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

 

Diserahkan: 3 April 2019/Diterima: 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; bendalir Carreau; MHD; permukaan mengecut

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*Pengarang untuk surat-menyurat; email: rusyairyanti@gmail.com

 

 

 

 

 

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