from a heated base has been treated analogous to that of solid fins. Based on this model, three performance parameters namely, foam efficiency, overall foam efficiency, and foam effectiveness have been evaluated for metal foam heat sinks. Parametric studies with varying foam length, porosity, pore density, material, and fluid velocity have been conducted. It has been observed that geometric mean of foam efficiency and foam effectiveness can be a useful parameter to exactly determine the optimum foam length. Additionally, the variation in temperature profile of different foams heated from one end has been determined experimentally by cooling these with atmospheric air. The experimental results have been presented for open-cell metal foams (10 and 30 PPI) made of copper/aluminium/Fe–Ni–Cr alloy with porosity in the range of 0.908–0.964.

FIGURES IN THIS ARTICLE
<>
Copyright © 2017 by ASME
Your Session has timed out. Please sign back in to continue.

References

Kern, D. Q. , and Kraus, A. D. , 1972, Extended Surface Heat Transfer, McGraw-Hill, New York.
Kays, W. M. , and London, A. L. , 1984, Compact Heat Exchangers, McGraw-Hill, New York.
Incropera, F. P. , and Dewitt, D. P. , 2006, Fundamentals of Heat and Mass Transfer, Wiley, New Delhi, India.
Ashby, M. F. , Evans, A. , Fleck, N. A. , Gibson, L. J. , Hutchinson, J. W. , and Wadley, H. N. G. , 2000, Metal Foams: A Design Guide, Butterworth-Heinmann, Oxford, UK.
Lu, T. , 2002, “ Ultralight Porous Metals: From Fundamentals to Applications,” Acta Mech. Sin., 18(5), pp. 457–479.
Kim, S. Y. , Paek, J. W. , and Kang, B. H. , 2000, “ Flow and Heat Transfer Correlations for Porous Fin in a Plate-Fin Heat Exchanger,” Trans. ASME, 122(3), pp. 572–578.
Calmidi, V. V. , and Mahajan, R. L. , 2000, “ Forced Convection in High Porosity Metal Foams,” ASME J. Heat. Transfer, 122(3), pp. 557–565.
Hwang, J. J. , Hwang, G. J. , Yeh, R. H. , and Chao, C. H. , 2002, “ Measurement of Interstitial Heat Transfer and Frictional Drag for Flow Across Metal Foams,” Trans. ASME, 124(1), pp. 120–129.
Bhattacharya, A. , and Mahajan, R. L. , 2002, “ Finned Metal Foam Heat Sinks for Electronics Cooling in Forced Convection,” ASME J. Electron. Packag., 124(3), pp. 155–163.
Hsieh, W. H. , Wu, J. Y. , Shih, W. H. , and Chiu, W. C. , 2004, “ Experimental Investigation of Heat-Transfer Characteristics of Aluminium-Foam Heat Sinks,” Int. J. Heat Mass Transfer, 47(23), pp. 5149–5157.
Shih, W. H. , Chiu, W. C. , and Hsieh, W. H. , 2006, “ Height Effect on Heat Transfer Characteristics of Aluminium-Foam Heat Sinks,” Trans. ASME, 128(6), pp. 530–537.
Ghosh, I. , 2009, “ Heat Transfer Correlation for High-Porosity Open-Cell Foam,” Int. J. Heat Mass Transfer, 52(5–6), pp. 1488–1494.
Mancin, S. , Zilio, C. , Cavallini, A. , and Rossetto, L. , 2010, “ Heat Transfer During Air Flow in Aluminium Foams,” Int. J. Heat Mass Transfer, 53(21–22), pp. 4976–4984.
Mancin, S. , Zilio, C. , Diani, A. , and Rossetto, L. , 2012, “ Experimental Air Heat Transfer and Pressure Drop Through Copper Foams,” Exp. Therm. Fluid Sci., 36, pp. 224–232.
Mancin, S. , Zilio, C. , Rossetto, L. , and Cavallini, A. , 2012, “ Foam Height Effects on Heat Transfer Performance of 20 PPI Aluminium Foams,” Appl. Therm. Eng., 49, pp. 55–60.
Mancin, S. , Zilio, C. , Diani, A. , and Rossetto, L. , 2013, “ Air Forced Convection Through Metal Foams: Experimental Results and Modeling,” Int. J. Heat Mass Transfer, 62, pp. 112–123.
Feng, S. S. , Kuang, J. J. , Lu, T. J. , and Ichimiya, K. , 2015, “ Heat Transfer and Pressure Drop Characteristics of Finned Metal Foam Heat Sinks Under Uniform Impinging Flow,” ASME J. Electron. Packag., 137(2), p. 021014.
Salas, K. I. , and Waas, A. M. , 2007, “ Convective Heat Transfer in Open Cell Metal Foams,” ASME J. Heat Transfer, 129(9), pp. 1217–1229.
Lu, T. J. , Stone, H. A. , and Ashby, M. F. , 1998, “ Heat Transfer in Open-Cell Metal Foams,” Acta Mater., 46(10), pp. 3619–3635.
Dukhan, N. , Negron, J. M. G. , and Feliciano, R. P. , 2004, “ An Approach for Simulating Metal Foam Cooling of High Power Electronics,” 26th IEEE Annual International Telecommunications Energy Conference (INTELEC), Chicago, IL, Sept. 19–23, pp. 385–391.
Dukhan, N. , Ramos, P. D. , Ruiz, E. , Reyes, M. , and Scott, E. P. , 2005, “ One-Dimensional Heat Transfer Analysis in Open-Cell 10 PPI Metal Foam,” Int. J. Heat Mass Transfer, 48(25–26), pp. 5112–5120.
Dukhan, N. , Feliciano, R. , and Hernandez, A. R. , 2006, “ Heat Transfer Analysis in Metal Foams With Low Conductivity Fluids,” Trans. ASME, 128(8), pp. 784–792.
Dukhan, N. , and Chen, K. C. , 2007, “ Heat Transfer Measurements in Metal Foam Subjected to Constant Heat Flux,” Exp. Therm. Fluid Sci., 32(2), pp. 624–631.
Jeng, T. , Tzeng, S. , and Hung, Y. , 2006, “ An Analytical Study of Local Thermal Equilibrium in Porous Heat Sinks Using Fin Theory,” Int. J. Heat Mass Transfer, 49(11–12), pp. 1907–1914.
Ghosh, I. , 2008, “ Heat-Transfer Analysis of High Porosity Open-Cell Metal Foam,” ASME J. Heat Transfer., 130(3), p. 034501.
Kiwan, S. , and Al-Nimr, M. A. , 2001, “ Using Porous Fins for Heat Transfer Enhancement,” Trans. ASME, 123(4), pp. 790–795.
Hooman, K. , and Merrikh, A. A. , 2006, “ Analytical Solution of Forced Convection in a Duct of Rectangular Cross Section Saturated by a Porous Medium,” Trans. ASME, 128(6), pp. 596–600.
Xu, H. J. , Qu, Z. G. , and Tao, W. Q. , 2011, “ Thermal Transport Analysis in Parallel-Plate Channel Filled With Open-Celled Metallic Foams,” Int. Commun. Heat Mass Transfer, 38(7), pp. 868–873.
Moffat, R. J. , Eaton, J. K. , and Onstad, A. , 2009, “ A Method for Determining the Heat Transfer Properties of Foam-Fins,” ASME J. Heat Transfer, 131(1), p. 011603.
Zhang, H. Y. , Pinjala, D. , Joshi, Y. K. , Wong, T. N. , Toh, K. C. , and Iyer, M. K. , 2005, “ Fluid Flow and Heat Transfer in Liquid Cooled Foam Heat Sinks for Electronic Packages,” IEEE Trans. Compon. Packag. Technol., 28(2), pp. 272–280.
DeGroot, C. T. , Straatman, A. G. , and Betchen, L. J. , 2009, “ Modeling Forced Convection in Finned Metal Foam Heat Sinks,” ASME J. Electron. Packag., 131(2), p. 021001.
Ghosh, I. , 2009, “ How Good is Open-Cell Metal Foam as Heat Transfer Surface?,” ASME J. Heat Transfer, 131(10), p. 101004.
Seyf, H. R. , and Layeghi, M. , 2010, “ Numerical Analysis of Convective Heat Transfer From an Elliptic Pin Fin Heat Sink With and Without Metal Form Insert,” ASME J. Heat Transfer, 132(7), p. 071401.
Feng, S. S. , Kuang, J. J. , Wen, T. , Lu, T. J. , and Ichimiya, K. , 2014, “ An Experimental and Numerical Study of Finned Metal Foam Heat Sinks Under Impinging Air Jet Cooling,” Int. J. Heat Mass Transfer, 77, pp. 1063–1074.
Dixit, T. , and Ghosh, I. , 2015, “ Review of Micro- and Mini-Channel Heat Sinks and Heat Exchangers for Single Phase Fluids,” Renewable Sustainable Energy Rev., 41, pp. 1298–1311.
Sawei, Q. , Xinna, Z. , Qingxian, H. , Renjun, D. , Yan, J. , and Yuebo, H. , 2015, “ Research Progress on Simulation Modeling of Metal Foams,” Rare Met. Mater. Eng., 44(11), pp. 2670–2676.
Iasiello, M. , Cunsolo, S. , Oliviero, M. , Harris, W. H. , Bianco, N. , Chiu, W. , and Naso, V. , 2014, “ Numerical Analysis of Heat Transfer and Pressure Drop in Metal Foams for Different Morphological Models,” ASME J. Heat Transfer, 136(11), p. 112601.
Krishnan, S. , Murthy, J. Y. , and Garimella, S. V. , 2006, “ Direct Simulation of Transport in Open-Cell Metal Foam,” ASME J. Heat Transfer, 128(8), pp. 793–799.
Krishnan, S. , Garimella, S. V. , and Murthy, J. Y. , 2008, “ Simulation of Thermal Transport in Open-Cell Metal Foams: Effect of Periodic Unit-Cell Structure,” ASME J. Heat Transfer, 130(2), p. 024503.
Sullivan, R. M. , Ghosn, L. J. , and Lerch, B. A. , 2008, “ A General Tetrakaidecahedron Model for Open-Celled Foams,” Int. J. Solids Struct., 45(6), pp. 1754–1765.
Inayat, A. , Schwerdtfeger, J. , Freund, H. , Korner, C. , Singer, R. F. , and Schwieger, W. , 2011, “ Periodic Open-Cell Foams: Pressure Drop Measurements and Modeling of an Ideal Tetrakaidecahedra Packing,” Chem. Eng. Sci., 66(12), pp. 2758–2763.
Bock, J. , and Jacobi, A. M. , 2013, “ Geometric Classification of Open-Cell Metal Foams Using X-Ray Micro-Computed Tomography,” Mater. Charact., 75, pp. 35–43.
Cunsolo, S. , Oliviero, M. , Harris, W. M. , Andreozzi, A. , Bianco, N. , Chiu, W. K. S. , and Naso, V. , 2015, “ Monte Carlo Determination of Radiative Properties of Metal Foams: Comparison Between Idealized and Real Cell Structures,” Int. J. Therm. Sci., 87, pp. 94–102.
Ranut, P. , Nobile, E. , and Mancini, L. , 2014, “ High Resolution Microtomography-Based CFD Simulation of Flow and Heat Transfer in Aluminium Metal Foams,” Appl. Therm. Eng., 69(1–2), pp. 230–240.
Boomsma, K. , Poulikakos, D. , and Ventikos, Y. , 2003, “ Simulations of Flow Through Open Cell Metal Foams Using an Idealized Periodic Cell Structure,” Int. J. Heat Fluid Flow, 24(6), pp. 825–834.
Dixit, T. , and Ghosh, I. , 2016, “ An Experimental Study on Open Cell Metal Foam as Extended Heat Transfer Surface,” Exp. Therm. Fluid Sci., 77, pp. 28–37.
Fuller, A. J. , Kim, T. , Hodson, H. P. , and Lu, T. J. , 2005, “ Measurement and Interpretation of the Heat Transfer Coefficients of Metal Foams,” Proc. Inst. Mech. Eng. Part C, 219(2), pp. 183–191.
Prasad, B. S. V. , 1997, “ Fin Efficiency and Mechanisms of Heat Exchange Through Fins in Multistream Plate Fin Heat Exchangers: Development and Application of a Rating Algorithm,” Int. J. Heat Mass Transfer, 40(18), pp. 4279–4288.
Poulikakos, D. , and Bejan, A. , 1982, “ Fin Geometry for Minimum Entropy Generation in Forced Convection,” Trans. ASME, 104(4), pp. 616–623.
Fleming, P. J. , and Wallace, J. J. , 1986, “ How Not to Lie With Statistics: The Correct Way to Summarize Benchmark Results,” Commun. ACM, 29(3), pp. 218–221.
Kubat, M. , and Matwin, S. , 1997, “ Addressing the Curse of Imbalanced Training Sets: One-Sided Selection,” 14th International Conference on Machine Learning (ICML '97), Morgan Kaufmann, Nashville, TN, pp. 179–186.
Akbani, R. , Kwek, S. , and Japkowicz, N. , 2004, “ Applying Support Vector Machines to Imbalanced Datasets,” Machine Learning: ECML 2004, J.-F. Boulicaut , F. Esposito, F. Giannotti, D. Pedreschi, eds., Springer-Verlag, Berlin, pp. 39–50.
Saleh, A. Y. , Shamsuddin, S. M. , and Hamed, H. N. A. , 2015, “ Multi-Objective Differential Evolution of Evolving Spiking Neural Networks for Classification Problems,” Artificial Intelligence Applications and Innovations (IFIP Advances in Information and Communication Technology, Vol. 458), R. Chbeir, Y. Manolo-poulos, I. Maglogiannis, R. Alhajj, eds., Springer International Publishing, Cham, Switzerland, pp. 351–368.

Figures

Grahic Jump Location
Fig. 1

Simple cubic structure representation of open cell metal foams attached to base plate[25]

Grahic Jump Location
Fig. 2

Pictorial view of the metal foam test samples

Grahic Jump Location
Fig. 3

(a) Schematic and (b) pictorial view of experimental test rig for measurement of foam thermohydraulic properties [46]

Grahic Jump Location
Fig. 4

Variation of dimensionless foam temperature ratio θ/θ1 against dimensionless foam length x/L with change in (a) fluid velocity, (b) material, (c) porosity, and (d) pore density

Grahic Jump Location
Fig. 5

Variation of experimentally measured (a) outlet air dimensionless temperature against distance from the heated base and (b) pressure drop against fluid velocity

Grahic Jump Location
Fig. 6

Foam efficiency (ηf) and foam effectiveness (εf) variation against dimensionless foam length x/L with change in (a) fluid velocity, (b) material, (c) porosity, and (d) pore density

Grahic Jump Location
Fig. 7

(a) Overall foam efficiency (ηf,o) and (b) foam-finned surface efficiency (Ω*) variation against foam length L

Grahic Jump Location
Fig. 8

Variation of (a) foam efficiency (ηf) and (b) overall foam efficiency (ηf,o) against mfL

Grahic Jump Location
Fig. 9

Variation of geometric foam efficiency (ηg) against dimensionless foam length x/L with change in (a) fluid velocity, (b) material, (c) porosity, and (d) pore density

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In