IOSR Journal of Mathematics (IOSR-JM) e-ISSN: 2278-5728, p-ISSN: 2319-765X. Volume 10, Issue 6 Ver. V (Nov - Dec. 2014), PP 78-83 www.iosrjournals.org www.iosrjournals.org 78 | Page Numerical solution of the Falkner Skan Equation by using shooting techniques Dr. Summiya Parveen Abstract:The aim of the paper is to examine the boundary value problems characterized by the well-known Falkner- Skan Equation.The Falkner -Skan Equation is governed by the third order non liner ordinary differential equation and then to solve numerically using the RungeKutta 4 th order with shooting techniques .and solve the Falkner Skan Equation for different parameters  and the numerical results are obtain by using Mat lab Software and compare the results of the literature [1],[2],[3]. Key words: Boundary layer, Blasius flow, Falkner Skan flow, RungeKutta method, Shooting Technique. I. Introduction: TheFalkner- Skanequationarisesinthestudyoflaminarboundarylayersflowexhibitingsimilaritysolution. Assumingsteady,incompressible,laminarflowwithconstantfluidpropertiesandnegligibleviscousdissipation,the boundarylayerequationscanbereducedto[1]    +    =      +   2   2  (1)   +   =0 (2)    +    =   2   2  (3) whereU e (x)isthefreestreamvelocity,uandvarethevelocitycomponentsinxandydirectionsrespectivelyan dv is the kinematic viscosity. Solution of these equations is simplified by the fact that for constant properties, conditionsinthevelocityboundarylayerareindependent oftemperature speciesconcentration. Hencewemay beginbysolvingthehydrodynamicproblem(1)and(2)totheexclusionofEq.(3).Oncethehydrodynamicproblem has been s o l v e d , s o l u t i o n t o e q u a t i on ( 3) c a n be obtained. In the particular case ofthe two-dimensional, incompressibleboundary-layerflowoverawedge,whenthefreestreamvelocityisoftheformU e (x)=Kx m ,the governing partial differential equations can be converted to ordinary differential equation by employing the followingsimilaritytransformation:  ,  =    ,  = √  +1 −1 2 2 This leads Esq.(1) and (2) to the well know Falkner Skan Equation.  3   3 +   2   2 + 1 −    2  =0 With the boundary conditions: 0 =0  ′ 0 =0 ′ = ∞ =1 The Falkner-Skan equation constitutesathirdorder, nonlinear twopoint boundary-valueproblem,no exactanalyticalsolutionisknown.Inthecase of = 0,the Falkner-Skan equationreducestothewell- known Blasiusequationwhichisperhapsoneofthemostfamousequationsoffluiddynamicsandrepresentstheproblemof anincompressiblefluidthatpassesona semi-infinityflatplate.Inthecaseofacceleratingflows(  >0),thevelocity profileshavenopointsofinflection,whereasinthecaseofdeceleratedflows[4],[5],[6] ( <0).Physicallyrelevantsolutions existonlyfor-0.19884<≤ 2[2].