Incompressible laminar 2D steady thermal boundary layers with temperature-dependent kinematic viscosity and thermal diffusivity |
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Authors: | CWafo Soh |
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Institution: | Centre for Differential Equations, Continuum Mechanics and Applications, School of Computational and Applied Mathematics, University of the Witwatersrand, Private Bag 3, Wits 2050, Johannesburg, South Africa |
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Abstract: | We prove that the incompressible 2D steady thermal boundary layer equations with temperature-dependent kinematic viscosity ν and thermal diffusivity α is maximally symmetric provided the Prantl number Pr=ν/α is constant and or ν=K2(AT+B)K1 if we neglect energy dissipation and if we take into account dissipation. This result corroborates assumptions often made in applications. When we disregard dissipation, the symmetry Lie algebra assumes the forms Lr⊕L∞, where L∞ is an infinite-dimensional Lie algebra and Lr is an r-dimensional Lie algebra with r∈{3,4,5,6}. If we include dissipation, r∈{2,3}. We notice that dissipation has a symmetry breaking effect.We also show how the symmetries can be employed for the calculation of invariant solutions. |
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Keywords: | Incompressible Laminar flows Thermal boundary layer Lie point symmetry Invariant solutions |
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