Sains Malaysiana 49(4)(2020): 899-908

http://dx.doi.org/10.17576/jsm-2020-4904-19

Analisis Kestabilan Aliran Genangan bagi Bendalir Mikrokutub terhadap Permukaan

Mencancang dengan Fluks Haba Ditetapkan

(Stability Analysis of Stagnation Flow of a Micropolar Fluid towards a Vertical Surface with Prescribed Heat Flux)

FATINNABILA KAMAL¹, KHAIRY ZAIMI¹ & ANUAR ISHAK^2*

¹Institut Matematik Kejuruteraan, Kampus Pauh Putra, Universiti Malaysia Perlis, 02600 Arau, Perlis, Malaysia

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

Diserahkan: 18 September 2018/Diterima: 27 Disember 2019

ABSTRAK

Tujuan penyelidikan ini adalah untuk mengkaji kestabilan aliran bendalir bagi masalah aliran genangan dalam bendalir mikrokutub terhadap permukaan mencancang yang telap dengan fluks haba ditetapkan. 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 serta profil halaju dan suhu bagi beberapa nilai parameter menakluk yang terlibat. Penyelesaian dual didapati wujud bagi julat-julat tertentu parameter keapungan atau parameter olakan campurandalam kedua-dua aliran membantu dan aliran menentang. Analisis kestabilan dilakukan untuk menentukan penyelesaian yang stabil dalam masa panjang. Didapati bahawa hanya satu daripada penyelesaian tersebut yang stabil apabila masa berlalu.

Kata kunci: Analisis kestabilan; aliran genangan; bendalir mikrokutub; penyelesaian dual; sedutan/semburan

ABSTRACT

The purpose of this study was to investigate the stability of fluid flow for the problem of stagnation flow in a micropolar fluid towards a vertical permeable surface with prescribed heat flux. 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 as well as the velocity and temperature profiles for some values of the governing parameters involved. Dual solutions are found to exist for a certain range of the bouyancy parameter or the mixed convection parameter in both assisting and opposing flows. A stability analysis is performed to determine which solution is stable in a long run. It is found that only one of the solutions is stable as time passes.

Keywords: Dual solutions; micropolar fluid; stability analysis; stagnation flow; suction/injection

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*Pengarang untuk surat-menyurat: email: anuar_mi@ukm.edu.my