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Direct and Inverse Problems Solutions in Micro-Scale Forced Convection

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Microfluidics Based Microsystems

Abstract

The analysis of internal flows in the slip-flow regime gained an important role along the last two decades in connection with micro-electromechanical systems (MEMS) applications and in the thermal control of microelectronics, as reviewed in different sources [1–5].

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References

  1. P. Tabeling, Introduction a la Microfluidique, Belin, Collection Échelles, Paris (2003).

    Google Scholar 

  2. G. Karniadakis, A. Beskok, and N. Aluru, Microflows and Nanoflows: Fundamentals and Simulation, Springer, NY (2005).

    Google Scholar 

  3. Y. Yener, S. Kakaç, M.R. Avelino, and T. Okutucu, Single-phase Forced Convection in Micro-channels - a State-of-the-art Review, in: S. Kakaç, L.L. Vasiliev, Y. Bayazitoglu, Y. Yener. (Eds.), Microscale Heat Transfer - Fundamentals and Applications, NATO ASI Series, Kluwer Academic Publishers, The Netherlands, pp. 1–24 (2005).

    Chapter  Google Scholar 

  4. R.W. Barber and D.R. Emerson, Challenges in Modeling Gas-Phase Flow in Microchannels: From Slip to Transition, Heat Transfer Eng., V. 27, no. 4, pp. 3–12 (2006).

    Article  ADS  Google Scholar 

  5. C.B. Sobhan and G.P. Peterson, Microscale and Nanoscale Heat Transfer: Fundamentals and Engineering Applications, CRC Press, FL (2008).

    Google Scholar 

  6. M.D. Mikhailov and R.M. Cotta, Mixed Symbolic-Numerical Computation of Convective Heat Transfer with Slip Flow in Microchannels, Int. Comm. Heat & Mass Transfer, Vol. 32, ssues 3-4, pp. 341–348 (2005).

    Article  Google Scholar 

  7. R.M. Cotta, M.D. Mikhailov, and S. Kakaç, Steady and Periodic Forced Convection in Microchannels, NATO Science Series II: Microscale Heat Transfer: Fundamentals and Applications, V. 193, S. Kakaç et al. (eds.), pp. 49–74 (2005).

    Google Scholar 

  8. S. Yu and T.A. Ameel, Slip Flow Heat Transfer in Rectangular Microchannels, Int. J. Heat Mass Transfer, Vol. 44, pp. 4225–4234 (2001).

    Article  MATH  Google Scholar 

  9. G. Tunc and Y. Bayazitoglu, Heat Transfer in Microtubes with Viscous Dissipation, Int. J. Heat Mass Transfer, Vol. 44, pp. 2395–2403 (2001).

    Article  MATH  Google Scholar 

  10. G. Tunc and Y. Bayazitoglu, Heat Transfer in Rectangular Microchannels, Int. J. Heat Mass Transfer, Vol. 45, pp. 765–773 (2002).

    Article  MATH  Google Scholar 

  11. F.V. Castellões and R.M. Cotta, Analysis of Transient and Periodic Convection in Micro-channels via Integral Transforms, Progress in Computational Fluid Dynamics, Vol. 6, 321–326 (2006).

    Article  MATH  Google Scholar 

  12. F.V. Castellões, C.R. Cardoso, P. Couto, and R.M. Cotta, Transient Analysis of Slip Flow and Heat Transfer in Microchannels, Heat Transfer Engineering, Vol. 28, 549–558 (2007).

    Article  ADS  Google Scholar 

  13. C.P. Naveira-Cotta, R.M. Cotta, H.R.B. Orlande, and O. Fudym, Eigenfunction Expansions for Transient Diffusion in Heterogeneous Media, Int. J. Heat and Mass Transfer, Vol. 52, pp. 5029–5039 (2009).

    Article  MATH  Google Scholar 

  14. M.D. Mikhailov and M.N. Ozisik, Unified Analysis and Solution of Heat and Mass Diffusion, John Wiley, NY (1994); also, Dover Publications (1993).

    Google Scholar 

  15. R.M. Cotta, Integral Transforms in Computational Heat and Fluid Flow, CRC Press, USA (1993).

    MATH  Google Scholar 

  16. R.M. Cotta and M.D. Mikhailov, Heat Conduction: Lumped Analysis, Integral Transforms, Symbolic Computation, Wiley-Interscience, NY (1997).

    Google Scholar 

  17. R.M. Cotta, The Integral Transform Method in Thermal and Fluids Sciences and Engineering, Begell House, New York (1998).

    MATH  Google Scholar 

  18. R.M. Cotta and M.D. Mikhailov, Hybrid Methods and Symbolic Computations, in: W.J. Minkowycz, E.M. Sparrow, and J.Y. Murthy (Eds.), Handbook of Numerical Heat Transfer, 2nd ed., Wiley, NY, pp. 493–522 (2006).

    Google Scholar 

  19. M.D. Mikhailov and R.M. Cotta, Integral Transform Method for Eigenvalue Problems, Comm. Num. Meth. Eng., Vol. 10, pp. 827–835 (1994).

    Article  MathSciNet  MATH  Google Scholar 

  20. M.C. Oliveira, R. Ramos, and R.M. Cotta, On the Eigenvalues Basic to the Analytical Solution of Convective Heat Transfer with Axial Diffusion Effects, Comm. Num. Meth. Eng., Vol. 11, pp. 287–296 (1995).

    Article  MATH  Google Scholar 

  21. L.A. Sphaier and R.M. Cotta, Integral Transform Analysis of Multidimensional Eigenvalue Problems Within Irregular Domains, Num. Heat Transfer, Part B-Fundamentals, Vol. 38, pp. 157–175 (2000).

    Article  ADS  Google Scholar 

  22. Agrawal and S.V. Prabhu, Survey on Measurement of Tangential Momentum Accommodation Coefficient, J. Vac. Sci. Technol. A, Vol. 26, Issue 4, pp. 634–645 (2008).

    Google Scholar 

  23. E.B. Arkilic, K.S. Breuer, and M.A. Schmidt, Mass Flow and Tangential Momentum Accommodation in Silicon Micromachined Channels, J. Fluid Mech., V. 437, pp. 29–43 (2001).

    ADS  Google Scholar 

  24. S.S. Hsieh, H.H. Tsai, C.Y. Lin, C.F. Huang, and C.M. Chien, Gas Flow in a Long Micro-channel, Int. J. Heat & Mass Transfer, Vol. 47, pp. 3877–3887 (2004).

    Article  Google Scholar 

  25. D.J. Rader, W.M. Trott, J.R. Torczynski, J.N. Castañeda, and T.W. Grasser, Measurements of Thermal Accommodation Coefficients, Report SAND2005-6084, Sandia National Laboratories, Albuquerque (2005).

    Book  Google Scholar 

  26. J. Beck and K. Arnold, Parameter Estimation in Engineering and Science, Wiley Interscience, New York (1977).

    MATH  Google Scholar 

  27. M.N. Ozisik and H.R.B. Orlande, Inverse Heat Transfer: Fundamentals and Applications, Taylor and Francis, New York (2000).

    Google Scholar 

  28. J. Kaipio and E. Somersalo, Statistical and Computational Inverse Problems, Springer-Verlag (2004).

    Google Scholar 

  29. D. Gamerman and H.F. Lopes, Markov Chain Monte Carlo: Stochastic Simulation for Bayesian Inference, Chapman & Hall/CRC, 2nd edition, FL (2006).

    MATH  Google Scholar 

  30. O. Fudym, H.R.B. Orlande, M. Bamford, and J.C. Batsale, Bayesian Approach for Thermal Diffusivity Mapping from Infrared Images Processing with Spatially Random Heat Pulse Heating, Journal of Physics. Conference Series (Online), v. 135, p. 012–042 (2008).

    Google Scholar 

  31. S. Wolfram, The Mathematica Book, version 7.0, Cambridge-Wolfram Media (2008).

    Google Scholar 

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Acknowledgements

The authors would like to acknowledge the partial financial support provided by CNPq, CAPES and FAPERJ, Brazilian agencies for the fostering of sciences.

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Correspondence to R. M. Cotta .

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Naveira-Cotta, C.P., Cotta, R.M., Orlande, H.R.B., Kakaç, S. (2010). Direct and Inverse Problems Solutions in Micro-Scale Forced Convection. In: Kakaç, S., Kosoy, B., Li, D., Pramuanjaroenkij, A. (eds) Microfluidics Based Microsystems. NATO Science for Peace and Security Series A: Chemistry and Biology. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-9029-4_3

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