Abstract
One of the fundamental problems in unsteady viscous flows is that of impulsively started motion of a body in an infinite fluid medium which is referred as Stokes’s first problem. On the basis of the fundamental understanding, we have developed a mechanistic modelling and thereby to improve existing technical applications. In this study, one of the particular non-Newtonian Spriggs fluid has considered that it is a truncated power law type of fluid. Flow of non-Newtonian Spriggs fluid caused by the unsteady impulsively moving plate is investigated using a similarity transformation. The use of similarity transformation reduces the unsteady boundary layer equations to linear and nonlinear ordinary differential equations governed by a non-dimensional material parameter. The effect of material parameter on velocity boundary layer is explained by an efficient and robust Homotopy Analysis Method. Variations of the velocity profile are presented graphically for distinct values of material constant. A physical interpretation is also provided. The flow past a plate has received much attention because of its major significance role in numerous disciplines which include the chemical engineering, manufacturing industry, heat conduction problems and geophysical flows (such as in earthquakes and fracture of ice sheets).
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References
Adusumilli RS, Hill GA (1984) Transient laminar flows of truncated power law fluids in pipes. Can J Chem Eng 62(5):594–601
Christov IC (2010) Stokes’s first problem for some non-Newtonian fluids: results and mistakes. Mech Res Commun 37(8):717–723
Cuouusv KR (1985) The impulsive motion of a flat plate in a viscoelastic fluid in the presence of a transverse magnetic field. Indian J Pure App Math, 19(8):931
Currie IG (2012) Fundamental mechanics of fluids, 4th edn. CRC Press
El-Shahed M (2004) On the impulsive motion of flat plate in a generalized second grade fluid. Zeitschrift für Naturforschung A 59(11):829–837
Erdoǧan ME (2002) On the unsteady unidirectional flows generated by impulsive motion of a boundary or sudden application of a pressure gradient. Int J Non-Linear Mech 37(6):1091–1106
Ezzat M, Sabbah AS, El-Bary AA, Ezzat S (2014) Stokes’s first problem for a thermoelectric fluid with fractional-order heat transfer. Rep Math Phys 74(2):145–158
Fetecau C, Fetecau C (2003) The first problem of stokes for an Oldroyd-B fluid. Int J Non-Linear Mech 38(10):1539–1544
Hayat T, Shahzad F, Ayub M, Asghar S (2008) Stokes’s first problem for a third grade fluid in a porous half space. Commun Nonlinear Sci Numer Simul 13(9):1801–1807
Irgens F (2014) Rheology and non-newtonian fluids. Springer International Publishing
Lavrov A (2015) Flow of truncated power-law fluid between parallel walls for hydraulic fracturing applications. J Nonnewton Fluid Mech 223:141–146
Liao S (1992) The proposed homotopy analysis technique for the solution of nonlinear problems, Ph.D. thesis, Shanghai Jiao Tong University
Liao S (1998) Homotopy analysis method: a new analytic method for nonlinear problems. Appl Math Mech 19(10):957–962
Liao S (2003) Beyond perturbation: introduction to the homotopy analysis method. CRC press
Liao S (2004) On the homotopy analysis method for nonlinear problems. Appl Math Comput 147(2):499–513
Liao S (2012) Homotopy analysis method in nonlinear differential equations, Beijing, Higher education press, pp 153–165
Liao S (ed) (2013) Advances in the homotopy analysis method. World Scientific
Muzychka YS, Yovanovich MM (2010) Unsteady viscous flows and stokes’s first problem. Int J Therm Sci 49(5):820–828
Puri P (1984) Impulsive motion of a flat plate in a Rivlin-Ericksen fluid. Rheol Acta 23(4):451–453
Sajid M, Hayat T (2009) Comparison of HAM and HPM solutions in heat radiation equations. Int Commun Heat Mass Transf 36(1):59–62
Soundalgekar VM (1974) Stokes’s problem for elastico-viscous fluid. Rheol Acta 13(2):177–179
Spriggs TW (1965) A four-constant model for viscoelastic fluids. Chem Eng Sci 20(11):931–940
Stokes GG (1851) On the effect of the internal friction of fluids on the motion of pendulums, vol 9. Pitt Press, Cambridge
Tan W, Masuoka T (2005) Stokes’s first problem for a second grade fluid in a porous half-space with heated boundary. Int J Non-Linear Mech 40(4):515–522
Tanner RI (1962) Note on the Rayleigh problem for a visco-elastic fluid. Zeitschrift fur angewandte Mathematik und Physik ZAMP 13(6):573–580
Teipel I (1981) The impulsive motion of a flat plate in a viscoelastic fluid. Acta Mech 39(3):277–279
Vieru D, Nazar M, Fetecau C, Fetecau C (2008) New exact solutions corresponding to the first problem of stokes for Oldroyd-B fluids. Comput Math Appl 55(8):1644–1652
Wenchang T, Mingyu X (2002) Plane surface suddenly set in motion in a viscoelastic fluid with fractional Maxwell model. Acta Mech Sin 18(4):342–349
Zaman H, Sohail A (2014) Stokes’s first problem for an unsteady MHD third-grade fluid in a non-porous half space with hall currents. Open J Appl Sci 4(03):85
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Ray, A.K., Vasu, B. (2018). Hydrodynamics of Non-Newtonian Spriggs Fluid Flow Past an Impulsively Moving Plate. In: Singh, M., Kushvah, B., Seth, G., Prakash, J. (eds) Applications of Fluid Dynamics . Lecture Notes in Mechanical Engineering. Springer, Singapore. https://doi.org/10.1007/978-981-10-5329-0_7
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DOI: https://doi.org/10.1007/978-981-10-5329-0_7
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