ORIGINAL PAPER

Homotopy Simulation of Non-Newtonian Spriggs Fluid Flow Over a Flat Plate with Oscillating Motion

1

Department of Mathematics, Motilal Nehru National Institute of Technology, Allahabad, India

2

Department of Mechanical Engineering, Cleveland State University, Ohio, USA

Online publication date: 2019-06-03

Publication date: 2019-06-01

International Journal of Applied Mechanics and Engineering 2019;24(2):359-385

KEYWORDS

ABSTRACT

An incompressible flow of a non-Newtonian Spriggs fluid over an unsteady oscillating plate is investigated using the Homotopy Analysis Method (HAM). An analytic solution of sine and cosine oscillations of the plate has been obtained. The similarity transformation is introduced to reduce the governing partial differential equations into a single non-linear dimensionless partial differential equation. The effects of the power index of Spriggs fluid and convergence control parameter of HAM for the flow are studied extensively. The range of the convergence control parameter for convergence of series solution for different values of the power index of Spriggs fluid is obtained. The solution for a Spriggs fluid is noticeably different from the solution obtained for a Newtonian fluid. The influences of the shear thinning and shear thickening fluid on the velocity profile are shown graphically. The transient flow effect is higher for non-Newtonian Spriggs fluid than that of a Newtonian fluid. It is also observed that the interval to reach the steady state for the cosine case is less than the sine case. The applications of Stokes’ second problem have been widely found in the variety of fields of biomedical, medical, chemical, micro and nanotechnology.

REFERENCES (40)

1.

Chhabra R.P. and Richardson J. (2008): Non-Newtonian Flow and Applied Rheology: Engineering Applications (second ed). – Oxford: Butterworth-Heinemann.

2.

Irgens F. (2014): Rheology and non-Newtonian Fluids. – New York: Springer Int. Publ..

3.

Arada N. and Pires M. (2007): Viscosity effects on flows of generalized Newtonian fluids through curved pipes. – Comput. Math. with Appl., vol.53, pp.625-646.

4.

Bair S and Qureshi F. (2003): The generalized Newtonian fluid model and elastohydrodynamic film thickness. – J. Tribol., vol.125, pp.70.

5.

Spriggs T. (1965): A four-constant model for viscoelastic fluids. – Chem. Eng. Sci., vol.20, pp.931-940.

6.

Lavrov A. (2015): Flow of truncated power-law fluid between parallel walls for hydraulic fracturing applications. – J. Nonnewton. Fluid Mech., vol.223, pp.141-146.

7.

Greenwood J.A. and Kauzlarich J.J. (2015): Elastohydrodynamic film thickness for shear- thinning lubricants. – Proc. Inst. Mech. Eng. Part J. Jouranal Eng., vol.212, pp.179-191.

8.

Adusmilli R.S. and Hill G.A. (1984): Transient laminar flows of truncated power law fluids in pipes. – Can. J. Chem. Eng., vol.62, pp.594-601.

9.

Raju C.S.K. and Sandeep N. (2016): Heat and mass transfer in MHD non-Newtonian bio-convection flow over a rotating cone/plate with cross diffusion. – J. Mol. Liq., vol.215, pp.115-126.

10.

Rashidi M.M., Bagheri S., Momoniat E. and Freidoonimehr N. (2017): Entropy analysis of convective MHD flow of third grade non-Newtonian fluid over a stretching sheet. – Ain Shams Eng. J., vol.8, pp.77-85.

11.

Mohyud-din S.T., Khan U., Ahmed N. and Rashidi M.M. (2017): Stokes first problem for MHD flow of Casson nanofluid. – Multidiscip. Model. Mater. Struct., vol.13, pp.2-10.

12.

Gorla R.S.R. and Vasu B. (2016): Unsteady convective heat transfer to a stretching. – J. Nanofluid, vol.5, pp.1-14.

13.

Gorla R.S.R., Vasu B. and Siddiqa S. (2016): Transient combined convective heat transfer over a stretching surface in a non-Newtonian nanofluid using Buongiorno’s model. – J. Appl. Math. Phys., vol.4, pp.443-460.

14.

Christov I.C. (2010): Stokes first problem for some non-Newtonian fluids: Results and mistakes. – Mech. Res. Commun., vol.37, pp.717-723.

15.

Stokes G.G. (1851): On the effect of internal friction of fluids on the motion of pendulums. – Math. Phys. Pap., vol.3, pp.1880-1905.

16.

Ezzat M.A., El-bary A.A. and Ezzat S.M. (2013): Stokes first problem for a thermoelectric Newtonian fluid. – Meccanica, vol.48, pp.1161-1175.

17.

Liu W., Peng J. and Zhu K. (2016): Finite depth Stokes’ first problem of thixotropic fluid. – Appl. Math. Mech., vol.37, pp.59-74.

18.

Zaman H., Ubaidullah, Shah M.A. and Ibrahim M. (2014): Stokes first problem for an unsteady MHD fourth grade fluid in a non-porous half space with Hall currents. – IOSR J. Appl. Phys., vol.6, pp.7-14.

19.

Rajagopal K.R. (1982): A note on unsteady undirectional flows of a non-Newtonian fluid. – Int. J. Non. Linear. Mech., vol.17, pp.369-373.

20.

Ishfaq N., Khan W.A. and Khan Z.H. (2017): The Stokes’ second problem for nanofluids. – J. King Saud Univ. - Sci., pp.1-5.

21.

Duan J. and Qiu X. (2014): The periodic solution of Stokes’ second problem for viscoelastic fluids as characterized by a fractional constitutive equation. – J. Nonnewton. Fluid Mech., vol.205, pp.11-15.

22.

Farkhadnia F., Kamrani R. and Ganji D.D. (2014): Analytical investigation for fluid behavior over a flat plate with oscillating motion and wall transpiration. – New Trends Math. Sci., vol.2, pp.178-189.

23.

Ali F., Norzieha M., Sharidan S., Khan I. and Hayat T. (2012): New exact solutions of Stokes’ second problem for an MHD second grade fluid in a porous space. – Int. J. Non. Linear. Mech., vol.47, pp.521-525.

24.

Asghar S., Nadeem S., Hanif K. and Hayat T. (2006): Analytic solution of Stokes second problem for secondgrade fluid. – Math. Probl. Eng., vol.2006, pp.1-8.

25.

Fetecau C., Jamil M., Fetecau C. and Siddique I. (2009): A note on the second problem of Stokes for Maxwell fluids. – Int. J. Non. Linear. Mech., vol.44, pp.1085-1090.

26.

Ai L. and Vafai K. (2005): An investigation of Stokes’ second problem for non-Newtonian fluids. – Numer. Heat Transf. Part A Appl., vol.47, pp.955-980.

27.

Erdogan M.E. (2000): A note on an unsteady flow of a viscous fluid due to an oscillating plane wall. – Int. J. Non. Linear. Mech., vol.35, pp.1-6.

28.

Holmes M.H. (2013): Introduction to Perturbation Methods. – Springer New York Heidelberg Dordrecht London.

29.

Bhimsen S. (2012): Perturbation Methods for Differential Equations. – Springer Sci. Bus. Media..

31.

Rashidi M.M., Ashraf M., Rostami B., Rastegari M.T. and Bashir S. (2016): Mixed convection boundary - layer flow of a micro polar fluid towards a heated shrinking sheet by Homoptopy Analysis Method. – Theraml Sci., vol. 20, pp.21-34.

32.

Hayat T., Qayyum S., Alsaedi A. and Ahmad B. (2017): Nonlinear convective flow with variable thermal conductivity and Cattaneo-Christov heat flux. – Neural Comput. Appl., pp.1-11.

33.

Das D., Ray P.C. and Bera R.K. (2016): Solution of Nonlinear Fractional Differential Equation (NFDE) by four different approximate methods. – Int. J. Sci. Res. Educ., vol.4, pp.5598-5620.

34.

Al-Shara S., Awawdeh F. and Abbasbandy S. (2017): An automatic scheme on the Homotopy analysis method for solving non-linear algebraic equations. – Ital. J. Pure Appl. Math., vol.37, pp.5-14.

35.

Zhong X. and Liao S. (2017): Analytic Solutions of Von Karman plate under arbitrary uniform pressure (I): Equations in differential form analytic solutions of Von Karman plate under arbitrary uniform pressure Part I : Equations in differential form. – Stud. Appl. Math., vol.138, pp.371-400.

36.

Turkyilmazoglu M. (2010): A note on the homotopy analysis method. – Appl. Math. Lett., vol.23, pp.1226-1230.

37.

Sajid M. and Hayat T. (2009): Comparison of HAM and HPM solutions in heat radiation equations. – Int. Commun. Heat Mass Transfer, vol.36, pp.59-62.

38.

Marinca V., Ene R.D. and Marinca B. (2014): Analytic approximate solution for Falkner-Skan equation. – Sci. World J., vol.2014.

39.

Liao S. (1999): An explicit, totally analytic approximate solution for Blasius’ viscous flow problems. – Int. J. Non. Linear. Mech., vol.34, pp.759-778.

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