Sains Malaysiana 50(9)(2021): 2819-2832

http://doi.org/10.17576/jsm-2021-5009-25

Aliran Titik Genangan MHD dan Pemindahan Haba terhadap Permukaan Telap Meregang/Mengecut dalam Nanobendalir Hibrid

(MHD Stagnation Point Flow and Heat Transfer towards a Permeable Stretching/Shrinking Surface in a Hybrid Nanofluid)

ISKANDAR WAINI¹, ANUAR ISHAK²* & IOAN POP³

¹Fakulti Teknologi Kejuruteraan Mekanikal dan Pembuatan, Universiti Teknikal Malaysia Melaka, Hang Tuah Jaya, 76100 Durian Tunggal, Melaka, 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: 18 March 2019/Accepted: 17 October 2019

ABSTRAK

Aliran mantap dan pemindahan haba dua matra terhadap titik genangan pada permukaan telap yang meregang/mengecut dalam nanobendalir hibrid dengan kesan medan magnet dikaji. Persamaan menakluk bagi masalah tersebut dijelmakan kepada satu set persamaan keserupaan dengan menggunakan penjelmaan keserupaan. Persamaan keserupaan yang terhasil kemudiannya diselesaikan secara berangka menggunakan penyelesai masalah nilai sempadan (bvp4c) dalam perisian Matlab. Kesan beberapa parameter terhadap pekali geseran kulit dan nombor Nusselt setempat serta profil halaju dan suhu dibentangkan dan dibincangkan. Keputusan berangka menunjukkan bahawa penyelesaian dual wujud bagi julat tertentu parameter regangan/kecutan dan fluks jisim. Didapati juga bahawa kadar pemindahan haba meningkat dengan peningkatan pecahan isi padu nanozarah tembaga (Cu) dan parameter fluks jisim. Analisis kestabilan dilakukan untuk menentukan kestabilan penyelesaian dual dalam jangka masa panjang dan keputusan menunjukkan bahawa hanya satu daripada penyelesaian tersebut yang stabil manakala yang lain adalah tidak stabil.

Kata kunci: Analisis kestabilan; MHD; nanobendalir hibrid; penyelesaian dual; permukaan meregang/mengecut; titik genangan

ABSTRACT

The steady two-dimensional stagnation point flow and heat transfer past a permeable stretching/shrinking surface in a hybrid nanofluid with magnetic field effects is investigated. The governing equations of the problem are converted into a set of similarity equations by using similarity transformation. The resulting similarity equations are then solved numerically using the boundary value problem solver (bvp4c) in Matlab software. The effects of several parameters on the skin friction coefficient and the local Nusselt number as well as the velocity and temperature profiles are presented and discussed. Results found that dual solutions exist for a certain range of the stretching/shrinking and mass flux parameters. It is also found that the heat transfer rate increases with the increasing of the copper (Cu) nanoparticle volume fractions and mass flux parameter. A temporal stability analysis is performed to determine the stability of the dual solutions in a long run, and it is shown that only one of them is stable while the other is unstable.

Keywords: Dual solutions; hybrid nanofluid; MHD; stability analysis; stagnation point; stretching/shrinking surface

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*Corresponding author: anuar_mi@ukm.edu.my