A. Ishak, R. Nazar and I. Pop October 2006 The Arabian Journal for Science and Engineering, Volume 31, Number 2B 165 UNSTEADY MIXED CONVECTION BOUNDARY LAYER FLOW DUE TO A STRETCHING VERTICAL SURFACE A. Ishak and R. Nazar ∗ School of Mathematical Sciences, Faculty of Science & Technology National University of Malaysia, 43600 UKM Bangi, Selangor, Malaysia and I. Pop Faculty of Mathematics, University of Cluj R-3400 Cluj, CP 253, Romania اﻟﺨﻼﺻــﺔ: ﺎورѧΠϣ Ϫϳ ˴ﺪΣ ﺔϘΒτϟ ΖΑﺎΜϟ اﺮϴϏ ςϠΘΨϤϟ اϖϓﺪΘϟ اΚΤΒϟ ا هﺬاϲϓ ﺪرسϧ ةﻮعѧοﻮϣ ﺪѧΘϤ˵ ϣ ﻮديѧϤϋ ΢τδѧϟ ﺎطϐπѧϧϼϟ ϞѧΑﺎϗ ﺮѧϴϏ ﺰجѧϟ ϊ ﺎﺋѧϣ ϲѧϓ . ﺪѧϗ وϊѧϣ  ﺎѧϴτΧ ﺮѧϴϐΘΗ ﺮارةѧΤϟ ا ﺔѧΟ ودرﺪةѧΘϤϤϟ اﺔϋﺮδѧϟ ا أنﺎϨѧοﺮΘϓ ا ΢τδϟ اﻰϠϋ ﺪةΘϤϤϟ اﺔϓﺎδϤϟ ا. ΘδﺎآόΘϣ وﺪارϘϤϟ اϲϓ ϦϴΘϳﺎوδΘϣ ϦϴΗﻮϗ ﺎϨϘΒσ وϴ ϲѧϓ وﺮϴμѧϗ Ϧϣﺰϟ ϩﺎΠΗϻ اϲϓ Ϧ ﻮرΤϣ ϩﺎΠΗ ا) x ( ﺪΘϤϣ ΢τδϟ اﻰϘΒϳ ΚϴΤΑ  اϞﺎﺋδѧϟ اﺮارةѧΣ ﺔѧΟ درﺎويδѧΗ وϞѧλ اﻷﺔѧτϘϧ ﻰѧϠϋ ﺔѧﻈϓﺎΤϤϟ اϊѧϣ ϪτϴΤϣ ϊϣ ﺰجϠϟ ا) T ∞ .( ﺔѧϘϳﺮσ ﺪامΨΘγﺎΑ ﻚϟ وذﺔ،ΘΑﺎΜϟ اﺮϴϏ ﺔϳ ﱢ ˵ﺪΤϟ اﺔϘΒτϠϟ ﺔϟﻮΤϤϟ اﺔϟﺎدόϤϠϟ  ﺎϳﺪدϋ  ϼΣ ﺪمϘϧ ﺪوقϨλ – ﺮϠϴ آﺔϳﺪاΒϟ اϦϣ ϲϟﺎϘΘϧϻ اϦϣﺰϟ الϼΧ ) 0 t = ( ﺔϳﻬﺎϨϟ اﻰϟ إ) t →∞ ( ѧϴﻬﺎﺋϨϟ اﺔϟﺎΤϟ ا أيϖϓﺪѧΘϠϟ ﺔ ΖΑﺎΜϟ ا. ﺪϗ وϲϠϴϠΤΗ  ˳ ϞΣ ﺮادϳﺈΑ ﺎϨϤϗ ΖѧΑﺎΜϟ اﺮѧϴϏ ϖϓﺪѧΘϠϟ ﺔϴﺪاﺋΘΑϻ اﺔϠΣﺮϤϟ اﺔϟﺎدόϤϟ ) 0 < t << 1 .( وﺪѧϗ ﺎϧﺪѧΟ اﻷϞ˴ Σ Ϧϣ ﺎلϘΘϧϻ ا أن ﺎϴΑﺎϴδѧϧ ا آﺎنﺔϠϳﻮτϟ اﺔϨϣ اﻷزﺪϨϋ ϞΤϟ اﻰϟ إﺮةϴμϘϟ اﺔϨϣ ز. ΚѧΤΒϟ اﺬاѧ هϲѧϓ ﻮردѧϧ ﺎѧϤ آ ،ϲϠΤϤϟ اΖϠγﻮϧ Ϣϗ ور،ϲϠΤϤϟ اϲΤτδϟ اﻜﺎكΘΣϻ اϞϣﺎόϣ ΞﺎﺋΘϧ وϦѧϣ ﺔѧϔϠΘΨϣ ϢϴѧϘϟ ﺔϋﺮδѧϟ واﺮارةѧΤϟ اϊϳﻮزΗ ϊϓﺮϟ اϞϣﺎϋ Ϧϣ ϢﻜΤΘϟ اϞϣﻮاϋ = ϞΗﺪϧﺮاΑ Ϣϗ ور،ΖΑﺎΛ Pr . ∗ Author for correspondence e-mail: rmn72my@yahoo.com Paper Received 11 May 2005; Revised 23 July 2005; Accepted 4 January 2006.