ABSTRACT Heat transfer to pins swimming in non-isothermal fluidic systems is theoretically analyzed. Four different cases are considered: [A] pins aligned longitudinally in flowing fluid having constant temperature gradient, [B] pins aligned transversely in flowing fluid flow with constant temperature gradient, [C] pins moving longitudinally towards a heated surface, and [D] pins moving transversely towards the heated surface. The Appropriate unsteady energy transport equations are solved and closed form solutions for the fin temperatures are obtained. Accordingly, different performance indicators are calculated. It is found that heat transfer to the swimming fin increases as the fin thermal length, Peclet number and fluid temperature difference along the fin length increase. It decreases as fluid temperature index along the motion direction increases. Moreover, the swimming pins of case C are found to produce the maximum system effective thermal conductivity. In addition, pins of case B with thermal lengths above 11 produce system thermal conductivity independent on the thermal length. Meanwhile, pins of case A having thermal lengths above 10 produce system thermal conductivities less responsive to the thermal length. The system thermal conductivity is noticed to increase as the thermal length and Peclet number increase. Eventually, pins of case D produce system thermal conductivities that are independent on the transverse temperature. Finally, the results of this work provide a basis for modeling super convective fluidic systems that can be used in cooling of electronic components.
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nullKhaled, A. (2011) Enhancement of Heat Transfer Using Pins Swimming in Non-isothermal Fluidic Systems: Exact Solutions. Journal of Electronics Cooling and Thermal Control, 1, 1-13. doi: 10.4236/jectc.2011.11001.
 W. M. Kays, “Pin-fin Heat-exchanger Surfaces”, Journal of Heat Transfer-Transactions of the ASME, Vol. 77, 1955, pp. 471-483.
 D. O. Kern and A. D. Kraus, “Extended Surface Heat Transfer”, McGraw-Hill, New York, 1972.
 A. D. Kraus, A. Aziz, and J. R. Welty, “Extended Surface Heat Transfer”, John Wiley & Sons, Inc. New York, 2001.
 A. Nuntaphan, T. Kiatsiriroat and C. C. Wang, “Air Side Performance at Low Reynolds Number of Cross-flow Heat Exchanger using Crimped Spiral Fins”, International Communications in Heat and Mass Transfer, Vol. 32, Issue 1-2, 2005, pp. 151-165.
 X. –Q. Wang and A. S. Mujumdar, “Heat Transfer Characteristics of Nanofluids: A Review”, International Journal of Thermal Sciences, Vol. 46, Issue 1, 2007, pp. 1-19.
 A. E. Bergles, “Handbook of Heat Transfer-3rd edition”, McGraw-Hill, New York, pp. 11.1-11.76, 1998.
 D.-K. Yang, K.-S. Lee and S. Song, “Fin Spacing Optimization of a Fin-tube Heat Exchanger Under Frosting Conditions”, International Journal of Heat and Mass transfer, Vol. 49, Issue 15-16, 2006, pp. 2619-2625.
 N. Sahiti, A. Lemouedda, D. Stojkovic, F. Durst and S. Franz, “Performance Comparison of Pin Fin In-duct Flow Arrays with Various Pin Cross-sections”, Applied Thermal Engineering, Vol. 26, Issue 11-12, 2006, pp. 1176- 1192.
 M. Almogbel and A. Bejan, “Cylindrical Trees of Pin Fin”, International Journal of Heat and Mass Transfer, Vol. 43, Issue 23, 2000, pp. 4285-4297.
 M. Almogbel, “Constructal Tree-shaped Fins”, International Journal of Thermal Sciences, Vol. 44, Issue 4, 2005, pp. 342-348.
 L. Li, W. Cui, Q. Liao, X. Mingdao, T-C. Jen, Q. Chen, “Heat Transfer Augmentation in 3D Internally Finned and Microfinned Helical Tube”, International Journal of Heat and Mass Transfer, Vol. 48, 2005, pp. 1916-1925.
 S. Kiwan and M. A. Al-Nimr, “Using Porous Fin for Heat Transfer Enhancement”, Journal of Heat Transfer-Transactions of the ASME, Vol. 123, Issue 4, 2001, pp. 617-623.
 T. K. Aldoss, M. A. Al-Nimr and M. Hader, “Using Capsulated Liquid Metal Fins for Heat Transfer Enhancement”, Journal of Enhanced Heat Transfer, Vol. 11, Issue 2, 2004, pp. 151-160.
 A.-R. A. Khaled, “Maximizing Heat Transfer Through Joint Fin Systems”, Journal of Heat Transfer-Transactions of The ASME, Vol. 128, 2006, Issue 2, pp. 203-206.
 A.-R. A. Khaled, “Investigation of Heat Transfer Enhancement Using Permeable Fins, Journal of Heat Transfer-Transactions of ASME, Vol. 132, 2010, Issue 3, Article no. 034503, pp. 1-5.
 A.-R. A. Khaled, “Heat Transfer Analysis through Solar and Rooted Fins”, Journal of Heat Transfer-Transactions of the ASME, Vol. 130, Issue 8, 2008, Article no. 74503, pp. 1-4..
 A.-R. A. Khaled, “Thermal Characterizations of Fin-Thin Film Systems”, Journal of Heat Transfer-Transactions of the ASME, Vol. 132, Issue 10, 2010, Article no. 104503, pp. 1-6.
 J. A. Eastman, S. U. S. Choi, S. Li, W. Yu and L. J. Thompson, “Anomalously Increased Effective Thermal Conductivities of Ethylene Glycol-based Nanofluids Containing Copper Nanoparticles”, Applied Physics Letters, Vol. 78, Issue 6, 2001, pp. 718-720.
 Y. Xuan and Q. Li, “Investigation on Convective Heat Transfer and Flow Features of Nanofluids”, Journal of Heat Transfer – Transactions of The ASME, Vol. 125, Issue 1, 2003, pp. 151-155.
 M. Siddique, A.-R. A.Khaled, N. I. Abdulhafiz and A. Y. Boukhary, “Recent Advances in Heat Transfer Enhancements: A Review Report”, International Journal of Chemical Engineering, Vol. 2010, 2010, Article ID 106461, pp.1-28.
 F. P. Incorpera, D. P. DeWitt, T. L. Bergman, and A. S. Lavine, “Fundamentals of Heat and Mass Transfer-6th Edition”, John Wiley, New York, 2006.
 M. N. Ozisik, “Heat Conduction-2nd edition”, John Wiley & Sons, Inc., New York, pp. 97-98, 1993.
 A.-R. A. Khaled and K. Vafai, “Heat Transfer Through Control of Thermal Dispersion Effects”, International Journal of Heat and Mass Transfer, Vol. 48, Issue 11, 2005, pp. 2172-2185.