Incompressible laminar 2D steady thermal boundary layers with temperature-dependent kinematic viscosity and thermal diffusivity

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 ν=K 2 e K 1T or ν= K 2( AT+ B) K 1 if we neglect energy dissipation and ν=K 2 e K 1T 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 L r ⊕ L ∞, where L ∞ is an infinite-dimensional Lie algebra and L r 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.