Sommario
In questa nota si applicano i metodi di Lie alle equazioni dello strato limite laminare nella forma di Prandtl per un fluido viscoso, compressibile, con gradiente di pressione non nullo e con viscosità e conducibilità termica variabili. L'analisi gruppale fornisce soluzioni di similarità per date distribuzioni di pressione e valori particolari dei parametri del gruppo di invarianza. La trasformazione di Crocco si ottiene in corrispondenza della parte infinito-dimensionale dell'algebra di Lie ammessa dalle equazioni.
Summary
In this paper the application of Lie's methods to the equations of the laminar boundary layer is discussed. The momentum and energy equations in Prandtl's form are considered for a steady, viscous, compressible laminar flow with non zero pressure gradient, variable viscosity and thermal conductivity. Group analysis yields similarity solutions for given pressure distributions and particular values of the invariance group parameters (group classification). Crocco's transformation is obtained for the infinite-dimensional group of the Lie's algebra admitted by the equations.
References
Schlichting H.,Boundary Layer Theory, McGraw Hill (1968).
Rosenhead L.,Laminar Boundary Layer, Oxford University Press (1966).
Houghton E.L.,Boswell R.P.,Further Aerodynamics for Engineering Student, Edward Arnold (1969).
Howarth L.,Modern Developments in Fluid Dynamics High Speed Flow, Oxford Clarendom Press (1964).
Ames W.F.,Nonlinear Partial Differential Equations, Vol. I, Academic Press (1965).
Ames W.F.,Nonlinear Partial Differential Equations, Vol. II, Academic Press (1972).
Bluman G.W.,Cole J.D.,Similarity Methods for Differential Equations, Springer Verlag (1974).
Ovsiannikov L.V.,Group Analysis of Differential Equations, Academic Press (1982).
Olver P.J.,Applications of Lie Group to Differential Equations,Springer Verlag (1986).
Barrera P.,Brugarino T.,Analisi gruppale delle equazioni dello strato limite, IX Congresso AIDAA Palermo (1987).
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Barrera, P., Brugarino, T. Group analysis and similarity solutions of the compressible boundary layer equations. Meccanica 24, 211–215 (1989). https://doi.org/10.1007/BF01556452
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DOI: https://doi.org/10.1007/BF01556452