THERMAL SCIENCE

International Scientific Journal

Santosh Kumar Sahu

,

Prasanta Kumar Das

,

Souvik Bhattacharyya

HOW GOOD IS GOODMAN'S HEAT-BALANCE INTEGRAL METHOD FOR ANALYZING THE REWETTING OF HOT SURFACES?

ABSTRACT
This paper discusses the application of heat-balance integral method for solving the conduction equation in a variety of rewetting problems. A host of rewetting problems for various geometry, convective boundary conditions and internal heat generation as well as for variable property has been solved by employing the method. Closed form expressions for rewetting velocity and temperature field in the hot solid have been obtained. Further, a unified solution methodology for different geometry and dimension of the problem has been derived. The results obtained agrees well with other analytical techniques namely, Winer-Hopf technique, separation of variables method as well as with the numerical ones. The predicted solutions exhibit a good agreement with experimental data as well. Additionally, an optimal linearization technique has been applied to analyze the effect of temperature dependent properties on the phenomena of rewetting. The results obtained and optimal linearization techniques have been compared and a good agreement has been obtained. All the studies made so far demonstrates the suitability of employing HBIM in the analysis of various rewetting problems.
KEYWORDS
rewetting, quenching, heat balance integral method, effective Biot number, analytical methods, optimal linearization
PAPER SUBMITTED: 2008-01-24
PAPER REVISED: 2008-08-04
PAPER ACCEPTED: 2008-09-25
DOI REFERENCE: https://doi.org/10.2298/TSCI0902097S
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2009, VOLUME 13, ISSUE Issue 2, PAGES [97 - 112]
REFERENCES
  1. Goodman, T. R., The Heat Balance Integral and Its Application to Problems Involving a Change of Phase, ASME J. Heat Transfer, 80 (1958), 2, pp. 335-342
  2. Duffey, R. B., Porthouse, D.T.C., The Physics of Rewetting in Water Reactor Emergency Core Cooling, Nuclear Engineering and Design, 25 (1973), 3, pp. 379-394
  3. Tien, C. L., Yao, L. S., Analysis of Conduction-Controlled Rewetting of a Vertical Surface, ASME J. Heat Transfer, 97 (1975), 2, pp. 161-165
  4. Blair, J. M., An Analytical Solution to a Two-Dimensional Model of the Rewetting of a Hot Dry Rod, Nuclear Engineering and Design, 32 (1975), 2, pp. 159-170
  5. Satapathy, A. K., Sahoo, R. K., Rewetting of an Infinite Slab with Uniform Heating under Quasi-Steady Conditions, ASME J. Heat Transfer, 124 (2002), 5, pp. 875-880
  6. Satapathy, A. K., Kar, P. K., Rewetting of an Infinite Slab with Boundary Heat Flux, Numerical Heat Transfer, Part A, 37 (2000), 1, pp. 87-99
  7. Arpaci, V. S., Conduction Heat Transfer, Addison-Wesley Publishing Company, London, 1966, p. 66, 161
  8. Sfeir, A. A., The Heat Balance Integral in Steady-State Conduction, ASME J. Heat Transfer, 98 (1976), 3, pp. 466-470
  9. Burmeister, L. C., Triangular Fin Performance by the Heat Balance Integral Method, ASME J. Heat Transfer, 101 (1979), 3, pp. 562-564
  10. Sahu, S. K., Das, P. K., Bhattacharyya, S., A Comprehensive Analysis of Conduction-Controlled Rewetting by the Heat Balance Integral Method, International Journal of Heat and Mass Transfer, 49 (2006), 25-26, pp. 4978-4986
  11. Duffey, R. B., Correlation between Effective Biot Number and Coolant Flow Rate, Private communication, 2006
  12. Duffey, R. B., Porthouse, D. T. C., The Physics of Rewetting in Water Reactor Emergency Core Cooling, Nuclear Engineering and Design, 25 (1973), pp. 379-394
  13. Yamanouchi, A., Effect of Core Spray Cooling in Transient State after Loss of Coolant Accident, J. Nucl. Sci. Tech. 5 (1968), 11, pp. 547-558
  14. Sun, K. H., Dix, G. E., Tien, C. L., Cooling of a Very Hot Vertical Surface by Falling Liquid Film, ASME J. Heat Transfer, 96 (1974), 2, pp. 126-131
  15. Sawan, M., Zaki, G., Temraz, H., A Three-Regions Rewetting Model with Heat Generation and Sub Cooling, Atomkernenergie, 34 (1979), 1, pp. 199-204
  16. Sawan, M., Temraz, H., A Three-Region Semi-Analytical Rewetting Model, Nuclear Engineering and Design, 64 (1981), 3, pp. 319-327
  17. Bonakdar, H., McAssey Jr., E. V., A Method for Determing Rewetting Velocity under Generalized Boiling Conditions, Nuclear Engineering and Design, 66 (1981), 1, pp. 7-12
  18. Sahu, S. K., Das,P. K., Bhattacharyya, S., A Three-Region Conduction-Controlled Rewetting Analysis by the Heat Balance Integral Method, International Journal of Thermal Sciences, (2009), in press
  19. Hsu, C.-H., Chieng, C.-H., Hua, T., Two-Dimensional Analysis of Conduction-Controlled Rewetting with Internal Heat Generation, Proceedings, 4th International Conference on Numerical Methods in Engineering, Montreal, Canada, 1983
  20. Salcuden, M., Bui, T. M., Heat Transfer During Rewetting of Hot Horizontal Channels, Trans. Nuclear Engineering Design, 59 (1988), 2, pp. 323-330
  21. Sun, K. H., Dix, G. E., Tien, C. L., Effect of Precursory Cooling on Falling-Film Rewetting, Trans. ASME, J. Heat Transfer, 97 (1975), 3, pp. 360-365
  22. Dua, S. S., Tien, C. L., Two Dimensional Analysis of Conduction-Controlled Rewetting with Precursory Cooling, ASME J. Heat Transfer, 98 (1976), 3, pp. 407- 413
  23. Olek, S., The Effect of Precursory Cooling on Rewetting of Slab, Nuclear Engineering Design, 108 (1988), 3, pp. 323-330
  24. Olek, S., Wiener-Hopf Technique Solution to a Rewetting Model with Precursory Cooling, Nuclear Science and Engineering, 105 (1990), 2, pp. 271-277
  25. Sahu, S. K., Das, P. K., Bhattacharyya, S., Rewetting Analysis of Hot Vertical Surfaces with Precursory Cooling by the Heat Balance Integral Method, ASME Journal of Heat Transfer, 130 (2008), 3, 024504
  26. Yao, L. S., Rewetting of a Vertical Surface with Internal Heat Generation, AIChe Symposium Series: Solar and Nuclear Heat Transfer, 73 (1976), 164, pp. 46-50
  27. Peng, X. F., Peterson, G. P., Analysis of Rewetting for Surface Tension Induced Flow, ASME J. Heat Transfer, 114 (1992), 3, pp. 703-707
  28. Duffey, R. B., Hughes, E. D., Dry Out Stability and Inception at Low Flow Rates, International Journal of Heat and Mass Transfer, 34 (1991), 2, pp. 473-481
  29. Sawan, M., Zaki, G., Temraz, H., Analysis of Rewetting of Hot Cladding Surfaces with Heat Generation, Arab Journal of Nuclear Science and Applications, 11 (1978), 2, pp. 237-259
  30. Chan, S. H., Zhang, W., Rewetting Theory and the Dryout Heat Flux of Smooth and Grooved Plates with Uniform Heating, ASME J. Heat Transfer, 116 (1994), 1, pp. 173-179
  31. Sahu, S. K., Das, P. K., Bhattacharyya, S., Rewetting Analysis of Hot Surfaces with Internal Heat Source by the Heat Balance Integral Method, Heat and Mass Transfer, 44 (2008), 10, pp. 1247-1256
  32. Olek, S., Zvirin, Y., The Effect of Temperature Dependent Properties on the Rewetting Velocity, Int. J. Multiphase Flow, 11 (1985), 4, pp. 577-581
  33. Schlichting, H., Boundary Layer Theory, 6th ed., McGraw Hill, New York, USA, 1968, p. 144
  34. Mosally, F., Wood, A. S., Al-Fhaid, A., An Exponential Heat Balance Integral Method, Applied Mathematics and Computation, 130 (2002), 10, pp. 87-100
  35. West, J. C., Analytical Techniques for Nonlinear Control Systems, London, 1960
  36. Blaquiere, A., New Method for Local Linearization of Non-Linear Operators: Optimal Approximation, Proceedings, 2nd Conference on Non-Linear Vibrations, Warsaw, 1962
  37. Vujanovic, B., Application of the Optimal Linearization Method to the Heat Transfer Problem, Int. J. Heat and Mass Transfer, 16 (1972), 6, pp. 1111-1117
  38. Iwan, W. D., Patula, E. J., The Merit of Different Error Minimization Criteria in Approximate Analysis, ASME Journal of Applied Mechanics, 39 (1971), 1, pp. 257-262
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How good is Goodman's heat-balance integral method for analyzing the rewetting of hot surfaces?

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