International Scientific Journal

Authors of this Paper

External Links


Helical flows of generalized Maxwell fluid is researched between two infinite co-axial circular cylinders. The velocity field and the adequate shear stress corresponding to the flow of a Maxwell fluid with fractional derivative model, between two infinite coaxial cylinders, are determined by means of the Laplace and finite Hankel transforms. The first solutions that have been obtained, presented under integral and series form in terms of the generalized G- and R-functions, satisfy all imposed initial and boundary conditions. The similar solutions for ordinary Maxwell and Newtonian fluid can be also obtained as the limit of the solution of generalized Maxwell fluid.
PAPER REVISED: 2021-07-26
PAPER ACCEPTED: 2021-07-29
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2022, VOLUME 26, ISSUE Issue 2, PAGES [1113 - 1121]
  1. Batchelor, G. K., An Introduction to fluid dynamics, Cambridge University Press, Cambridge, UK, 1967
  2. Ting, T. W., Certain Non-Steady flows of Second-Order fluids, Archive for Rational Mechanics and Analysis, 14 (1963), 1, pp. 1-26
  3. Srivastava, P. N., Non-Steady Helical Flow of a Viscoelastic Liquid, Archiwum Mechaniki Stosowanej, 18 (1966), 1, pp. 145-150
  4. Casarella, M. J., et al., Drag on an Oscillating Rod with Longitudinal and Torsional Motion, Journal of Hydronautics, 3 ( 2012), 4, pp. 180-183
  5. Rajagopal, K. R., Longitudinal and Torsional Oscillations of a Rod in a Non-Newtonian Fuid, Acta Mechanica, 49 (1983), 3, pp. 281-285
  6. Rajagopal, K. R., et al., Exact Solutions for Some Simple flows of an Oldroyd-B fluid, Acta Mechanica, 113 (1995), 1-4, pp. 233-239
  7. Khan, M., et al., Oscillating Flow of a Burgers Fluid in a Pipe, Abdus Salam International Center for Theoretical Physics, No. IC/2005/071
  8. Rajagopal, K. R., A Note on Unsteady Unidirectional flows of a Non-Newtonian Fluid, International Journal of Non-Linear Mechanics, 17 (1982), 5-6, pp. 369-373
  9. Fetecau, C., et al., Starting Solutions for the Motion of a Second Grade Fluid Due to Longitudinal and Torsional Oscillations of a Circular Cylinder, International Journal of Engineering Science, 44 (2006), 11-12, pp. 788-796
  10. Yang, X.-J., New Rheological Problems Involving General Fractional Derivatives with Non-Singular Power-Law Kernels, Proceedings of the Romanian Academy-Series A, 19 (2018), 1, pp. 45-52
  11. Yang, X.-J., et al., General Fractional Derivatives with Applications in Viscoelasticity, Academic Press, New York, USA, 2020
  12. Huilgol, R. R., et al., Fluid Mechanics of Viscoelasticity, Elsevier, New York, USA, 1997
  13. Yu, Z. S., et al., Numerical Research on the Coherent Structure in the Viscoelastic Second-Order Mixing Layers, Applied Mathmatics and Mechanics, 19 (1998), 8, pp. 717-723
  14. Rivlin, R. S., Solution of Some Problems in the Exact Theory of Visco-Elasticity, Archive for Rational Mechanics and Analysis, 5 (1956), 2, pp. 179-188
  15. Coleman, B.-N. W., Helical Flow of General fluid, Journal of Applied Physics, 30 (1959), 2, pp. 1508-1512
  16. Wood, W. P., Transient Viscoelastic Helical flows in Pipes of Circular and Annular Cross-Section, Journal of Non-Newtonian Fluid Mechanics, 100 ( 2001), 1-3, pp. 115-126
  17. Fetecau, C., et al., Unsteady Helical flows of a Maxwell Fluid, Proceedings of the Romanian Academy Series A, 5 (2004), 1, pp. 13-19
  18. Tong, D., et al., Exact Solutions for the Flow of Non-Newtonian Fluid with Fractional Derivative in an Annular Pipe, Science in China Series G (Physics, Mechanics and Astronomy), 48 (2005), 4, pp. 485-495
  19. Hilfer, R., Applications of Fractional Calculus in Physics, World Scientific, Singapore, 2000
  20. Truesdell, C., et al., The Non-Linear Field Theories of Mechanics, Encyclopedia of Physics. III/3, Springer, Heidelberg, Berlin, Germany, 1965
  21. Lorenzo, C. F., et al., Generalized Functions for the Fractional Calculus, NASA/TP-1999-209424/Rev1, 1999
  22. Polyanin, A. D., et al., Handbook of Integral Equations, CRC Press, Boca Raton, Fla., USA, 1998
  23. Sneddon, I. N., Functional analysis, Encyclopedia of physics, vol. II., Springer-Heidelberg, Berlin, Ger-many, 1955
  24. Wang, F., et al., The Analytic Solutions for the Unsteady Rotation Flows of the Generalized Maxwell Fluid Between Coaxial Cylinders, Thermal Science, 24 (2020), 6B, pp. 4041-4048

© 2023 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