THERMAL SCIENCE

International Scientific Journal

Branislav Bačlić

,

Dušan D. Gvozdenac

,

Gordan Dragutinović

EASY WAY TO CALCULATE THE ANZELIUS — SCHUMANN J FUNCTION

ABSTRACT
The paper deals with the computational aspects of the so called Anzelius function. This special function is the fundamental one for describing the kinetics of a fixed-bed adsorber and is widely used on the theory of : breakthrough curves not only in adsorption and ion exchange, but in the other operations with isomorphous mathematical models as well. Instead of the use of graphical and tabular presentations of the numerical values of this function (what is common practice in chemical engineering literature) the paper proposes a simple algorithm as an alternative for its evaluation. The algorithm is very efficient and extremely accurate for entire range of parameters of interest.
PUBLISHED ONLINE: 2020-09-27
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 1997, VOLUME 1, ISSUE Issue 1, PAGES [109 - 116]
REFERENCES
  1. Anzelius, A., Über Erwärmung vermittels durchströmender Medien, Z. angew. Math. Mech., 6 (1926), pp. 291-294
  2. Schumann, T. E. W., Heat Transfer: A Liquid Flowing through a Porous Prism, J. Franklin Institute, 208 1929, pp. 405-416,
  3. Vermeulen, T., Klein, G., Heister, N. K., Section 16 in Chemical Engineers' Handbook (Ed. J. H. Perry). McGraw-Hill, New York, 1973
  4. Sherwood, T. K., Pigford, R. L., Wilke, C. R., Mass Transfer, McGraw -Hill, New York, 1975
  5. Liaw, C. H., Wang, J. S. P., Greenkorn, R. A., Chao, K. C., Kinetics of Fixed-Bed Adsorption: A New Solution, AIChE J., 25 (1979), pp. 376-381
  6. Goldstein, S.,On the Mathematics of Exchange Processes in Fixed Columns: I. Mathematical Solutions and Asymptotic Expansions, Proc. Royal Society, A 219, London, 1953, pp. 151-185
  7. Klinkerberg, A., Heat Transfer in Cross-Flow Heat Exchangers and Packed Beds, Ind. Eng. Chem., 46 (1954), pp. 2285-2289
  8. Korol'kov, B. P., Special Functions for Investigation of Transient Heat Transfer, (in Russian), Nauka, Moscow, 1976
  9. Parl, S., A New Method for Calculating the Generalized Q Function, JEEE Trans. Inform. Theory IT-26, 1980, pp. 121-124
  10. Rosen, J. B., Kinetics of a Fixed-Bed System for Solid Diffusion into Spherical Particles, J. Chem. Phys., 20 (1952), p. 387 |
  11. Camp, D. T., Letter to the Editor, AIChE J. 26 (1980), p. 333
  12. Rice, R. G., Letter to the Editor, AIChE J. 26 (1980), p. 334
  13. Tien, C., Letter to the Editor, AIChE J. 26 (1980), p. 334
  14. Heister, N. K., Vermeulen, T., Saturation Performance of lon-Exchange and Adsorption Columns, Chem. Eng. Progress, 48 (1952), pp. 505-516
  15. Vermeulen, T., Heister, N. K., lon-Exchange Chromatography of Trace Components, Ind. Eng. Chem., 44 (1952), pp. 636-651
  16. Hougen, O. A., Marshall, Jr., W. R., Adsorption from a Fluid Stream Flowing through a Stationary Granular Bed, Chem. Eng. Progress, 43 (1947), pp. 197-208
  17. Kast, W., Adsorption aus der Gasphase - Grundlagen und Verfahren, Chem.-Ing.-Tech. 53 (1981), pp. 160-172
  18. Cooney, D. O., Column Configuration and Performance in Fixed-Bed Ion Exchange Systems, Ind. Eng. Chem. Fundam.., 6 (1967), 1959
  19. Bird, R. B., Stewart, W. E., Lightfoot, E. N., Transport Phenomena, Wiley, New York, 1960, pp. 702—705
  20. Thomas, H.C., Chromatography: A Problem in Kinetics, Annals New York Academy of Sciences, 49 (1948), pp. 161-182
  21. Kyte, W.S., Non-linear Adsorption in Fixed Beds: The Freundlich Isotherm, Chem. Engng Sci., 28 ( 1973), pp. 1853-1856
  22. Thomas, H. C., Heterogeneous Ion Exchange in Flowing System, J. Amer. Chem. Soc., 66 (1944), pp. 1664-1666
  23. Carslaw H. S., Jaeger, J. C., Conduction of Heat in Solids, 2nd Edition, Oxford University Press, London, 1959
  24. Romie, F. E., Periodic Thermal Storage: The Regenerator, Trans. ASME, Journal of Heat Transfer, 101 (1979), pp. 726-731
  25. Romie, F. E., Transient Response of Gas-to-Gas Crossflow Heat Exchangers with Neither Gas Mixed, Trans. ASME, Journal of Heat Transfer, 105 (1983), pp. 563-570
PDF VERSION [DOWNLOAD]
EASY WAY TO CALCULATE THE ANZELIUS — SCHUMANN J FUNCTION

© 2024 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence