Sains Malaysiana 48(1)(2019): 243–250

http://dx.doi.org/10.17576/jsm-2019-4801-28

 

Stability Analysis of MHD Stagnation-point Flow towards a Permeable Stretching/Shrinking Sheet in a Nanofluid with Chemical Reactions Effect

(Analisis Kestabilan Aliran Titik Genangan MHD terhadap Permukaan Telap Meregang/Mengecut dalam Nanobendalir dengan Kesan Tindak Balas Kimia)

 

FATINNABILA KAMAL1, KHAIRY ZAIMI1, ANUAR ISHAK2* & IOAN POP3

 

1Institut Matematik Kejuruteraan, Universiti Malaysia Perlis, 02600 Arau, Perlis Indera Kayangan, Malaysia

 

2Pusat Pengajian Sains Matematik, Fakulti Sains dan Teknologi, Universiti Kebangsaan Malaysia, 43600 UKM Bangi, Selangor Darul Ehsan, Malaysia

 

3Department of Mathematics, Babeş-Bolyai University, 400084 Cluj-Napoca, Romania

 

Received: 11 September 2017/Accepted: 5 September 2018

 

ABSTRACT

The magnetohydrodynamic (MHD) stagnation-point flow of a nanofluid towards a permeable stretching/shrinking sheet with chemical reaction effect is investigated. The governing nonlinear partial differential equations are transformed into a system of nonlinear ordinary differential equations using a similarity transformation which are then solved numerically using the boundary value problem solver, bvp4c built in Matlab software. The numerical results are obtained for the skin friction coefficient, local Nusselt number, local Sherwood number as well as the velocity, temperature and concentration profiles for some values of the governing parameters, namely suction/injection parameter and chemical reaction parameter. Dual solutions are found to exist for a certain range of the stretching/shrinking parameter. A stability analysis is performed to determine which solutions are stable and physically reliable. It is found that the first solutions are stable and the second solutions are unstable.

 

Keywords: Chemical reaction effect; magnetohydrodynamic (MHD); nanofluid; stagnation-point flow; stretching/shrinking sheet; suction/injection

 

ABSTRAK

Aliran titik genangan magnetohidrodinamik (MHD) nanobendalir terhadap permukaan telap meregang/mengecut dengan kesan tindak balas kimia dikaji. Persamaan menakluk dalam bentuk persamaan pembezaan separa tak linear dijelmakan kepada sistem persamaan pembezaan biasa tak linear menggunakan penjelmaan keserupaan seterusnya diselesaikan secara berangka menggunakan penyelesai masalah nilai sempadan, bvp4c dibina dalam perisian Matlab. Keputusan berangka diperoleh bagi pekali geseran kulit, nombor Nusselt setempat dan nombor Sherwood setempat serta profil halaju, suhu dan pecahan isi padu nanozarah bagi beberapa nilai parameter menakluk, iaitu parameter sedutan/semburan dan parameter tindak balas kimia. Penyelesaian dual didapati wujud bagi julat tertentu parameter regangan/kecutan. Analisis kestabilan dijalankan untuk menentukan penyelesaian yang stabil dan bermakna secara fizikal. Didapati bahawa penyelesaian pertama adalah stabil dan penyelesaian kedua tidak stabil.

 

Kata kunci: Aliran titik genangan; kesan tindak balas kimia; magnetohidrodinamik (MHD); nanobendalir; permukaan meregang/mengecut; sedutan/semburan

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*Corresponding author; email: anuar_mi@ukm.edu.my

 

 

 

 

 

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