Effects of uniform radial electric field on the MHD and heat transfer due to a shrinking stretching rotating disk

Year 2019, , 588 - 599, 01.08.2019

Nihan Uygun Ercan

https://doi.org/10.16984/saufenbilder.466151

Cited By: 2

Abstract

Flow and heat transfer of an incompressible electrically conducting fluid on radially shrinking/stretching rotating disk in presence of uniform magnetic field are studied in the present paper. The problem is an extension of the well-known von Karman viscous pump problem to the configuration with a shrinkable/stretchable disk with or without rotation. Navier-Stokes equations, Maxwell equation and energy equation have been modied in presence of uniform radial electric field and magnetic field. The governing partial differential equations have been transformed into ordinary differential form by using similarity transformations. The system of equations generated by Navier-Stokes, Maxwell and energy equations has been solved by using Chebyshev collocation technique for varying values of radial electric, magnetic interaction parameters, Eckert and rotation numbers. Accuracy of the method is verified through comparing results in the literature. Effects of parameters in the governing equations are depicted graphically and are analyzed.

Keywords

Electric potential, Radial shrinking, Radial stretching, MHD flow, Heat transfer

References

• Altan T., Oh S. and Gerel H. Metal forming Fundamentals and Applications, American Society of Metals, Metals Park, 1979.
• Backok N., Ishak A., Pop I. Unsteady boundary-layer flow and heat transfer of a nanofuid over a permeable stretching/shrinking sheet. Int J Heat Mass Transfer,55, 2102-2109, 2012.
• Benton E. T., On the flow due do rotating disk. Journal of Fluid Mechanics, 24, 781-800, 1966.
• Cochran W. G., The flow due to rotating disk. Proceeding of the Cambridge Philosophical Society, 30, 365-375, 1934.
• Cortell R., On a certain boundary value problem arising in shrinking sheet flows, Appl Math Comput,217, 4086-4093, 2010.
• Crane L., J., Flow past a stretching plate, Z. Angew. Math. Phys. 21, 645-647, 1970.
• Evans H. L., Laminar Boundary Layer Theory. Addison-Wesley, 1968.
• Fang T., Flow over a stretchable disk. Phys. Fluids bf 19 ,128105, 2007.
• Fang T., Zhang J., Thermal boundary layers over a shrinking sheet: an analytical solution.Acta Mech, 209, 325-343,2010.
• Fang T., Lee C. F. F.& Zhang J. The boundary layers of an unsteady incompressible stagnation-point flow with mass transfer. Int J Nonlinear Mech ,46(7), 942-948, 2011.
• Fisher E. G., Extrusion of Plastics, Wiley, New York, 1976.
• Hossain, M. A.; Hossain, A.; Wilson, M., Unsteady flow of viscous incompressible fluid with tempreture-dependent viscosity due to a rotating disk in the presence of transverse magnetic field and heat transfer. International Journal of Thermal Sciences, 40, 11-20, 2001.
• Karman, T. V.", Uber laminare und turbulente Reibung. Zeitschnnift fur angewantee Mathematik und Mechanik. 1, 233-252, 1921.
• Khan Y., Wu Q., Faraz N., Yildirim A., The effects of variable viscosity and thermal conductivity on a thin film flow over a shrinking/stretching sheet Comput Math Appl, 61,3391-3399, 2011.
• Makukula Z. G., Sibanda P., Motsa S. S., Shateyi S., On new numerical techniques for the mhd flow past a shrinking sheet with heat and mass transfer in the presence of a chemical reaction Math Probl Eng, 2011, 1-19, 2011.
• Miklavcic M., Wang C. Y., Viscous flow due to a shrinking sheet Q Appl Math, 64, 283-290,2006.
• Schlichting H., Boundary Layer Theory McGraw-Hill, New York, 1968.
• Sparrow E. M., Cess, R. D. Magnetohydrodynamic flow and heat transfer about a rotating disk. Trans. ASME Ser. E. J. Appl. Mech. 29, 181-192, 1962.
• Tadmor Z, Klein I. Engineering principles of plasticating extrusion, Polymer Science andEngineering Series, New York, Van Norstrand Reinhold, 1970.
• Turkyilmazoglu M.,Effects of uniform radial electric field on the MHD heat and fluid flowdue to a rotating disk. Internat. J. Engrg. Sci. 51, 233-240, 2012.
• Turkyilmazoglu M., A class of exact solutions for the incompressible viscous magnetohydrodynamic flow over a porous rotating disk. Acta Mech. Sin. 28, bf 2, 335-347, 2012.
• Turkyilmazoglu M., MHD fluid flow and heat transfer due to a stretching rotating disk. Int.J. Therm. Sci. 51, 195-201, 2012.
• Turkyilmazoglu M., MHD fluid flow and heat transfer due to a shrinking rotating disk. Computers & Fluids, 90, 51-56, 2014.
• Uygun N., Effect of Hall current on the MHD Fluid Flow and Heat Transfer due to a rotating disk with uniform radial electric field. HJMS 46(6), 1445-1462, 2015.
• Wang C. Y., The three-dimensional flow due to a stretching at surface. Phys. Fluids 27, 1915, 1984.
• Wang C. Y., Exact solutions of the unsteady Navier-Stokes equations. Appl. Mech. Rev. 42, S269, 1989.
• Wang C. Y., Exact solutions of the steady state Navier-Stokes equations. Annu. Rev. Fluid Mech. 23, 159, 1991.
• Wang C. Y., Stagnation flow towards a shrinking sheet Int J Non-linear Mech, 43, 377-382,2008.
• Watson L. T., Wang C. Y., Deceleration of a rotating disk in a viscous fluid. Phys Fluids 22(12), 2267-2269, 1979.