شبیه سازی عددی و ارائه روش حل برای جریان سیال غیر نیوتنی تحت تاثیر میدان مغناطیسی در لایه مرزی یک صفحه کشسان

نویسندگان

1 دانشگاه سمنان

2 دانشگاه صنعتی امیرکبیر

چکیده

جریان آرام تراکم ناپذیر سیال غیر نیوتنی روی یک صفحه کشسان متحرک، در حضور یک میدان مغناطیسی یکنواخت مطالعه شده است. سرعت صفحه مشخص و در طول آن به صورت خطی تغییر می‌کند. به کمک تبدیلات تشابهی، دستگاه معادلات پاره‌ای حاکم بر جریان به یک دستگاه معادلات دیفرانسیل معمولی غیر خطی تبدیل و سپس توسط روش‌ عددی ارئه شده بر مبنای تفاضل محدود ، حل گردیده است. اثرات پارامتر‌های سیال، جریان و میدان مغناطیسی بر میدان سرعت در لایه مرزی بررسی شده است. نتایج نشان می‌دهند که با افزایش میدان مغناطیسی ضخامت لایه مرزی کاهش می‌یابد. همچنین دیده شده است که در نظر گرفتن مدل نیوتنی برای سیالات غیر نیوتنی که تحت تاثیر میدان مغناطیسی هستند، می‌تواند تا 100% خطا به دنبال داشته باشد.

کلیدواژه‌ها


عنوان مقاله [English]

NUMERCIAL FORMULATION AND SIMULATION OF A NON-NEWTONIAN MAGNETIC FLUID FLOW IN THE BOUNDARY LAYER OF A STRETCHING SHEET

نویسندگان [English]

  • M. Dehghan 1
  • M. Mirzaei 2
  • A. Mohammadzadeh 1
1 semnan
2 mm
چکیده [English]

Steady flow of a non-Newtonian fluid over a stretching sheet under influence of a constant transverse magnetic field has been investigated based on the power-law model. Velocity of the sheet varies linearly along the flow direction. PDE type equations of motion of fluid were transformed to a nonlinear ODE type equation using similarity transformation. A numerical scheme based on finite difference and shooting method has been proposed to solve the governing equations. Effects of characteristics of flow, fluid and magnetic field have been investigated. Results show that the magnetic field acts as a drag force and decreases the boundary layer thickness. Finally, considering the Newtonian model for a non-Newtonian fluid causes considerable errors up to 100% especially for the skin friction coefficient.

کلیدواژه‌ها [English]

  • Non-Newtonian fluid
  • Magnetic field
  • Stretching Sheet
  • Similarity Transformation
  • Numerical simulation
 
[1]     Crane LJ. Flow past a stretching plate. Z Angew Math Phys (1970); 21: 645–7.
[2]     Gupta PS, Gupta AS. Heat and mass transfer on a stretching sheet with suction or blowing. Can J Chem Eng (1977); 55: 744–6.
[3]     Chen CK, Char MI. Heat transfer of a continuous stretching surface with suction or blowing. J Math Anal Appl (1988); 135: 568–80.
[4]     A. Acrivos, M. Shah, E.E. Petersen, Momentum and heat transfer in laminar boundary layer flows of non-Newtonian fluids past external surfaces, AIChE J. 6 (1960) 312–317.
[5]     W.R. Schowalter, The application of boundary-layer theory to power-law pseudoplastic fluids: similarity solutions, AIChE J. 6 (1960) 25–28.
[6]     Pavlov KB. Magnetohydrodynamic flow of an incompressible viscous fluid caused by deformation of a plane surface. Magninaya Gidrodinamika (USSR)(1974);4:146–7.
[7]     Char MI. Heat and mass transfer in a hydromagnetic flow of a visco-elastic fluid over a stretching sheet. J Math Anal Appl (1994); 186: 674–89.
[8]     Andersson HI. MHD flow of a visco-elastic fluid past a stretching surface. Acta Mech (1992); 95: 227–30.
[9]     Chiam TC. Magnetohydrodynamic heat transfer over a non-isothermal stretching sheet. Acta Mech (1997); 122: 169–79.
[10] J.C. Misra, G.C. Shit, Biomagnetic viscoelastic fluid flow over a stretching sheet, Appl. Math. Comput. , (2009), 210 (2), 350–361.
[11] M. SubhasAbel, P.G. Siddheshwar, N. Mahesha, Effects of thermal buoyancy and variable thermal conductivity on the MHD flow and heat transfer in a power-law fluid past a vertical stretching sheet in the presence of a non-uniform heat source, International Journal of Non-Linear Mechanics 44 (2009) 1—12.
[12] W.A. Khan, I. Pop, Boundary-layer flow of a nanofluid past a stretching sheet, International Journal of Heat and Mass Transfer 53 (2010) 2477–2483.
[13] O.D. Makinde, A. Aziz, Boundary layer flow of a nanofluid past a stretching sheet with a convective boundary condition, International Journal of Thermal Sciences 50 (2011) 1326e1332.
[14] N. Bachok, A. Ishak, I. Pop, Unsteady boundary-layer flow and heat transfer of a nanofluid over a permeable stretching/shrinking sheet, International Journal of Heat and Mass Transfer 55 (2012) 2102–2109.
[15] W. Ibrahim, B. Shanker, Unsteady MHD boundary-layer flow and heat transfer due to stretching sheet in the presence of heat source or sink, Computers & Fluids 70 (2012) 21–28.
[16] F.M. White, Viscous Fluid Flow, third ed. McGraw-Hill, New York, 2006.
[17] G. Astarita and G. Marrucci, Principles of Non-Newtonian Fluid Mechanics, McGraw-Hill Book Company (UK), 1974.
[18] Andersson HI, Dandapat BS. Flows of a power law fluid over a stretching sheet. Stability Appl Anal Continuous Media (1991); 1: 339–47.
[19] Wang, Y.; Hayat, T.; Hutter, K., On non-linear magnetohydrodynamic problems of an Oldroyd 6-constant fluid, International Journal of Non-Linear Mechanics, 40 (2005), pp. 49– 58.
[20] Denier JP, Dabrowski PP. On the boundary layer equation for power law fluid. Proc R Soc London Ser A (2004); 460: 3143–58.
[21] K.V. Prasad, Dulal Pal, P.S. Datti, MHD power-law fluid flow and heat transfer over a non-isothermal stretching sheet, Commun Nonlinear Sci Numer Simulat 14 (2009) 2178–2189.