Sains Malaysiana 46(2)(2017): 349–358
http://dx.doi.org/10.17576/jsm-2017-4602-20
Dual Solutions
of Forced Convection Flow along a Stretching Sheet with Variable
Thickness in Presence of Free Stream and Magnetic Field
(Dual Penyelesaian Aliran
Perolakan Dipaksa di Sepanjang Lembaran Regangan dengan Ketebalan
Pemboleh Ubah dalam
Kehadiran Aliran Bebas dan Medan Magnet)
UPENDRA MISHRA1*
& GURMINDER SINGH2
1Department of Mathematics,
Amity University Rajasthan, Jaipur, India
2Department of Applied
Mathematics, Birla Institute of Technology (Ranchi), Ext. Center
Jaipur, 27 Malviya Industrial Area, Jaipur-302017, India
Diserahkan: 9 November
2015/Diterima: 18 Jun 2016
ABSTRACT
The paper aims at studying
forced convection in a viscous incompressible electrically conducting
fluid along stretching sheet with variable thickness in the presence
of variable free stream and magnetic field. The governing equations
of flow and heat transfer are subjected to similarity transformation
using boundary layer assumption and are then solved numerically.
The system of equations possesses dual solutions for negative value
of velocity power index (m). The impact of velocity parameter (λ)
and other parameters on velocity and temperature distributions,
skin friction and heat transfer are studied when system possesses
dual solutions and is presented through graphs and discussed suitably.
It is found that the first solution is in tune with natural physical
phenomena. The second solution possesses very large skin-friction
and fluid velocity as compared to the first solution. The second
solution is stable and is a mere outcome of non-linearity and does
not follow natural phenomena.
Keywords: Free stream; magnetic
field; similarity solution; stretching surface; variable thickness
ABSTRAK
Kertas ini bertujuan mengkaji
perolakan dipaksa dalam pengaliran bendalir likat tak termampat
elektrik di sepanjang lembaran regangan dengan ketebalan pemboleh
ubah dengan kehadiran pemboleh ubah aliran bebas dan medan magnet.
Persamaan pemindahan haba dan aliran tertakluk kepada transformasi
persamaan menggunakan andaian lapisan sempadan dan kemudian diselesaikan
secara berangka. Sistem persamaan mempunyai dua penyelesaian untuk
nilai negatif indeks tenaga halaju (m). Kesan parameter halaju (λ)
dan lain-lain parameter ke atas halaju dan taburan suhu, geseran
kulit dan pemindahan haba dikaji apabila sistem memiliki dual penyelesaian
dan ditunjukkan melalui graf dan dibincangkan penyesuaiannya. Didapati
bahawa penyelesaian yang pertama adalah sealiran dengan fenomena
fizikal semula jadi. Penyelesaian yang kedua memiliki geseran kulit
yang sangat besar dan halaju bendalir berbanding dengan penyelesaian
yang pertama. Penyelesaian kedua adalah stabil dan hasil daripada
kelinearan dan tidak mengikut fenomena semula jadi.
Kata kunci: Aliran bebas; medan magnet; penyelesaian persamaan; permukaan
regangan; ketebalan pemboleh ubah
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*Pengarang untuk surat-menyurat; email:
dr_umishra@yahoo.com
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