* Tel.: #1-412-386-4975;fax: #1-412-386-4806. E-mail address: massoudi@netl.doe.gov(M.Massoudi). InternationalJournalofNon-LinearMechanics36(2001)961}976 Localnon-similaritysolutionsforthe #owofa non-Newtonian #uidoverawedge MehrdadMassoudi* U.S. Department of Energy, National Energy Technology Laboratory, P.O. Box 19040, Pittsburgh, PA 15236, USA Received7January2000;accepted15June2000 Abstract Theboundarylayerandheattransferequationsforanon-Newtonian #uid,representedbyapower-lawmodel,over aporouswedgeisstudied.Thefreestreamvelocity,thesurfacetemperaturevariations,andtheinjectionvelocityatthe surfaceareassumedvariables.Similarandnon-similarsolutionsarepresentedandtherestrictionsforthesecasesare studied.Theresultsarepresentedforvelocityandtemperaturepro"lesforvariousvaluesofthedimensionlessnumbers. Thee!ectsofthedi!erentparametersontheskinfrictionco-e$cientandthelocalheattransferco-e$cientarealso studied. PublishedbyElsevierScienceLtd. Keywords: Power-lawmodel;Non-Newtonian #uid;Similarandnon-similarsolutions;Dragreduction;Fluidsofdi!erentialtype 1. Introduction Mechanicsofnon-linear #uidspresentaspecial challengetoengineers,physicists,andmathematic- ians.Thenon-linearitycanmanifestitselfinavar- ietyofways.Oneofthesimplestwaysinwhichthe viscoelastic #uidshavebeenclassi"edisthemeth- odology given by Rivlin and Ericksen [1] and Truesdell and Noll [2], who present constitutive relationsforthestresstensor T asafunctionofthe symmetricpartofthevelocitygradient D,andits higher(total)derivatives.(Anotherclassofmodels istherate-type #uidmodels,suchasOldroyd[3] model. A recent review is given by Rajagopal and Srinivasa [4]). Fluids of di!erential type have attracted much attention, as well as much controversy,inthelastfewdecades.Wereferthe readertoDunnandRajagopal[5]foracomplete andthoroughdiscussionofalltherelevantissues. Themajorattractivenessofthesemodelsisthefact thattheconstitutiverelations,whetherwetakethe second- or the third-grade #uids since they have been studied the most, are that they are derived based on "rst principles and unlike many other &phenomenological' models (cf. Reiner [6]), there are no curve-"ttings or parameters to adjust. Though,inbothofthesegrademodels,thereare material properties that need to be measured. At the same time, the &sign' of these material para- meters and the stability or instability of the motionshavecausedacertaindegreeofmisunder- standing. These issues for the second- and third- grade #uidshavebeendiscussedindetailbyDunn andFosdick[7],andFosdickandRajagopal[8], respectively. 0020-7462/01/$-seefrontmatter.PublishedbyElsevierScienceLtd. PII:S0020-7462(00)00061-5