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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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