MHD Flow of Casson Fluid Due to Quadratic Stretching of the Sheet

International Journal of Mechanical Engineering

© 2019 by SSRG - IJME Journal

Volume 6 Issue 2

Year of Publication : 2019

Authors : B. Lakshmi, G. V. Pradeep, K. Rama Narasimha, K.R. JayaKumar

10.14445/23488360/IJME-V6I2P102

How to Cite?

B. Lakshmi, G. V. Pradeep, K. Rama Narasimha, K.R. JayaKumar, "MHD Flow of Casson Fluid Due to Quadratic Stretching of the Sheet," SSRG International Journal of Mechanical Engineering, vol. 6,  no. 2, pp. 8-12, 2019. Crossref, https://doi.org/10.14445/23488360/IJME-V6I2P102

Abstract:

The study on steady Non-Newtonian incompressible magnetohydrodynamic Casson fluid flow over a quadratic stretching sheet stretched with a velocity
u_s=ax+bx² is conducted. The resulting equations, along with the suitable boundary conditions, are solved, and numerical values are tabulated. The velocity fields are studied through graphs, and the numerical values of parameters like Magnetic parameter, Suction parameter, Casson parameter are varied, and their effect on the velocity profiles are discussed. Also, the effect of these parameters on the value of the Skin friction coefficient is analyzed.

Keywords:

Quadratic, Casson, MHD, incompressible.

References:

[1] LJCrane, Flow past a stretching plate. Journal of Applied Mathematics and Physics, vol. 21, No.4, (1970), pp. 645-647.
[2] Crepeau J C, Clarksean R. “Similarity solutions of natural convection with internal heat generation”. Transactions of A.S.M.E. – Journal of Heat Transfer. 119,(1997), 184-185.
[3] Bararnia H, Gori M. “An analytical study of boundary layer flows on a continuous stretching surface”. Acta Appl Math,(2009) 106, 125-33.
[4] Bidin Biliana, Nazar Roslinda. “Numerical solution of the boundary layer flow over an exponentially stretching sheet with thermal radiation”. Eur J Sci Res, (2009), 3394:710-7.
[5] Ahmad N and Mishra M. “Unsteady boundary layer flow and heat transfer over a stretching sheet”. Proceedings of 28th U.I.T. Heat transfer Congress, Brescia, 21-23 June (2010), and pp.37-40.
[6] Bataller RC. “Magnetohydrodynamic flow and heat transfer of an upper convicted Maxwell fluid due to a stretching sheet”. Fluid Dynamics and Materials Processing (2011), vol.7, no.2, pp.153-173.
[7] Turkyilmazoglu M. “Analytic heat and mass transfer of the mixed hydrodynamic/thermal slip MHD viscous flow over a stretching sheet”. Int. J. Mech. Sci. 53 (2011), 886–896.
[8] Cortell R. “Heat transfer in a fluid through a porous medium over a permeable stretching surface with thermal radiation and variable thermal conductivity”. Canadian Journal of Chemical Engineering,(2012), vol.90, no.5, pp.1347-1355.
[9] Pavithra G M and Gireesha B J. “Unsteady flow and heat transfer of a fluid particle suspension over an exponentially stretching sheet”. Ain Shams Engineering Journal, (2014),5, pp.613-624.
[10] Sajid M, Ahmed I, Hayat T. “Unsteady flow and heat transfer of a second-grade fluid over a stretching sheet”. Communications in Nonlinear Science and Numerical Simulation,14(2009)096-108.
[11] Awang Kechil S and Hashim I. “Series Solution of flow over a nonlinearly stretching sheet with chemical reaction and magnetic field”. Physics Letters,(2008) Section A, vol. 372, no. 13, pp. 2258–2263.
[12] Raftari Behrouz, Mohyud-din Syed Tauseef. “The solution to the MHD flow over a nonlinearly stretching sheet by a homotopy perturbation method”. Science China Physics, Mechanics & Astronomy,(2011), Volume 54, Issue 2, pp. 342–345.
[13] Rana P, Bhargava R. “Flow and heat transfer of a Nanofluid over a nonlinearly stretching sheet: A numerical study”. Commun Nonlin Sci Numer Simul,(2012), Vol. 17, 212–226.
[14] Fekry M Hady, Fouad S Ibrahim. “The boundary layer viscous flow of a Nanofluid and heat transfer over a nonlinearly stretching sheet with radiation” effect was analyzed. Nanoscale Research Letters,(2012), 7:229
[15] Khader MM, Megahed A M. “Numerical solution for boundary layer flow due to a nonlinearly stretching sheet with variable thickness and slip velocity”. Eur.Phys.J.Plus128:100 10.1140/epjp/I 2013-13100-7.
[16] Zaimi K, Ishak A, Pop I. “Boundary layer flow and heat transfer over a nonlinearly permeable stretching/shrinking sheet in a Nano-fluid”. Scientific Reports 4,(2014), 4404(1-8).
[17] Kumaran V and Ramanaiah G. “A note on the flow over a stretching sheet”. Acta Mechanical,(1996), vol.116, pp.229-233.
[18] Khan S K and Sanjayanand E. “Viscoelastic boundary layer MHD flow through a porous medium over a porous quadratic stretching sheet”. Archives of Mechanics, (2004), vol.56, no.3, pp.191-204.
[19] Kelson N A. “Note on Similarity solutions for viscous flow over an impermeable and nonlinearly (Quadratic) stretching sheet” International Journal of Nonlinear Mechanics,(2011),vol.46, no.8, pp.1090-1091.
[20] Rafael Cortell. “Further results on nonlinearly stretching permeable sheets: Analytic Solution for MHD flow and mass transfer”. Mathematical Problems in Engineering. vol2012, Article ID 743130, 18pages.