Sains Malaysiana 40(12)(2011): 1359–1367


Viscous Flow Due to a Permeable Stretching/Shrinking Sheet in a Nanofluid

(Aliran Likat dengan Helaian Meregang/Mengecut dalam Nanobendalir)



Norihan Md. Arifin

Department of Mathematics and Institute for Mathematical Research, Universiti Putra Malaysia

43400 UPMSerdang, Selangor D.E. Malaysia


Roslinda Nazar

School of Mathematical Sciences, Faculty of Science & Technology

& Solar Energy Research Institute, Universiti Kebangsaan Malaysia

43600 UKM Bangi, Selangor D.E. Malaysia


Ioan Pop*

Faculty of Mathematics, University of Cluj, R-3400 Cluj, CP 253, Romania


Received: 1 December 2010 / Accepted: 3 March 2011




The classical problems of forced convection boundary layer flow and heat transfer near the stagnation point on a permeable stretching/shrinking surface in a nanofluid is studied theoretically. The similarity equations were solved numerically for two types of nanoparticles, namely copper and silver in the base fluid of water with the Prandtl number Pr = 6.7850 to investigate the effect of the solid volume fraction or nanoparticle volume fraction parameter φ of the nanofluid. Also the case of conventional or regular fluid (φ = 0) with Pr = 0.7 is considered for comparison with previously known results from the open literature. The comparison showed excellent agreement. The skin friction coefficient, the Nusselt number and the velocity and temperature profiles were presented and discussed in detail. It was found that the nanoparticle volume fraction substantially affects the fluid flow and heat transfer characteristics.


Keywords: Boundary layer; heat transfer; nanofluid; stagnation-point flow; stretching/shrinking sheet




Masalah klasik bagi aliran lapisan sempadan olakan paksa dan pemindahan haba berdekatan titik genangan pada permukaan meregang/mengecut yang telap dalam nanobendalir telah dikaji secara teori. Persamaan keserupaan telah diselesaikan secara berangka bagi dua jenis nanozarah, iaitu kuprum dan perak dalam bendalir asas air dengan nombor Prandtl Pr = 6.7850 untuk mengkaji kesan parameter pecahan isipadu pepejal atau pecahan isipadu nanozarah φ bagi nanobendalir. Kes bagi bendalir biasa atau konvensional (φ = 0) dengan Pr = 0.7 dipertimbangkan bagi tujuan perbandingan dengan keputusan terdahulu yang diketahui. Hasil perbandingan tersebut adalah sangat baik. Pekali geseran kulit, nombor Nusselt serta profil-profil halaju dan suhu telah dipersembah dan dibincangkan dengan terperinci. Didapati bahawa pecahan isipadu nanozarah banyak mempengaruhi ciri-ciri aliran bendalir dan pemindahan haba.


Kata kunci: Aliran titik-genangan; helaian meregang/mengecut; lapisan sempadan; nanobendalir; pemindahan haba 



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