J4 ›› 2017, Vol. 34 ›› Issue (6): 691-699.

• Quantum Physics • Previous Articles     Next Articles

New exact solutions of the Brinkman model describing the natural convection in porous media

  

  • Received:2016-06-24 Revised:2016-10-19 Published:2017-11-28 Online:2017-12-11

Abstract: The theory of Lie symmetry is a systematic and effective method to find exact solutions of mathematical and physical equations. The symmetries and reduction equations of the Brinkman model are derived by means of Lie symmetry theory. By solving the reduced equations,many new exact solutions of the Brinkman model including solutions of separating variables and traveling wave solutions are obtained. Some variable-separating solutions considers the anisotropic effect of thermal conductivity. These solutions and the traveling wave solutions have not been reported in the existent literature and they can reflect the natural convection more really.

Key words: Brinkman model, symmetry, reduction equations, exact solutions