Research Papers

A Simple Thermal Resistance Model for Open Cell Metal Foams

[+] Author and Article Information
C. Balaji

e-mail: balaji@iitm.ac.in

S. P. Venkateshan

e-mail: spv@iitm.ac.in
Heat Transfer and Thermal Power Laboratory,
Department of Mechanical Engineering,
Indian Institute of Technology Madras,
Chennai 600036, India

1Corresponding authors.

Contributed by the Heat Transfer Division of ASME for publication in the Journal of Heat Transfer. Manuscript received March 12, 2012; final manuscript received October 6, 2012; published online February 8, 2013. Assoc. Editor: Andrey Kuznetsov.

J. Heat Transfer 135(3), 032601 (Feb 08, 2013) (9 pages) Paper No: HT-12-1091; doi: 10.1115/1.4007827 History: Received March 12, 2012; Revised October 06, 2012

This paper presents a methodology for obtaining the convective heat transfer coefficient from the wall of a heated aluminium plate, placed in a vertical channel filled with open cell metal foams. For accomplishing this, a thermal resistance model from literature for metal foams is suitably modified to account for contact resistance. The contact resistance is then evaluated using the experimental results. A correlation for the estimation of the contact resistance as a function of the pertinent parameters, based on the above approach is developed. The model is first validated with experimental results in literature for the asymptotic case of negligible contact resistance. A parametric study of the effect of different foam parameters on the heat transfer is reported with and without the presence of contact resistance. The significance of the effect of contact resistance in the mixed convection and forced convection regimes is discussed. The procedure to employ the present methodology in an actual case is demonstrated and verified with additional, independent experimental data.

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Kurtbas, I., and Celik, N., 2009, “Experimental Investigation of Forced and Mixed Convection Heat Transfer in a Foam_filled Horizontal Rectangular Channel,” Int. J. Heat Mass Transfer, 52(5–6), pp. 1313–1325. [CrossRef]
Mahjoob, S., and Vafai, K., 2008, “A Synthesis of Fluid and Thermal Transport Models for Metal Foam Heat Exchangers,” Int. J. Heat Mass Transfer, 51(15–16), pp. 3701–3711. [CrossRef]
Calmidi, V. V., and Mahajan, R. L., 2000, “Forced Convection in High Porosity Metal Foams,” ASME J. Heat Transfer, 122, pp. 557–565. [CrossRef]
Kaviany, M., 1995, Principles of Heat Transfer in Porous Media, Springer, New York.
Schmierer, E. N., and Razani, A., 2006, “Self-Consistent Open-Celled Metal Foam Model for Thermal Applications,” ASME J. Heat Transfer, 128(11), pp. 1194–1203. [CrossRef]
Sadeghi, E., Djilali, N., and Bahrami, M., 2009, “Thermal Conductivity and Thermal Contact Resistance of Metal Foams,” ASME Summer Heat Transfer Conference, San Francisco, CA, July 19–23, pp. 355–365. [CrossRef]
Paek, J. W., Kang, B. H., Kim, S. Y., and Hyun, J. M., 2000, “Effective Thermal Conductivity and Permeability of Aluminum Foam Materials,” Int. J. Thermophys., 21(2), pp. 453–464. [CrossRef]
Boomsma, K., and Poulikakos, D., 2001, “On the Effective Thermal Conductivity of a Three-Dimensionally Structured Fluid-Saturated Metal Foam,” Int. J. Heat Mass Transfer, 44(4), pp. 827–836. [CrossRef]
Fiedler, T., Solorzano, E., Garcia-Moreno, F., Ochsner, A., Belova, I. V., and Murch, G. E., 2009, “Lattice Monte Carlo and Experimental Analyses of the Thermal Conductivity of Random-Shaped Cellular Aluminum,” Adv. Eng. Mater., 11(10), pp. 843–847. [CrossRef]
Nield, D., and Kuznetsov, A., 2010, “Forced Convection in Cellular Porous Materials: Effect of Temperature-Dependent Conductivity Arising From Radiative Transfer,” Int. J. Heat Mass Transfer, 53(13–14), pp. 2680–2684. [CrossRef]
Lu, T., Ashby, M., and Stone, H., 1998, “Heat Transfer in Open-Cell Metal Foams,” Acta Mater., 46(10), pp. 3619–3635. [CrossRef]
Ghosh, I., 2008, “Heat-Transfer Analysis of High Porosity Open-Cell Metal Foam,” ASME J. Heat Transfer, 130(3), p. 034501. [CrossRef]
Bai, M., and Chung, J. N., 2011, “Analytical and Numerical Prediction of Heat Transfer and Pressure Drop in Open-Cell Metal Foams,” Int. J. Therm. Sci., 50(6), pp. 869–880. [CrossRef]
Tamayol, A., and Hooman, K., 2011, “Thermal Assessment of Forced Convection Through Metal Foam Heat Exchangers,” ASME J. Heat Transfer, 133, p. 111801. [CrossRef]
Cavallini, A., Mancin, S., Rossetto, L., and Zilio, C., 2009, “Air Flow in Aluminum Foam: Heat Transfer and Pressure Drops Measurements,” Exp. Heat Transfer, 23(1), pp. 94–105. [CrossRef]
DeGroot, C. T., Gateman, D., and Straatman, A. G., 2010, “The Effect of Thermal Contact Resistance at Porous-Solid Interfaces in Finned Metal Foam Heat Sinks,” ASME J. Electron. Packag., 132(4), p. 041007. [CrossRef]
Howard, S. R., and Korinko, P. S., 2003, “Vacuum Furnace Brazing Open Cell Reticulated Foam to Stainless Steel Tubing,” 2nd International Brazing and Soldering Conference, San Diego, CA, pp. 2–9.
Boomsma, K., Poulikakos, D., and Zwick, F., 2003, “Metal Foams as Compact High Performance Heat Exchangers,” Mech. Mater., 35(12), pp. 1161–1176. [CrossRef]
Kamath, P. M., Balaji, C., and Venkateshan, S. P., 2013, “Convection Heat Transfer From Aluminium and Copper Foams in a Vertical Channel—An Experimental Study,” Int. J. Therm. Sci., 64, pp. 1–10. [CrossRef]
Kamath, P. M., Balaji, C., and Venkateshan, S. P., 2011, “Experimental Investigation of Flow Assisted Mixed Convection in High Porosity Foams in Vertical Channels,” Int. J. Heat Mass Transfer, 54(25–26), pp. 5231–5241. [CrossRef]
Phanikumar, M. S., and Mahajan, R. L., 2002, “Non-Darcy Natural Convection in High Porosity Metal Foams,” Int. J. Heat Mass Transfer, 45(18), pp. 3781–3793. [CrossRef]
Calmidi, V. V., 1998, “Transport Phenomena in High Porosity Metal Foams,” Ph.D. thesis, University of Colorado, Boulder, CO.
Boomsma, K., and Poulikakos, D., 2002, “The Effects of Compression and Pore Size Variations on the Liquid Flow Characteristics in Metal Foams,” ASME J. Fluids Eng., 124(1), pp. 263–272. [CrossRef]
Zhao, C. Y., Kim, T., Lu, T. J., and Hodson, H. P., 2001, “Thermal Transport Phenomena in Porvair Metal Foams and Sintered Beds,” Technical Report, Micromechanics Centre and Whittle Lab, Department of Engineering, University of Cambridge, Cambridge. Available at http://www.fuelcellmarkets.com/content/images/articles/white_paper8.pdf
Ji, X., and Xu, J., 2012, “Experimental Study on the Two-Phase Pressure Drop in Copper Foams,” Heat Mass Transfer, 48, pp. 153–164. [CrossRef]
Liu, J. F., Wu, W. T., Chiu, W. C., and Hsieh, W. H., 2006, “Measurement and Correlation of Friction Characteristic of Flow Through Foam Matrixes,” Exp. Therm. Fluid Sci., 30(4), pp. 329–336. [CrossRef]
Girlich, D., 2009, “Open Pore Metal Foam,” retrieved June 2011, http://www.m-pore.de/Download/CellMet-Veroeffentlichung_4_.pdf
Bhattacharya, A., Calmidi, V. V., and Mahajan, R. L., 2002, “Thermophysical Properties of High Porosity Metal Foams,” Int. J. Heat Mass Transfer, 45(5), pp. 1017–1031. [CrossRef]
Zukauskas, A. A., 1987, “Convective Heat Transfer in Cross Flow,” , S.Kakac, R. K.Shah, and W.Aung, eds., Wiley, New York.
Fiedler, T., Belova, I. V., and Murch, G. E., 2012, “Critical Analysis of the Experimental Determination of the Thermal Resistance of Metal Foams,” Int. J. Heat Mass Transfer, 55(15–16), pp. 4415–4420. [CrossRef]


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Fig. 1

Distribution of pore diameter for aluminium and copper foams of 10 mm thickness

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Fig. 2

Distribution of fiber diameter for aluminium and copper foams of 10 mm thickness

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Fig. 3

Comparison of pore diameter with data in literature

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Fig. 4

Front sectional view of the test section with the physical model

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Fig. 5

Simplified two dimensional model with the resistance network

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Fig. 6

Model prediction for data reported by Calmidi and Mahajan [3] and Cavallini et al. [15]

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Fig. 7

Reduction in Nusselt number with the presence of contact resistance

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Fig. 8

Model prediction with and without the presence of contact resistance for metal foams

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Fig. 9

Comparison of enhancement ratio with and without contact resistance

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Fig. 10

Agreement of model prediction with experiment for additional, independent data sets



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