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Sains Malaysiana 48(10)(2019): 2285–2295
http://dx.doi.org/10.17576/jsm-2019-4810-25
Stability Analysis of MHD Carreau Fluid Flow
over a Permeable Shrinking Sheet with Thermal Radiation (Analisis Kestabilan Aliran Bendalir MHD Carreau pada Permukaan Mengecut Boleh Telap
dengan Terma Radiasi) RUSYA IRYANTI
YAHAYA1*,
NORIHAN
MD
ARIFIN1,2
& SITI SUZILLIANA PUTRI
MOHAMED
ISA1,3 1Institute for Mathematical Research,
Universiti Putra Malaysia, 43400 UPM Serdang, Selangor Darul Ehsan,
Malaysia 2Department of Mathematics, Universiti
Putra Malaysia, 43400 UPM Serdang, Selangor Darul Ehsan, Malaysia 3Centre of Foundation
Studies for Agricultural Science, Universiti Putra Malaysia, 43400
UPM Serdang, Selangor
Darul Ehsan, Malaysia Received: 3 April 2019/Accepted: 7 September
2019 ABSTRACT Dual
solutions are discovered in the problem of magnetohydrodynamics
(MHD)
boundary layer flow of Carreau fluid over a permeable shrinking
sheet with thermal radiation. Therefore, a stability analysis is
carried out to identify the stable solution of this problem. For
the stability analysis, the problem is considered to be unsteady
with time derivative introduced into the governing equations. Next,
time-dependent solutions are substituted into these equations to
form linear eigenvalue equations. The smallest eigenvalue of these
equations is then computed using the bvp4c solver in MATLAB.
The results showed that the first solution is stable, while the
second solution is unstable. The first solution is physically meaningful
and realizable in practice, and thus significant to the problem.
Keywords:
Carreau fluid; MHD; shrinking sheet; stability analysis ABSTRAK Penyelesaian
dual telah diperoleh dalam masalah aliran lapisan sempadan magnetohidrodinamik
(MHD)
bendalir Carreau terhadap permukaan telap mengecut dengan radiasi
terma. Sehubungan dengan itu, analisis kestabilan dilakukan bagi
mengenal pasti penyelesaian yang stabil dalam masalah ini. Bagi
analisis kestabilan tersebut, masalah ini telah dipertimbangkan
sebagai masalah yang tidak stabil dengan memperkenalkan terbitan
masa ke dalam persamaan menakluk. Kemudian, penyelesaian bersandar
masa digantikan ke dalam persamaan tersebut untuk menghasilkan persamaan
nilai eigen linear. Nilai eigen terkecil bagi persamaan ini kemudiannya
dihitung menggunakan solver bvp4c di MATLAB.
Keputusannya menunjukkan bahawa penyelesaian pertama adalah stabil
sementara penyelesaian kedua tidak stabil. Penyelesaian pertama
adalah bermakna secara fizikal dan boleh direalisasikan dalam amalan
sebenar. Oleh itu, penyelesaian pertama adalah penting bagi masalah
ini. Kata kunci: Analisis kestabilan;
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*Corresponding author; email: rusyairyanti@gmail.com
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