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 ISHAK^2* & 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

REFERENCES

Arifin, N.M., Nazar, R. & Pop, I. 2011. Viscous flow due to a permeable stretching/shrinking sheet in a nanofluid. Sains Malaysiana 40(12): 1359-1367.

Bachok, N., Ishak, A. & Pop, I. 2013. Boundary layer stagnation-point flow toward a stretching/shrinking sheet in a nanofluid. Journal of Heat Transfer 135: 1-5.

Choi, S.U.S. & Eastman, J.A. 1995. Enhancing Thermal Conductivity of Fluids with Nanoparticles. doi:. https://www. osti.gov/servlets/purl/196525.

Gogoi, M.K. 2015. Effects of chemical reaction on MHD boundary layer flow over an exponentially stretching sheet with Joule heating and thermal radiation. International Research Journal of Engineering and Technology 2: 768-773.

Haile, E. & Shankar, B. 2015. Boundary-layer flow of nanofluids over a moving surface in the presence of thermal radiation, viscous dissipation and chemical reaction. Applications and Applied Mathematics: An International Journal 10(2): 952-969.

Hayat, T., Aziz, A., Muhammad, T. & Alsaedi, A. 2016. On magnetohydrodynamic three-dimensional flow of nanofluid over a convectively heated nonlinear stretching surface. International Journal of Heat and Mass Transfer 100: 566- 572.

Ibrahim, S.M. & Suneetha, K. 2016. Heat source and chemical effects on MHD convection flow embedded in a porous medium with Soret, viscous and Joules dissipation. Ain Shams Engineering Journal 7(2): 811-818.

Kameswaran, P.K., Narayana, M., Sibanda, P. & Murthy, P.V.S.N. 2012. Hydromagnetic nanofluid flow due to a stretching or shrinking sheet with viscous dissipation and chemical reaction effects. International Journal of Heat and Mass Transfer 55: 7587-7595.

Krishnamurthy, M.R., Prasannakumara, B.C., Gireesha, B.J. & Gorla, R.S.R.G. 2016. Effect of chemical reaction on MHD boundary layer flow and melting heat transfer of Williamson nanofluid in porous medium. Engineering Science and Technology, An International Journal 19(1): 53-61.

Mansur, S. & Ishak, A. 2016. Unsteady boundary layer flow of a nanofluid over a stretching/shrinking sheet with a convective boundary condition. Journal of the Egyption Mathematical Society 24(4): 650-655.

Merkin, J.H. 1985. On dual solutions occurring in mixed convection in a porous medium. Journal of Engineering Mathematics 20(2): 171-179.

Mishra, U. & Singh, G. 2017. Dual solutions of forced convection flow along a stretching sheet with variable thickness in presence of free stream and magnetic field. Sains Malaysiana 46(2): 349-358.

Mohamed, M.K.A., Noar, N.A.Z.M., Salleh, M.Z. & Ishak, A. 2016. Free convection boundary layer flow on a horizontal circular cylinder in a nanofluid with viscous dissipation. Sains Malaysiana 45(2): 289-296.

Noor, A., Nazar, R. & Jafar, K. 2014. Stability analysis of stagnation-point flow past a shrinking sheet in a nanofluid. Journal of Quality Measurement and Analysis 10(2): 51-63.

Othman, N.A., Yacob, N.A., Bachok, N., Ishak, A. & Pop, I. 2017. Mixed convection boundary-layer stagnation point flow past a vertical stretching/shrinking surface in a nanofluid. Applied Thermal Engineering 115: 1412-1417.

Raees, A., Xu, H., Sun, Q. & Pop, I. 2015. Mixed convection in gravity-driven nano-liquid film containing both nanoparticles and gyrotactic microorganisms. Applied Mathematics and Mechanics (English Edition) 36(2): 163-178.

Shukla, N., Rana, P., Beg, O.A. & Singh, B. 2017. Effect of chemical reaction and viscous dissipation on MHD nanofluid flow over a horizontal cylinder: Analytical solution. AIP Conference Proceeding 1802: 20015.

Venkateswarlu, B. & Narayana, P.S. 2015. Chemical reaction and radiation absorption effects on the flow and heat transfer of a nanofluid in a rotating system. Applied Nanoscience 5(3): 351-360.

Weidman, P.D., Kubitschek, D.G. & Davis, A.M.J. 2006. The effect of transpiration on self- similar boundary layer flow over moving. International Journal of Engineering Science 44(11-12): 730-737.

Zaimi, K., Ishak, A. & Pop, I. 2017. Unsteady flow of a nanofluid past a permeable shrinking cylinder using Buongiorno’s model. Sains Malaysiana 46(9): 1667-1674.

 

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