Extension of Blasius Newtonian Boundary Layer to Blasius Non-Newtonian Boundary Layer
Keywords:Generalised Blasius equation, Sisko fluid model, Pradtl fluid model,, Deductive group, Non-linear ODE
Blasius equation is very well known and it aries in many boundary layer problems of fluid dynamics. In this present article, the Blasius boundary layer is extended by transforming the stress strain term from Newtonian to non-Newtonian. The extension of Blasius boundary layer is discussed using some non-newtonian fluid models like, Power-law model, Sisko model and Prandtl model. The Generalised governing partial differential equations for Blasius boundary layer for all above three models are transformed into the non-linear ordinary differewntial equations using the one parameter deductive group theory technique. The obtained similarity solutions are then solved numerically. The graphical presentation is also explained for the same. It concludes that velocity increases more rapidly when fluid index is moving from shear thickninhg to shear thininhg fluid.
MSC 2020 No.: 76A05, 76D10, 76M99
Asaithambi, A.: Numerical Solution of the Blasius Equation with Crocco-Wang Transformation. Journal of Applied Fluid Mechanics 9(5), 2595-2603 (2016). https://doi.org/10.18869/acadpub.jafm.68.236.25583
Basu, B., Foufoula-Georgiou, E. and Sharma, A.S.: Chaotic behavior in the flow along a wedge modeled by the Blasius equation, Nonlin. Processes Geophys 18, 171–178 (2011). https://doi.org/10.5194/npg-18-171-2011
Benlahsen, M., Guedda, M. and Kersner, R.: The Generalized Blasius equation revisited. Mathematical and Computer Modelling 47(9-10), 1063-1076 (2008). https://doi.org/10.1016/j.mcm.2007.06.019
Blasius, H.: Grenzschichten in flüssigkeiten mit kleiner reibung. Zeitschrift für Angewandte Mathematik und
Physik 56, 1–37 (1908).
Ganji, D.D., Badazadeh, H., Noori, F. and Janipour, M.: An application of Homotopy perturbation method for non linear Blasius equation to boundary layer flow over a flat plate. International Journal of Nonlinear Science 7(4), 399-404 (2009).
Hashim, I.: Comments on “A new algorithm for solving classical Blasius equation” by L. Wang. Applied Mathematics and Computation 176(2), 700-703 (2006). https://doi.org/10.1016/j.amc.2005.10.016
Liu, Y. and Kurra, S.N.: Solution of Blasius Equation by Variational Iteration. Applied Mathematics 1(1), 24-27 (2011). https://doi.org/10.5923/j.am.20110101.03
Patel, M., Patel, J. and Timol, M.G.: On the solution of boundary layer flow of Prandtl fluid past a flat surface. Journal of Advanced Mathematics and Applications 6(1), 73-78 (2017). https://doi.org/10.1166/jama.2017.1128
Patel, M. and Timol, M.: Non-Newtonian fluid models and Boundary Layer flow, LAP Lambert Academic Publishing, Mauritius (2020).
Moran, M.J. and Gaggioli, R.A.: Similarity analysis if compressible boundary layer flows via group theory, Technical summary report, No.838, mathematical Research center, U.S. Army, Madison, Wisconsin (1967).
Moran, M.J. and Gaggioli, R.A.: Similarity analysis via group theory. American Institute of Aeronautics and Astronautics Journal 6(10), 2014-2016 (1968). https://doi.org/10.2514/3.4919
Moran, M.J. and Gaggioli, R.A.: A new symmetric formalism for similarity analysis, with application to boundary layer flows, Technical summary report, No.918, mathematical Research center, U.S.Army, Madison, Wisconsin (1968).
Moran, M.J. and Gaggioli, R.A.: Reduction of the number of variables in systems of partial differential equations with auxiliary conditions. SIAM Jornal on Applied Mathematics, 16(1), 202-215 (1968). https://doi.org/10.1137/0116018
Prandtl, L.: Uber Flussigkeit – shewegung bei sehr kleiner Reibung (on fluid motions with very small friction), Verhandlunger, des. III, Internationlen Mathematiker congress, Heidelburg, pp. 484-491 (1904).
Robin, W.: Some remarks on the homotopy-analysis method and series solutions to the Blasius equation. International Mathematical Forum 8(25), 1205-1213 (2013). https://doi.org/10.12988/imf.2013.3478
Sakiadis, B.C.: Boundary layer behaviour on continuous solid surfaces I. The boundary layer equations for two dimensional and axisymmetric flows. AIChE Journal 7(1), 26–28 (1961). https://doi.org/10.1002/aic.690070108
Schlichting, H. and Gersten, K.: Boundary-Layer Theory. 8th Edition, Springer-Verlag (2000). https://doi.org/10.1007/978-3-642-85829-1
Wang, L.: A new algorithm for solving classical Blasius equation. Applied Mathematics and Computation 157(1), 1-9 (2004). https://doi.org/10.1016/j.amc.2003.06.011
How to Cite
Articles in Mathematical Journal of Interdisciplinary Sciences (Math. J. Interdiscip. Sci.) by Chitkara University Publications are Open Access articles that are published with licensed under a Creative Commons Attribution- CC-BY 4.0 International License. Based on a work at https://mjis.chitkara.edu.in. This license permits one to use, remix, tweak and reproduction in any medium, even commercially provided one give credit for the original creation.
View Legal Code of the above mentioned license, https://creativecommons.org/licenses/by/4.0/legalcode
View Licence Deed here https://creativecommons.org/licenses/by/4.0/
|Mathematical Journal of Interdisciplinary Sciences by Chitkara University Publications is licensed under a Creative Commons Attribution 4.0 International License. Based on a work at https://mjis.chitkara.edu.in|