On Taylor's scraping problem and flow of a Sisko fluid

References

• Abbasbandy , S. 2006 . Application of He's homotopy perturbation method for Laplace transform . Chaos, Solitons & Fractals, , 30 (5) : 1206 (doi:10.1016/j.chaos.2005.08.178)
   Google Scholar
• Bailey , William J. and Weir. , Iain S. 1998 . Investigation of methods for direct rheological model parameter estimation . Journal of Petroleum Science and Engineering, , 21 : 1 – 13 . (doi:10.1016/S0920–4105(98)00040–0)
   Web of Science ®Google Scholar
• Batchelor , G.K. 1967 . An introduction to fluid dynamics. , Cambridge University Press .
   Google Scholar
• Bhatnagar , R.K. , Rajagopal , K.R. and Gupta , G. 1993 . Flow of an oldroyd‐B fluid between intersecting planes . Journal of non‐Newtonian Fluid Mechanics, , 46 : 49 – 67 . (doi:10.1016/0377–0257(93)80003‐T)
   Google Scholar
• Bird , R.B. , Armstrong , R.C. and Hassager , O. 1987 . Dynamics of polymeric liquids, , New York : volume 1. John Wiley & Sons .
   Google Scholar
• Cveticanin , L. 2006 . Homotopy perturbation method for pure nonlinear differential equation . Chaos, Solitons & Fractals, , 30 (5) : 1221 – 1230 . (doi:10.1016/j.chaos.2005.08.180)
   Google Scholar
• El‐Shahed , M. 2005 . Application of He's homotopy perturbation method for Laplace transform . International Journal of Nonlinear Science Numerical Simulation, , 6 : 163
   Web of Science ®Google Scholar
• Gucuyener , I.H. 1992 . An evalution of the rheological models describing drilling fluids and cement slurries . Proceedings of the 9th Petroleum Congress of Turkey UCTEA Chamber of geophysical engineers . February 1992 . Turkey : Ankara .
   Google Scholar
• He , J.H. 1999 . Homotopy perturbation technique . Computer Methods in Applied Mechanics and Engineering, , 178 : 257 – 262 .
   Web of Science ®Google Scholar
• He , J.H. 2006 . New interpretation of homotopy perturbation method . International Journal of Modern Physics B, , 20 (18) : 2561 – 2568 .
   Google Scholar
• Hull , A.M. 1981 . An exact solution for the slow flow of a general linear viscoelastic fluid through a slit . Journal of non‐Newtonian Fluid Mechanics, , 8 : 327 – 336 . (doi:10.1016/0377–0257(81)80029–8)
   Google Scholar
• Kaloni , P.N. and Kamel , M.T. 1980 . A note on the hamel flow of cosserat fluids . ZAMP, , 31 : 293 – 296 . (doi:10.1007/BF01590754)
   Google Scholar
• Khan , M. , Ali , S. Hyder and Qi , Haitao . 2009 . Exact solutions of starting flows for a fractional burgers fluid between coaxial cylinders . Nonlinear Analysis: Real World Applications, , 10 (3) : 1775 – 1783 . (doi:10.1016/j.nonrwa.2008.02.015)
   Google Scholar
• Kolyshkin , A. and Nazarovs , S. 2007 . Stability of slowly diverging flows in shallow water . Math. Model. Anal., , 12 (1) : 101 – 106 . (doi:10.3846/1392–6292.2007.12.101–106)
   Google Scholar
• Krylovas , A. and Čiegis , R. 2001 . Asymptotical analysis of one dimensional gas dynamics equations . Math. Model. Anal., , 6 (1) : 117 – 128 .
   Google Scholar
• Kuzma , D.C. , Maki , E.R. and Donnelly , R.J. 1988 . The magnetohydrodynamic squeeze film . Journal of Tribology, , 110 : 375 – 377 .
   Google Scholar
• Mansutti , D. and Rajagopal , K.R. 1991 . Flow of shear thinning fluid between intersecting planes . International Journal of Nonlinear Mechanics, , 26 : 769 – 775 . (doi:10.1016/0020–7462(91)90027‐Q)
   Web of Science ®Google Scholar
• Marinca , V. , Herisanu , N. , Bota , C. and Marinca , B. 2009 . An optimal homotopy asymptotic method applied to the steady flow of a fourth‐grade fluid past a porous plate . Applied Mathematics Letters, , 22 : 245 – 251 . (doi:10.1016/j.aml.2008.03.019)
   Web of Science ®Google Scholar
• Moffat , H.K. 1964 . Viscous and resistive eddies near a sharp corner . Journal of Fluid Mechanics, , 18 : 1 – 8 . (doi:10.1017/S0022112064000015)
   Web of Science ®Google Scholar
• Nayfeh , A.H. 1981 . Introduction to Perturbation Techniques. , New York; Chichester : John Wiley & Sons .
   Google Scholar
• Siddiqui , A.M. , Ahmed , M. and Ghori , Q.K. 2006 . Couette and Poiseuille flow for non‐Newtonian fluids . International Journal of Nonlinear Sciences and Numerical Simulation, , 7 (1) : 15 – 26 .
   Google Scholar
• Siddiqui , A.M. , Mahmood , R. and Ghori , Q.K. 2006 . Thin film flow of a third grade on a moving belt by He's homotopy perturbation method . International Journal of Nonlinear Sciences and Numerical Simulation, , 7 (1) : 7 – 14 .
   Google Scholar
• Sisko , A.W. 1958 . The flow of lubricating greases . Industrial and Engineering Chemistry Research, , 50 (12) : 1789 – 1792 .
   Google Scholar
• Taylor , G.I. 1971 . “ On scraping viscous fluid from a plane surface. ” . In The scientific Papers of Sir Geoffrey Ingram Taylor Edited by: Batchelor , G.K. 410 – 413 .
   Google Scholar
• Xu , J. 2005 . Rheology of polymeric suspensions: Polymer nanocomposites and water‐borne coatings. , Ohio State University . Industrial and Engineering Chemistry coatings, PhD thesis
   Google Scholar