Exact solutions for generalized Burgers’ fluid in an annular pipe
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This paper deals with some unsteady unidirectional transient flows of generalized Burgers’ fluid in an annular pipe. Exact solutions of some unsteady flows of generalized Burgers’ fluid in an annular pipe are obtained by using Hankel transform and Laplace transform. The following two problems have been studied: (1) Poiseuille flow due to a constant pressure gradient; (2) axial Couette flow in a annulus. The well known solutions for Navier-Stokes fluid, as well as those corresponding to a Maxwell fluid, a second grade fluid and an Oldroyd-B fluid appear as limiting cases of our solutions.
KeywordsGeneralized Burgers’ fluid Exact solutions Velocity fields
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- 2.Rajagopal KR (1993) Mechanics of non-Newtonian fluids. In: Recent developments in theoretical fluids mechanics. Pirman research notes in mathematics, vol 291. Longman, New York, pp 129–162 Google Scholar
- 3.Han SF (2000) Constitutive equation and computational analytical theory of non-Newtonian fluids. Science, Beijing Google Scholar
- 4.Bandeli R, Rajagopal KR (1995) Start-up flows of second grade fluids in domains with one finite dimension. Int J Non-Linear Mech 30(6):818–839 Google Scholar
- 22.Zhu WH, Liu CQ (1993) Analytical solution of flow of second-order non-Newtonian fluid through annular pipes. Appl Math Mech 14(3):195–201 Google Scholar
- 23.Zhu WH, Liu CQ (1992) Analytical solution for the unsteady flow of Maxwell fluids through annular pipes. Acta Mech Sin 24(1):116–121 Google Scholar