Group Analysis And Some Exact Solutions For The
Thermal Boundary Layer
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
Keywords
Related Book
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