Twodimensionalequationsofsteadymotionforthirdorderfluidsareexpressedinaspecialcoordinatesystemgeneratedbythepotentialflowcorrespondingtoaninviscidfluid.Fortheinviscidflowaroundanarbitraryobject,thestreamlinesarethephicoordinatesandvelocitypotentiallinesarepsi-coordinateswhichformanorthogonalcurvilinearsetofcoordinates.Theoutcome,boundarylayerequations,isthenshowntobeindependentofthebodyshapeimmersedintotheflow.Asafirstapproximation,assumptionthatsecondgradetermsarenegligiblecomparedtoviscousandthirdgradeterms.Secondgradetermsspoilscalingtransformationwhichisonlytransformationleadingtosimilaritysolutionsforthirdgradefluid.ByusingLiegroupmethods,infinitesimalgeneratorsofboundarylayerequationsarecalculated.Theequationsaretransformedintoanordinarydifferentialsystem.NumericalsolutionsofoutcomingnonlineardifferentialequationsarefoundbyusingcombinationofaRunge-Kuttaalgorithmandshootingtechnique.