Abstract
This note is concerned with a laminar pipe flow of a non-Newtonian fluid under the action of a small pulsating pressure gradient superposed to a steady one. The constitutive law describing the rheological behaviour of the fluid is the so-called power law (Ostwald–de Waele). An approximated analytical solution is found for the velocity, as power series of the amplitude of the periodic disturbance. The analytic solution is compared with a direct numerical solution and the perfect accord of the values obtained is underscored.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Balmer T and Fiorina MA (1980). Unsteady flow of an inelastic Power-law fluid in a circular tube. J Non-Newtonian Fluid Mech 7: 189–198
Warsi ZUA (1994). Unsteady flow of power-law fluids through circular pipes. J Non-Newtonian Fluid Mech 55: 197–202
Adusumilli RS and Hill GA (1984). Transient laminar flows of truncated power law fluids in pipes. Canadian J Chem Eng 62: 594–601
Pontrelli G (1998). Pulsatile blood flow in a pipe. Comput Fluids 27: 367–380
Edwards MF, Nellist DA and Wilkinson WL (1972). Unsteady, laminar flows of non-Newtonian fluids in pipes. Chem Eng Sci 27: 295–306
Mai TZ and Davis MJ (1996). Laminar pulsatile two-phase non-newtonian flow though a pipe. Comput Fluids 25: 77–93
Ramkissoon H (1995). Some non-Newtonian axial pipe flow. ASME FED 231: 189–196
Rajagopal KR (1982). A note on unsteady unidirectional flows of a non-Newtonian fluid. Int J Non-Linear Mech 17: 369–373
Pascal H (1992). Similarity solutions to some unsteady flows of non- Newtonian fluids of power law behavior. Int J Non-Linear Mech 27: 759–771
Fetecau C (2004). Analytical solutions for non-Newtonian fluid flows in pipe-like domains. Int J Non-Linear Mech 39: 225–231
Fetecau C and Fetecau C (2005). Starting solution for some unsteady unidirectional flows of a second order fluid. Int J Non-Linear Mech 43: 781–789
Erdogan ME (2000). A note on an unsteady flow of a viscous fluid due to an oscillating plane wall. Int J Non-Linear Mech 35: 1–6
Kamke E (1956). Differentialgleichungen Lösungsmethoden und Lösungen. Akademische Verlagsgesellschaft, Leipzig
Abramowitz RM and Stegun IA (1965). Handbook of mathematical functions. Dover, New York
Peebles FN, Prados JW and Honeycutt EH (1963). Birefringent and rheologic properties of milling yellow suspensions. J Polymer Sci part C 5: 37–53
Magnus W, Oberhettinger F and Soni RP (1966). Formulas and theorems for the special functions of mathematical physics. Springer, Berlin
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Daprà, I., Scarpi, G. Pulsatile pipe flow of pseudoplastic fluids. Meccanica 41, 501–508 (2006). https://doi.org/10.1007/s11012-006-0007-6
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11012-006-0007-6