Analytical Investigation of Time-Dependent Two-Dimensional Non-Newtonian Boundary Layer Equations

Imre Ferenc Barna, Laszló Mátyás, Krisztián Hriczó and Gabriella Bognár ()
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Imre Ferenc Barna: Hungarian Research Network, Wigner Research Centre for Physics, Konkoly-Thege Miklós út 29–33, 1121 Budapest, Hungary
Laszló Mátyás: Department of Bioengineering, Faculty of Economics, Socio-Human Sciences and Engineering, Sapientia Hungarian University of Transylvania, Libertătii sq. 1, 530104 Miercurea Ciuc, Romania
Krisztián Hriczó: Institute of Mathematics, University of Miskolc, 3515 Miskolc-Egyetemváros, Hungary
Gabriella Bognár: Institute of Mathematics, University of Miskolc, 3515 Miskolc-Egyetemváros, Hungary

Mathematics, 2024, vol. 12, issue 23, 1-18

Abstract: In this study, five different time-dependent incompressible non-Newtonian boundary layer models in two dimensions are investigated with the self-similar Ansatz, including external magnetic field effects. The power-law, the Casson fluid, the Oldroyd-B model, the Walter fluid B model, and the Williamson fluid are analyzed. For the first two models, analytical results are given for the velocity and pressure distributions, which can be expressed by different types of hypergeometric functions. Depending on the parameters involved in the analytical solutions of the nonlinear ordinary differential equation obtained by the similarity transformation, a vast range of solution types is presented. It turned out that the last three models lack self-similar symmetry; therefore, no analytic solutions can be derived.

Keywords: non-Newtonian fluid; self-similar method; boundary layer; MHD flow; time-dependent solution (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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