Sains Malaysiana 41(11)(2012): 1475–1482


Free Convection Boundary Layer Flow of a Nanofluid from a Convectively Heated Vertical Plate with Linear Momentum Slip Boundary Condition

(Aliran Lapisan Sempadan Olakan Bebas Nanobendalir terhadap Plat Menegak yang dipanaskan

Secara Berolak dengan Syarat Sempadan Gelinciran Momentum Linear)



Md. Jashim Uddin & A.I. Md. Ismail

School of Mathematical Sciences, University of Sains Malaysia, 1800 USM, Penang, Malaysia


I. Pop*

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


Received: 2 February 2012 / Accepted: 9 April 2012



Two dimensional steady laminar boundary layer flow of a nanofluid over a convectively heated vertical flat plate with linear momentum slip boundary condition has been studied numerically. The governing boundary layer equations are non-dimensionalized and transformed into a two point boundary value problem of coupled nonlinear ordinary differential equations in similarity variable before being solved numerically. The resulting equations with corresponding boundary conditions have been solved numerically by Maple 13 which uses Runge-Kutta-Fehlberg fourth- fifth order numerical algorithm for solving nonlinear ordinary boundary value problems. Our analysis reveals that the similarity solution is possible if the convective heat transfer coefficient is directly proportional to x–1/4, where x is the axial distance from the leading edge of the plate. Solutions depend on the seven parameters: Prandtl number, buoyancy ratio, Brownian motion, thermophoresis, Lewis number, momentum slip and convective heat transfer. The effects of the governing parameters on the flow and heat transfer characteristics have been shown graphically and discussed. Comparisons of the present numerical solution with the existing results in the literature are made and our results are in very good agreement. Results for the skin friction factor, the reduced Nusselt and the Sherwood numbers are provided in tabular form for various values of the convective heat transfer parameter. It is found that the skin friction coefficint reduces with the momentum slip and the buoyancy ratio parameters whilst it enhances with the convective heat transfer parameter. It is also found that mass transfer rate enhances with the Lewis number and the convective heat transfer parameter whilst it falls with the thermophoresis parameter.


Keywords: Free convection; momentum slip boundary condition; nanofluids; thermal convective boundary condition




Aliran lapisan sempadan berlamina dua dimensi yang mantap bagi nanobendalir ke atas plat menegak yang dipanaskan secara berolak dengan syarat sempadan gelinciran momentum linear dikaji secara berangka. Persamaan menakluk lapisan sempadan dijadikan tanpa dimensi dan dijelmakan kepada masalah nilai sempadan dua titik yang terdiri daripada persamaan perbezaan biasa tidak linear terganding dalam bentuk pemboleh ubah keserupaan sebelum diselesaikan secara berangka. Persamaan yang terhasil bersama-sama syarat sempadan yang sepadan telah diselesaikan secara berangka melalui Maple 13 dengan menggunakan algoritma berangka Runge-Kutta-Fehlberg peringkat keempat-kelima untuk menyelesaikan masalah nilai sempadan tak linear. Analisis ini mendedahkan bahawa penyelesaian keserupaan adalah mungkin sekiranya pekali pemindahan haba berolak berkadar langsung dengan x–1/4, dengan x ialah jarak paksi dari pinggir depan plat. Penyelesaian bergantung kepada parameter berikut: pergerakan Brownian, perpindahan haba, nombor Lewis, nombor Prandtl, gelinciran momentum dan pemindahan haba berolak. Kesan parameter menakluk ke atas aliran dan ciri-ciri pemindahan haba telah dipamerkan secara bergraf dan dibincangkan. Perbandingan keputusan berangka kajian ini dilakukan dan didapati menepati keputusan yang sedia ada dalam kajian lepas. Keputusan bagi faktor geseran kulit, nombor Nusselt terturun dan nombor Sherwood diberikan dalam bentuk berjadual untuk pelbagai nilai parameter pemindahan haba berolak. Didapati bahawa faktor geseran kulit mengurang dengan slip momentum dan parameter nisbah keapungan dan pada masa yang sama ia meningkat dengan parameter pemindahan haba perolakan. Kadar pemindahan jisim juga didapati meningkat dengan nombor Lewis dan parameter pemindahan haba berolak dan pada masa yang sama ia jatuh dengan parameter thermophoresis.


Kata kunci: Nanobendalir; olakan bebas; syarat sempadan gelinciran momentum; syarat sempadan haba berolak



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