Hall impact on the MHD fluid flow and heat transfer with uniform radial electric field due to a stretching rotating disk

In the current paper, the steady flow of an incompressible electrically conducting fluid and heat transfer are studied. In these, we consider the Hall effect over an infinite stretching rotating disk in presence of a magnetic field. Navier-Stokes equations, Maxwell equation and energy equation have been modified in the presence of the Hall impact. Moreover, the uniform magnetic field, and the radial electric field are applied. With the help of the usual similarity transformations, these modified equations are simplified to a set of nonlinear ordinary differantial equations. Numerical solutions of the equations are obtained by using the Chebyshev collocation technique for different values of the entire of the physical parameters. The accuracy of the method is verified by comparing with the results in the literature. The influences of Hall parameter in these equations system are depicted graphically and analyzed.

___

  • [1] L. Aisling and R. Ake, Crystal Growth of Single Salicylamide Crystals, Cryst Growth Des., 2019.
  • [2] T. Altan, S. Oh and H. Gerel, Metal forming Fundamentals and Applications, American Society of Metals, Metals Park, 1979.
  • [3] H.A. Attia, K.M. Ewis, I.H.A. Elmaksoud and N. A. Awad-Allah, Hydromagnetic rotating disk flow of a non-Newtonian fluid with heat transfer and ohmic heating, J. Korean Soc. Ind. Appl. Math. 16 (3), 169-180, 2012.
  • [4] H.A. Attia, Effect of Hall current on the velocity and temperature distributions of Couette flow with variable properties and uniform suction and injection, Comput. Appl. Math. 28 (2), 195-212, 2009.
  • [5] A.L. Aboul-Hassan and H.A. Attia, The flow due to rotating disk with hall effect, Phys. Lett. A 228, 286-290, 1997.
  • [6] E.T. Benton, On the flow due do rotating disk, J. Fluid Mech. 24, 781-800, 1966.
  • [7] R.D. Cess, Unsteady heat transfer from a rotating disk to fluids with low Prandtl numbers, Appl. Sci. Res. 13 (1), 233-240, 1964.
  • [8] W.G. Cochran, The flow due to rotating disk, Proc. Cambridge Philos. Soc. 30, 365-375, 1934.
  • [9] K.R. Cramer and S.I. Pai, Magnetofluid Dynamics for Engineers and Applied Physicists, Scripta Publishing Company, 1973.
  • [10] L.J. Crane, Flow past a stretching plate, Z. Angew. Math. Phys. 21, 645-647, 1970.
  • [11] A. Das and B. Sahoo, Non-Newtonian stagnation point flow due to a stretchable rotating disk, Fluid Mech. Res. Int. 2 (2), 73-83, 2018.
  • [12] D.R. Davies, Heat transfer by laminar flow from a rotating disk at large Prandtl numbers, Quart. J. Mech. Appl. Math. 12, 14-21, 1959.
  • [13] T. Fang, Flow over a stretchable disk, Phys. Fluids 19, 128105, 2007.
  • [14] T. Fang, C.F.F. Lee and J. Zhang, The boundary layers of an unsteady incompressible stagnation-point flow with mass transfer, Int J Nonlinear Mech, 46 (7), 942-948, 2011.
  • [15] E.G. Fisher, Extrusion of Plastics, Wiley, New York, 1976.
  • [16] E.H. Hall, On a New Action of the Magnet on Electric Currents, Amer. J. Math. JSTOR. 2 (3), 287, 1879.
  • [17] T. Hayatab, S. Qayyuma, M. Imtiaza and A. Alsaedib Flow between two stretchable rotating disks with Cattaneo-Christov heat flux model, Results Phys. 7, 126-133, 2017.
  • [18] M.A. Hossain, A. Hossain and M. Wilson, 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, Int. J. Therm. Sci. 40, 11-20, 2001.
  • [19] H.A. Jasmine and J.S.B. Gajjar, Convective and absolute instability in the incompressible boundary layer on a rotating disk in the presence of a uniform magnetic field, J. Engrg. Math. 52 (4), 337-353, 2005.
  • [20] T.V. Kármán, Uber laminare und turbulente Reibung, ZAMM Z. Angew. Math. Mech. 1, 233-252, 1921.
  • [21] S.K. Kumar, W.I. Thacker and L.T. Watson, Magnetohydrodynamic flow and heat transfer about a rotating disk with suction and injection at the disk surface, Comput. Fluids, 16 (2), 183-193, 1988.
  • [22] P.A Laplante, Dictionary of Computer Science, Engineering and Technology CRC Press, 2014
  • [23] K. Millsaps and K. Pohlhausen, Heat transfer by laminar flow from a rotating plate, J. Aeronaut. Sci. 19, 120-126, 1952.
  • [24] A. Mushtaq and M. Mustafa, Computations for nanofluid flow near a stretchable rotating disk with axial magnetic field and convective conditions, Results Phys. 7, 3137-3144, 2017.
  • [25] P. Ram and V. Kumar, FHD flow with heat transfer over a stretchable rotating disk, Multidiscip. Model. Mater. Struct. 9 (4), 524-537, 2013.
  • [26] N. Riley, The heat transfer from a rotating disk., Quart. J. Mech. Appl. Math. 17, 331-349, 1964.
  • [27] B. Sahoo, Effects of partial slip, viscous dissipation and Joule heating on Von Kármán flow and heat transfer of an electrically conducting non-Newtonian fluid, Commun. Nonlinear Sci. Numer. Simul. 14, 2982-2998, 2009.
  • [28] A.M. Siddiqui, M.A. Rana and N. Ahmed, Effects of Hall current and heat transfer on MHD flow of a Burgers’ fluid due to a pull of eccentric rotating disks, Commun. Nonlinear Sci. Numer. Simul. 13 (8), 1554-1570, 2008.
  • [29] C. Soares, Gas Turbines (Second Edition) A Handbook of Air, Land and Sea Applications, 2015.
  • [30] E.M. Sparrow and R.D. Cess, Magnetohydrodynamic flow and heat transfer about a rotating disk, Trans. ASME Ser. E. J. Appl. Mech. 29, 181-192, 1962.
  • [31] E.M. Sparrow and J.L. Gregg, Nonsteady surface temperature effects on forced convection heat transfer, J. Aero. Sci. 24, 776-777, 1957.
  • [32] Z. Tadmor and I. Klein, Engineering principles of plasticating extrusion, Polym. Sci. Eng. Series, New York, Van Norstrand Reinhold, 1970.
  • [33] M. Turkyilmazoglu, Effects of uniform radial electric field on the MHD heat and fluid flow due to a rotating disk, Internat. J. Engrg. Sci. 51, 233-240, 2012.
  • [34] M. Turkyilmazoglu, A class of exact solutions for the incompressible viscous magnetohydrodynamic flow over a porous rotating disk, Acta Mech. Sin. 28 (2), 335-347, 2012.
  • [35] M. Turkyilmazoglu, The MHD boundary layer flow due to a rough rotating disk, ZAMM Z. Angew. Math. Mech. 90 (1), 72-82, 2010.
  • [36] M. Turkyilmazoglu, Resonance instabilities in the boundary-layer flow over a rotating disk under the influence of a uniform magnetic field, J. Engrg. Math. 59 (3), 337-350, 2007.
  • [37] M. Turkyilmazoglu, MHD fluid flow and heat transfer due to a stretching rotating disk, Int. J. Therm. Sci. 51, 195-201, 2012.
  • [38] N. Uygun, Effect of Hall current on the MHD Fluid Flow and Heat Transfer due to a rotating disk with uniform radial electric field, Hacet. J. Math. Stat. 46 (6), 1445-1462, 2015.
  • [39] N. Uygun, Effects of uniform radial electric field on the MHD and heat transfer due to a shrinking/streching rotating disk, SAUJS, 23 (4), 588-599, 2019.
  • [40] C.Y. Wang, The three-dimensional flow due to a stretching flat surface, Phys Fluids 27, 1915-1917, 1984.
  • [41] L.T. Watson and C.Y. Wang, Deceleration of a rotating disk in a viscous fluid, Phys. Fluids, 22 (12), 2267-2269, 1979.