{"title":"Exact Solutions of Steady Plane Flows of an Incompressible Fluid of Variable Viscosity Using (\u03be, \u03c8)- Or (\u03b7, \u03c8)- Coordinates","authors":"Rana Khalid Naeem, Asif Mansoor, Waseem Ahmed Khan, Aurangzaib","volume":35,"journal":"International Journal of Mathematical and Computational Sciences","pagesStart":996,"pagesEnd":1004,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/1733","abstract":"

The exact solutions of the equations describing the steady plane motion of an incompressible fluid of variable viscosity for an arbitrary state equation are determined in the (ξ,ψ) − or (η,ψ )- coordinates where ψ(x,y) \uf020is the stream function, ξ \uf020and η are the parts of the analytic function, ϖ =ξ( x,y )+iη( x,y ). Most of the solutions involve arbitrary function\/ functions indicating
\r\nthat the flow equations possess an infinite set of solutions. <\/p>\r\n","references":" R.K. Naeem, and S.A Nadeem, \"Study of plane steady plane flows of an\r\nincompressible fluid of variable viscosity using Martin-s method,\" Applied\r\nMechanics and Engineering J. , vol.1, no.3, pp. 397-433, 1996.\r\n M.H. Martins, \"The flow of a viscous fluid,\" Rat. Mech.Anal, no. 41,\r\npp266-287, 1971.\r\n R.K. Naeem, and S.A Ali, \"A class of exact solutions to equations\r\ngoverning the steady plane flows of an incompressible fluid of variable\r\nviscosity via von-Mises variables, International Journal of Applied\r\nMechanics and Engineering, vol .6, no. 2, pp. 395-436, 2001.\r\n F. Labropulu, and O.P. Chandna, \"Exact solutions of steady plane MHD\r\naligned flows using (\u256c\u00a5 ,\u256c\u00c0 )-or (\u256c\u00c0 ,\u00a4\u00ea )-coordinates,\" Int. J. Math. & Math.\r\nSc., vol.20, no.1, pp. 165-186, 1997.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 35, 2009"}