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viscoplastic fluid; constitutive model; pipe flow; semi-inverse method; exact solution

References:

[1] Bingham, E. C.: **Fluidity and Plasticity**. McGraw-Hill, New York (1922).

[2] Bird, R. B., Dai, G. C., Yarusso, B. J.: **The rheology and flow of viscoplastic materials**. Rev. Chem. Eng. 1 (1983), 1-70. DOI 10.1515/revce-1983-0102

[3] Blechta, J., Málek, J., Rajagopal, K. R.: **On the classification of incompressible fluids and a mathematical analysis of the equations that govern their motion**. SIAM J. Math. Anal. 52 (2020), 1232-1289. DOI 10.1137/19M1244895 | MR 4076814 | Zbl 1432.76075

[4] Casson, N.: **A flow equation for pigment-oil suspensions of the printing ink type**. Rheology of Disperse Systems Pergamon Press, Oxford (1959), 84-104. Zbl 0119.19901

[5] Edgeworth, R., Dalton, B. J., Parnell, U. T.: **The pitch drop experiment**. Eur. J. Phys. 5 (1984), 198-200. DOI 10.1088/0143-0807/5/4/003

[6] Herschel, W. H., Bulkley, R.: **Konsistenzmessungen von Gummi-Benzollösungen**. Kolloid-Z. 39 (1926), 291-300 German. DOI 10.1007/BF01432034

[7] Huilgol, R. R.: **Fluid Mechanics of Viscoplasticity**. Springer, Berlin (2015). DOI 10.1007/978-3-662-45617-0 | Zbl 1328.76001

[8] Mitsoulis, E.: **Flows of viscoplastic materials: Models and computations**. Rheology Rev. 2007 (2007), 135-178.

[9] Rajagopal, K. R.: **Conspectus of concepts of elasticity**. Math. Mech. Solids 16 (2011), 536-562. DOI 10.1177/1081286510387856 | MR 2857911 | Zbl 1269.74014