SIMILARITY SOLUTIONS OF BOUNDARY LAYER EQUATIONS FOR A SPECIAL NON-NEWTONIAN FLUID IN A SPECIAL COORDINATE SYSTME

(整期优先)网络出版时间:2004-05-15
/ 1
Twodimensionalequationsofsteadymotionforthirdorderfluidsareexpressedinaspecialcoordinatesystemgeneratedbythepotentialflowcorrespondingtoaninviscidfluid.Fortheinviscidflowaroundanarbitraryobject,thestreamlinesarethephicoordinatesandvelocitypotentiallinesarepsi-coordinateswhichformanorthogonalcurvilinearsetofcoordinates.Theoutcome,boundarylayerequations,isthenshowntobeindependentofthebodyshapeimmersedintotheflow.Asafirstapproximation,assumptionthatsecondgradetermsarenegligiblecomparedtoviscousandthirdgradeterms.Secondgradetermsspoilscalingtransformationwhichisonlytransformationleadingtosimilaritysolutionsforthirdgradefluid.ByusingLiegroupmethods,infinitesimalgeneratorsofboundarylayerequationsarecalculated.Theequationsaretransformedintoanordinarydifferentialsystem.NumericalsolutionsofoutcomingnonlineardifferentialequationsarefoundbyusingcombinationofaRunge-Kuttaalgorithmandshootingtechnique.