Application of Lie Group methods to problems in fluid mechanisms

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Abstract

This research ~~ udies two nonlinear proulcms anslllg m fluid HH.:chanic:s. Firstly the combined sinh-cosh-Gordon equation is considered. Lie symmetry analysis along with simplest equation method is used to carry out its integration. Also conservation

laws arc obtainrd for this equation using the direct method and the nrw conservation theorem.

Secondly, the nonlinci\r now problem of an incompressible viscous fluid is considered. The Auicl is taken in a channel having two porous walls. An incompressible Auid fills the porous spac·e inside the channel. Lie group method is applied along with perturbation method in the derivation of an analytical solution which is compared to numerical solution. alient features arc taken into account when th<' fluid saturates thr porous mrdium. Thr 0ffrds of porous mrclinm, permeation Rrynolds nnmhcr and wall dilation rate on the self-axial velocity arc shown and discussed. Lastly

temperature distribution is illustrated.

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