Symmetries of boundary layer equations of power-law fluids of second grade |
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Authors: | Mehmet Pakdemirli Yiğit Aksoy Muhammet Yürüsoy Chaudry Masood Khalique |
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Institution: | (1) Department of Mechanical Engineering, Celal Bayar University, 45140 Muradiye, Manisa, Turkey;(2) Technical Education Faculty, Afyon Kocatepe University, Afyon, Turkey;(3) Department of Mathematical Sciences, International Institute for Symmetry Analysis and Mathematical Modeling, North-West University, Mafikeng Campus, Private Bag X 2046, Mmabatho, 2735, South Africa |
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Abstract: | A modified power-law fluid of second grade is considered. The model is a combination of power-law and second grade fluid in
which the fluid may exhibit normal stresses, shear thinning or shear thickening behaviors. The equations of motion are derived
for two dimensional incompressible flows, and from which the boundary layer equations are derived. Symmetries of the boundary
layer equations are found by using Lie group theory, and then group classification with respect to power-law index is performed.
By using one of the symmetries, namely the scaling symmetry, the partial differential system is transformed into an ordinary
differential system, which is numerically integrated under the classical boundary layer conditions. Effects of power-law index
and second grade coefficient on the boundary layers are shown and solutions are contrasted with the usual second grade fluid
solutions.
The English text was polished by Yunming Chen. |
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Keywords: | Power-law fluid of second grade Boundary layers Liegroup theory |
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