Sains Malaysiana 46(2)(2017): 327–333

http://dx.doi.org/10.17576/jsm-2017-4602-18

Unsteady Magnetoconvective Flow of Bionanofluid with Zero Mass Flux Boundary Condition

(Aliran tak Mantap Magneto-Perolakan bagi Bionanobendalir dengan Keadaan Sempadan Fluks Jisim Sifar)

MD. FAISAL MD. BASIR¹*, M.J. UDDIN^1,2 & A.I. MD. ISMAIL¹

¹School of Mathematical Sciences, Universiti Sains Malaysia, 11800 Penang, Pulau Pinang

Malaysia

²American International University- Bangladesh, Banani Dhaka, 1213, Bangladesh

Received: 24 March 2015/Accepted: 9 May 2016

ABSTRACT

Induced magnetic field stagnation point flow for unsteady two-dimensional laminar forced convection of water based nanofluid containing microorganisms along a vertical plate has been investigated. We have incorporated zero mass flux boundary condition to get physically realistic results. The boundary layer equations with three independent variables are transformed into a system of ordinary differential equations by using appropriate similarity transformations. The derived equations are then solved numerically by using Maple which use the fourth-fifth order Runge-Kutta-Fehlberg algorithm to solve the system of similarity differential equations. The effects of the governing parameters on the dimensionless velocity, induced magnetic field, temperature, nanoparticle volume fraction, density of motile microorganisms, skin friction coefficient, local Nusselt number and motile density of microorganisms transfer rate are illustrated graphically and tabular form. It is found that the controlling parameters strongly affect the fluid flow and heat transfer characteristics. We compare our numerical results with published results for some limiting cases and found excellent agreement.

Keywords: Forced convection; induced magnetic field; microorganisms; nanofluid; unsteady; zero mass flux

ABSTRAK

Medan magnet teraruh pada titik genangan untuk aliran tak mantap lamina dua dimensi perolakan dipaksa daripada nanobendalir berasaskan air yang mengandungi mikroorganisma bersama plat menegak telah dikaji. Kami telah memasukkan keadaan sempadan fluks jisim sifar untuk mendapatkan keputusan yang realistik. Persamaan lapisan sempadan dengan tiga pembolehubah diubah menjadi sistem persamaan pembezaan biasa dengan menggunakan persamaan transformasi serupa yang sesuai. Persamaan yang telah diperoleh diselesaikan secara berangka dengan menggunakan algorithma Runge-Kutta-Fehlberg keempat-lima dalam Maple untuk menyelesaikan sistem persamaan pembezaan. Kesan parameter pada halaju tak berdimensi, medan magnet teraruh, suhu, pecahan isi padu zarah-zarah nano, ketumpatan mikroorganisma motil, pekali geseran kulit, nombor Nusselt dan ketumpatan motil kadar pemindahan mikroorganisma adalah dipamerkan secara grafik dan dalam bentuk jadual. Didapati bahawa parameter kawalan mempengaruhi aliran bendalir dan ciri-ciri pemindahan haba. Kami membandingkan keputusan berangka ini dengan keputusan yang telah diterbitkan bagi kes terhad dan ia menepati keputusan sedia ada di dalam kajian lepas.

Kata kunci: Keadaan sempadan fluks jisim sifar; medan teraruh magnet; mikroorganisma; bendalir nano; perolakan dipaksa; tak mantap

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*Corresponding author; emails: faisalbasir91@gmail.com