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Analytical and numerical solutions of nonlinear differential equations arising in non-Newtonian fluid flows. (English) Zbl 0974.34017

Using Schauder technique and a priori estimates, the authors study a boundary value problem for a nonlinear second-order ordinary differential equation which describes a rotational flow of a viscoelastic fluid around a circular cylinder. The authors prove existence and uniqueness results, and investigate the asymptotic behaviour of the solution as a material constant tends to zero. Finally, analytical results are compared with numerical solutions.

MSC:

34B15 Nonlinear boundary value problems for ordinary differential equations
76A10 Viscoelastic fluids
76U05 General theory of rotating fluids
34B30 Special ordinary differential equations (Mathieu, Hill, Bessel, etc.)
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[1] Beard, D. W.; Walters, K., Elastico-viscous boundary layer flows, Proc. Cambridge Philos. Soc., 60, 667-674 (1964) · Zbl 0123.41601
[2] Garg, V. K.; Rajagopal, K. R., Flow of a non-Newtonian fluid past a wedge, Acta Mech., 88, 113-123 (1991)
[3] Rajeswari, G. K.; Rathna, S. L., Flow of a particular class of non-Newtonian visco-elastic and visco-elastic fluids near a stagnation point, Z. Angew. Math. Phys., 13, 43-57 (1962) · Zbl 0105.19503
[4] Markovitz, H.; Coleman, B. D., Advances in Applied Mechanics (1964), Academic Press: Academic Press New York · Zbl 0133.19205
[5] Acrivos, A., A theoretical analysis of laminar natural convection heat transfer to non-Newtonian fluids, Amer. Inst. Chem. Engrg. J., 6, 584-590 (1960)
[6] Dunn, J. E.; Rajagopal, K. R., Fluids of differential type: Critical review and thermodynamic analysis, Internat. J. Engrg. Sci., 33, 689-729 (1995) · Zbl 0899.76062
[7] Vajravelu, K.; Rollins, D., Heat transfer in a viscoelastic fluid over a stretching sheet, J. Math. Anal. Appl., 158, 241-255 (1991) · Zbl 0725.76019
[8] Sarma, M. S.; Rao, B. N., Heat transfer in a viscoelastic fluid over a stretching sheet, J. Math. Anal. Appl., 222, 268-275 (1998) · Zbl 0907.76006
[9] Troy, W. C.; Overman, E. A.; Ermentrout, G. B.; Keener, J. P., Uniqueness of flow of a second order fluid past a stretching sheet, Quart. Appl. Math., 44, 753-755 (1987) · Zbl 0613.76006
[10] Chang, W. D., The nonuniqueness of the flow of a viscoelastic fluid over a stretching sheet, Quart. Appl. Math., 47, 365-366 (1989) · Zbl 0683.76012
[11] Lawrence, P. S.; Rao, B. N., Reinvestigation of the nonuniqueness of the flow of a viscoelastic fluid over a stretching sheet, Quart. Appl. Math., 51, 401-404 (1993) · Zbl 0781.76006
[12] Chang, W. D.; Kazarinoff, N. D.; Lu, C., A new family of explicit solutions for the similarity equations modelling flow of a non-Newtonian fluid over a stretching sheet, Arch. Rational Mech. Anal., 113, 191-195 (1991) · Zbl 0723.76010
[13] Vajravelu, K.; Roper, T., Flow and heat transfer in a second grade fluid over a stretching sheet, Internat. J. Nonlinear Mech., 34, 1031-1036 (1999) · Zbl 1006.76005
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