Sains Malaysiana 43(8)(2014): 1239-1247

 

Note on Dual Solutions for the Mixed Convection Boundary Layer Flow Close to the Lower Stagnation Point of a Horizontal Circular Cylinder: Case of Constant Surface Heat Flux

(Nota Dua Penyelesaian bagi Aliran Lapisan Sempadan Perolakan Bercampur Hampir

dengan Rendah Silinder Bulat Mendatar: Kes Fluks Haba Permukaan Malar)

 

Alin V. Roşca1, Natalia C. Roşca2 & Ioan Pop2*

 

1Faculty of Economics and Business Administration, Department of Statistics, Forecasts and Mathematics

Babeş-Bolyai University, R-400084 Cluj-Napoca, Romania

 

2Faculty of Mathematics and Computer Science, Department of Mathematics, Babeş-Bolyai University

R-400084 Cluj-Napoca, Romania

 

Diserahkan: 29 April 2013/Diterima: 4 Disember 2013

 

 

ABSTRACT

 

The paper reconsiders the problem of the mixed convection boundary layer flow near the lower stagnation point of a horizontal circular cylinder with a second order slip velocity model and a constant surface heat flux studied recently by Roşca et al. (2013). The ordinary (similarity) differential equations are solved numerically using the function bvp4c from Matlab for different values of the governing parameters. It is found that the similarity equations have two branches, upper and lower branch solutions, in a certain range of the mixed convection parameters. A stability analysis has been performed to show that the upper branch solutions are stable and physically realizable, while the lower branch solutions are not stable and therefore, not physically possible. This stability analysis is different by that presented by Roşca et al. (2013), who have presented a time-dependent analysis to determine the stability of the solution branches.

 

Keywords:  Dual solutions; mixed convection; numerical solution; second-order slip flow; similarity solution; stagnation point

 

ABSTRAK

 

Kertas ini mempertimbangkan semula masalah aliran lapisan sempadan perolakan bercampur berhampiran titik genang rendah silinder bulat mendatar dengan model halaju gelincir peringkat kedua dan fluks haba permukaan malar yang dikaji oleh Roşca et al. (2013) sebelum ini. Persamaan pembezaan biasa (keserupaan) diselesaikan secara berangka menggunakan bvp4c fungsi dari Matlab bagi nilai berbeza daripada parameter pengelasan. Adalah didapati bahawa keserupaan persamaan mempunyai dua cabang, penyelesaian cabang atas dan bawah dalam sesetengah julat parameter perolakan bercampur. Analisis kestabilan yang telah dijalankan menunjukkan bahawa penyelesaian cabang atas adalah stabil dan tersedia secara fizikal, manakala penyelesaian cabang bawah adalah tidak stabil dan oleh itu, tidak mungkin tersedia secara fizikal. Analisis kestabilan ini adalah berbeza daripada yang dikemukakan oleh Roşca et al. (2013) yang telah menyampaikan analisis bersandar- masa untuk menentukan kestabilan cabang penyelesaian.

 

Kata kunci: Dua penyelesaian; halaju gelincir peringkat kedua; penyelesaian berangka; penyelesaian persamaan; perolakan bercampur; titik stagnasi

 

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*Pengarang untuk surat-menyurat; email: popm.ioan@yahoo.co.uk

 

 

 

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