Study of oscillating flow of viscoelastic fluid with the fractional Maxwell model

Journal of Fluids Engineering, Transactions of the ASME

Volumn 130, Issue 4, 2008, Pages 0412011-0412014

  Jia, Jiu Hong ^a   Hua, Hong Xing ^a  

^a SHANGHAI JIAO TONG UNIVERSITY   (China)

Author keywords

Fractional derivative Maxwell model; Oscillating flow; Pipe flow; Richardson annular effect; Viscoelastic fluid

Indexed keywords

MAXWELL EQUATIONS; PETROLEUM CHEMISTRY; POLYNOMIAL APPROXIMATION; PRESSURE GRADIENT; STEADY FLOW;

CENTER LINES; CYLINDRICAL PIPES; EXACT SOLUTIONS; FLOW REVERSALS; FRACTIONAL DERIVATIVES; MAXWELL MODELS; MODEL PARAMETERS; OSCILLATING FLOWS; OSCILLATING FREQUENCIES; PHASE LAGS; POISEUILLE FLOWS; SERIES APPROXIMATIONS; VELOCITY PROFILING; VISCO-ELASTIC FLUIDS;

CRUDE PETROLEUM;

EID: 47049123515     PISSN: 00982202     EISSN: None     Source Type: Journal    
DOI: 10.1115/1.2903517     Document Type: Article

References (18)

1. Gorla, R. S. R., 1981, "Unsteady Thermal Boundary Layer Flow of a Non-Newtonian Fluid Over a Flat Plate," Int. J. Eng. Sci., 19, pp. 1391-1399.
2. Rahaman, K. D. and Ramkissoon, H., 1995, "Unsteady Axial Viscoelastic Pipe Flows," J. Non-Newtonian Fluid Mech., 57, pp. 27-28.
3. Andrienko, Yu. A., Siginer, D. A., and Yanovsky, Yu. G., 2000, "Resonance Behavior of Viscoelastic Fluids in Poiseuille Flow and Application to Flow Enhancement," Int. J. Non-Linear Mech., 35, pp. 9-102.
4. Makris, N., 1991, "Theoretical and Experimental Investigation of Viscous Dampers in Applications of Scismic and Vibration Isolation [D]," State University of New York at Buffalo, Buffalo, N. Y.
5. Dao, Y. S., and Ti, Q. J., 1998, "Study on the Constitutive Equation With Fractional Derivative for the Viscoelastic Fluids-Modified Jeffreys Model and Its Application," Rheol. Acta, 37, pp. 512-517.
6. Palade, L. I., Attane, P., Huilgol, R. R., and Mena, B., 1999, "Anomalous Stability Behavior of a Properly Invariant Constitutive Equation Which Generalises Fractional Derivative Models," Int. J. Eng. Sci., 37, pp. 315-329.
7. Rossikhin, Y. A., and Shitikova, M. V., 2001, "A New Method for Solving Dynamic Problems of Fractional Derivative Viscoelasticity," Int. J. Eng. Sci., 39, pp. 149-176.
8. Hernández-Jiménez, A., Hernández-Santiago, J., Macias-García, A., and Sánchez-González, J., 2002, "Relaxation Modulus in PMMA and PTFE Fitting by Fractional Derivative Maxwell Model," Polym. Test., 21, pp. 325-331.
9. Kulish, V. V., and Lage, J. L., 2002, "Application of Fractional Calculus to Fluid Mechanics, Journal of Fluids Engineering," ASME Trans. J. Fluids Eng., 124, pp. 803-806.
10. Tan, W., Pan, W., and Xu, M., 2003, "A Note on Unsteady Flows of a Viscoelastic Fluid With the Fractional Derivative Maxwell Model Between Two Parallel Plates," Int. J. Non-Linear Mech., 38, pp. 645-650.
11. Hayat, T., Nadeem, S., and Asghar, S., 2004, "Periodic Unidirectional Flows of a Viscoelastic Fluid With the Fractional Derivative Maxwell Model," Appl. Math. Comput., 151, pp. 153-161.
12. Yin, Y. B., and Zhu, K. Q., 2006, "Oscillating Flow of a Viscoelastic Fluid in a Pipe With the Fractional Derivative Maxwell Model," Appl. Math. Comput., 173, pp. 231-242.
13. Qi, H. T. and Xu, M. Y., 2007, "Unsteady Flow of Viscoelastic Fluid With Fractional Maxwell Model in a Channel," Mech. Res. Commun., 34, pp. 210-212.
14. Jia, J. H., Shen, X. Y., and Hua, H. X., 2007, "Viscoelastic Behavior Analysis and Application of Fractional Derivative Maxwell Model," J. Vib. Control, 13, pp. 385-401.
15. Schlichting, H., 2000, Boundary-Layer Theory, Springer, New York.
16. Uchida, S. Z., 1956, "The Pulsating Viscous Flow Superposed on the Steady Laminar Motion of Imcompressible Fluid in a Circular Pipe," Z. Angew. Math. Phys., 7, pp. 197-204.
17. White, F. M., 1974, Viscous Fluid Flow, McGraw-Hill, New York.
18. Richardson, E. G., and Tyler, E., 1929, "The Transverse Velocity Gradient Near the Mouth of Pipes in Which an Alternating Or Continuous Flow of Air Is Established," Proc. Phys. Soc., 42, pp. 1-15.