Author(s)

P. Barrera & T. Brugarino

Abstract

We perform the group analysis of the thermal boundary layer in laminar flow. We obtain the classification of the solutions in terms of the asymptotic velocity. Some solutions of the boundary layer equations, for some distributions of outer flow velocity, are obtained also. 1 Introduction It is very important to have the similarity solutions for the partial differential equations for the flow field near a body in a fluid flow. Generally the solutions of these equations are obtained by means of dimensional analysis which is a particular case of the group analysis. This is based on the theory of S. Lie developed more than one hundred years ago in order to have solutions of ordinary and partial, linear and non linear differential equations [1–6]. Considering systems of partial differential equations containing an arbitrary number of dependent and independent variables, the group analysis provides similarity solutions reducing the original system to a system with a reduced number of independent variables [7–9]. Now we turn our attention to the group analysis of the equations of the thermal boundary layer for some particular cases. 2 Group analysis We show in brief the theory of one-parameter Lie groups of transformations for a partial differential equation in which the number of independent variables is equal

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