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AN INTEGRAL TRANSFORM SOLUTION FOR UNSTEADY COMPRESSIBLE HEAT TRANSFER IN FLUIDS NEAR THEIR THERMODYNAMIC CRITICAL POINT

ABSTRACT
The classical thermodynamic model for near critical heat transfer is an integral-differential equation with constant coefficients. It is similar to the heat equation, except for a source term containing the time derivative of the bulk temperature. Despite its simple form, analytical methods required the use of approximations to generate solutions for it, such as an approximate Fourier transformation or a numerical Laplace inversion. Recently, the Generalized Integral Transform Technique or GITT has been successfully applied to this problem, providing a highly accurate analytical solution for it and a new expression of its relaxation time. Nevertheless, very small temperature differences, on the order of mK, have to be imposed so that constant thermal properties can be assumed very close to the critical point. The present paper generalizes this study by relaxing its restriction and accounting for the strong dependence on temperature and pressure of supercritical fluid properties, demonstrating that a) the GITT can be applied to realistic nonlinear unsteady compressible heat transfer in fluids with diverging thermal properties and b) temperature and pressure have opposite effects on all properties, but their variation causes no additional thermo-acoustic effect, increasing the validity range of the constant property model.
KEYWORDS
PAPER SUBMITTED: 2012-08-26
PAPER REVISED: 2013-01-08
PAPER ACCEPTED: 2013-04-24
PUBLISHED ONLINE: 2013-06-16
DOI REFERENCE: https://doi.org/10.2298/TSCI120826068D
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2013, VOLUME 17, ISSUE 3, PAGES [673 - 686]
REFERENCES
  1. Carlès, P., A brief review of the thermophysical properties of supercritical fluids, The Journal of Supercritical Fluids, 53 (2010), pp. 2-11.
  2. Nitsche, K. and Straub, J., The critical hump of under microgravity, results from d-spacelab experiment, Proceedings of the 6th European Symposium on Material Sciences under Microgravity Conditions, ESA SP-256, 1987.
  3. Onuki, A., Hao, H., Ferrell, R. A., Fast adiabatic equilibration in a single-component fluid near the liquid-vapor critical point, Physical Review A, 41 (1990) 4, pp. 2256-2259.
  4. Boukari, H., et al., Critical speeding up in pure fluids, Phys. Rev. A, 41 (1990) 4, pp. 2260-2263.
  5. Onuki, A., Ferrell, R. A., Adiabatic heating effect near the gas-liquid critical point, Physica A, 164 (1990), pp. 245-264.
  6. Zappoli, B., et al., Anomalous heat transport by the piston effect in supercritical fluids under zero gravity, Physical Review A, 41 (1990) 4, pp. 2264-2267.
  7. Ferrell, R.A., Hao, H., Adiabatic temperature changes in a one-component fluid near the liquid-vapor critical point, Physica A, 197 (1993), pp. 23-46.
  8. Garrabos, Y., et al., Relaxation of a supercritical fluid after a heat pulse in the absence of gravity effects: Theory and experiments, Physical Review E, 57 (1998) 5, pp. 5665-5681.
  9. Carlès, P., et al., Temperature and density relaxation close to the liquid-gas critical point: An analytical solution for cylindrical cells, Physical Review E, 71 (2005), p. 041201.
  10. Alves, L. S. de B., Unsteady Compressible Heat Transfer in Supercritical Fluids, Proceedings of ENCIT, 14th Brazilian Congress of Thermal Sciences and Engr., Rio de Janeiro, RJ, Brazil, 2012.
  11. Teixeira, P. C., Alves, L. S. de B., Piston Effect Characteristic Time Dependence on Equation of State Model Choice, ICHMT, Int. Symp. on Adv. in Comp. Heat Transfer, Bath, England, 2012.
  12. Masuda, Y., et al., One dimensional heat transfer on the thermal diffusion and piston effect of supercritical water, International Journal of Heat and Mass Transfer, 45 (2002), pp. 3673-3677.
  13. Zappoli, B., The response of a nearly supercritical pure fluid to a thermal disturbance, Physics of Fluids, 4 (1992) 5, pp. 1040-1048.
  14. Carlès, P., Zappoli, B., The unexpected response of near-critical fluids to low-frequency vibrations, Physics of Fluids, 7 (1995) 11, pp. 2905-2914.
  15. Carlès, P., The effect of bulk viscosity on temperature relaxation near the critical point, Physics of Fluids, 10 (1998) 9, pp. 2164-2176.
  16. Cotta, R. M., Integral Transforms in Computational Heat and Fluid Flow, CRC Press, Boca Raton, FL, USA, 1993.
  17. Özisik, M. N., Heat Conduction, 2nd ed., Wiley Interscience, New York, NY, USA, 1993.
  18. Cotta, R. M., The Integral Transform Method in Thermal and Fluids Science and Engineering, Begell House, Inc., New York, NY, USA, 1998.
  19. Alves, L. S. de B., Cotta, R. M., Transient natural convection inside porous cavities: hybrid numerical- analytical solution and mixed symbolic-numerical computation, Numerical Heat Transfer, Part A - Applications, 38 (2000), pp. 89-110.
  20. Alves, L. S. de B., Cotta, R. M., Mikhailov, M. D., Covalidation of hybrid inte- gral transforms and method of lines in nonlinear convection-diffusion with Mathematica, Journal of the Brazilian Society of Mechanical Sciences, 23 (2001), pp. 303-320.
  21. Alves, L. S. de B., Cotta, R. M., Pontes, J., Stability analysis of natural convection in porous cavities through integral transforms, International Journal of Heat and Mass Transfer, 45 (2002), pp. 1185-1195.
  22. Wolfram, S., The Mathematica book, 5th ed., Wolfram Media, Cambridge University Press, New York, NY, USA, 2003.
  23. Shen, B., Zhang, P., On the transition from thermoacoustic convection to diffusion in a near-critical fluid, International Journal of Heat and Mass Transfer, 53 (2010), pp. 4832-4843.

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