Revolving Ferrofluid Flow in Porous Medium with Rotating Disk
An attempt has been made to study the effect of rotation on incompressible, electrically non-conducting ferrofluid in porous medium on Axi-symmetric steady flow over a rotating disk excluding thermal effects. Here, we solved the boundary layer equations with boundary conditions using Neuringer-Rosensweig model considering the z-axis as the axis of rotation. The non linear boundary layer equations involved in the problem are transformed to the non linear coupled ordinary differential equations by Karman's transformation and solved by power series approximations. Besides numerically calculating the velocity components and pressure for different values of porosity parameter with the variation of Karman's parameter we have also calculated the displacement thickness of boundary layer, the total volume flowing outward the z-axis and angle between wall and ferrofluid. The results for all above variables are obtained numerically and discussed graphically.
[1] R. P. Feynman, R. B. Leighton, and M. Sands, The Feynman Lecturers on Physics. USA: Addison-Wesley, vol. 1, 1964.
[2] M. I. Shliomis, "Ferrofluids as thermal ratchets,” Physical Review Letters, vol. 92, pp. 188901, 2004.
[3] J. L. Neuringer, and R. E. Rosensweig, "Magnetic fluids,” Physics of Fluids, vol. 7, pp. 1927, 1964.
[4] P. D. S. Verma, and M. J. Vedan, "Helical flow of ferrofluid with heat conduction,” Jour. Math. Phy. Sci., 12, pp. 377-389, 1978.
[5] P. D. S. Verma, and M. J. Vedan, "Steady rotation of a sphere in a paramagnetic fluid,” Wear, vol. 52, pp. 201-218, 1979.
[6] P. D. S. Verma, and M. Singh, "Magnetic fluid flow through porous annulus,” Int. J. Non-Linear Mechanics, vol. 16, pp. 371-378, 1981.
[7] S. Odenbach, Magnetoviscous Effects in Ferrofluids. Berlin: Springer-Verlag, 2002.
[8] R. E. Rosensweig, Ferrohydrodynamics. Cambridge: Cambridge University Press, 1965.
[9] V. Karman, "Uber laminare and turbulente reibung,” Z. Angew. Math. Mech., vol. I, pp. 232- 252, 1921.
[10] W. G. Cochran, "The flow due to a rotating disc,” Proc. Camb. Phil. Soc., vol. 30, pp. 365-375, 1934.
[11] E. R. Benton, "On the flow due to a rotating disk,” Journal of Fluid Mechanics, vol. 24, pp. 781–800, 1966.
[12] H. A. Attia, "Unsteady MHD flow near a rotating porous disk with uniform suction or injection,” Journal of Fluid Dynamics Research, vol. 23, pp. 283-290, 1998.
[13] P. Ram, A. Bhandari, and K. Sharma, "Axi-Symmetric ferrofluid flow with rotating disk in a porous medium,” International Journal of Fluid Mechanics, vol. 2, pp. 151-161, 2010.
[14] H. A. Attia, "Rotating disk flow and heat transfer through a porous medium of a non-Newtonian fluid with suction and injection,” Communication in Non-linear science and numerical simulation, vol. 13, pp. 1571-1580, 2008.
[15] Sunil, and A. Mahajan, "A nonlinear stability analysis of a double-diffusive magnetized ferrofluid with magnetic field-dependent viscosity,” Journal of Magnetism and Magnetic Materials, vol. 321, pp. 2810-2820, 2009.
[16] P. Ram, A. Bhandari, and K. Sharma, "Effect of magnetic field-dependent viscosity on revolving ferrofluid,” Journal of Magnetism and Magnetic Materials, vol. 322, pp. 3476-3480, 2010.
[17] P. Ram, K. Sharma, and A. Bhandari, "Effect of porosity on ferrofluid flow with rotating disk,” International Journal of Applied Mathematics and Mechanics, vol. 6, pp. 67-76, 2010.
[18] G. Komurgoz, A. Arikoglu, and I. Ozkol, "Analysis of the magnetic effect on entropy generation in an inclined channel partially filled with a porous medium,” Numerical Heat Transfer, Part A: Application: An International Journal of Computation and Methodology, vol. 61, pp. 786-799, 2012.
[19] P. Ram, and V. Kumar, "Ferrofluid flow with magnetic field dependent viscosity due to a rotating disk in porous medium,” International Journal of Applied Mechanics, vol. 4, pp. 1250041 (18 pages), 2012.
[20] P. Ram, and V. Kumar, "FHD flow with heat transfer over a stretchable rotating disk,” Multidiscipline Modeling in Materials and Structures, vol. 9, pp. 524-537.
[21] H. Schlichting, Boundary Layer Theory. New York: McGraw-Hill Book Company, 1960.
[1] R. P. Feynman, R. B. Leighton, and M. Sands, The Feynman Lecturers on Physics. USA: Addison-Wesley, vol. 1, 1964.
[2] M. I. Shliomis, "Ferrofluids as thermal ratchets,” Physical Review Letters, vol. 92, pp. 188901, 2004.
[3] J. L. Neuringer, and R. E. Rosensweig, "Magnetic fluids,” Physics of Fluids, vol. 7, pp. 1927, 1964.
[4] P. D. S. Verma, and M. J. Vedan, "Helical flow of ferrofluid with heat conduction,” Jour. Math. Phy. Sci., 12, pp. 377-389, 1978.
[5] P. D. S. Verma, and M. J. Vedan, "Steady rotation of a sphere in a paramagnetic fluid,” Wear, vol. 52, pp. 201-218, 1979.
[6] P. D. S. Verma, and M. Singh, "Magnetic fluid flow through porous annulus,” Int. J. Non-Linear Mechanics, vol. 16, pp. 371-378, 1981.
[7] S. Odenbach, Magnetoviscous Effects in Ferrofluids. Berlin: Springer-Verlag, 2002.
[8] R. E. Rosensweig, Ferrohydrodynamics. Cambridge: Cambridge University Press, 1965.
[9] V. Karman, "Uber laminare and turbulente reibung,” Z. Angew. Math. Mech., vol. I, pp. 232- 252, 1921.
[10] W. G. Cochran, "The flow due to a rotating disc,” Proc. Camb. Phil. Soc., vol. 30, pp. 365-375, 1934.
[11] E. R. Benton, "On the flow due to a rotating disk,” Journal of Fluid Mechanics, vol. 24, pp. 781–800, 1966.
[12] H. A. Attia, "Unsteady MHD flow near a rotating porous disk with uniform suction or injection,” Journal of Fluid Dynamics Research, vol. 23, pp. 283-290, 1998.
[13] P. Ram, A. Bhandari, and K. Sharma, "Axi-Symmetric ferrofluid flow with rotating disk in a porous medium,” International Journal of Fluid Mechanics, vol. 2, pp. 151-161, 2010.
[14] H. A. Attia, "Rotating disk flow and heat transfer through a porous medium of a non-Newtonian fluid with suction and injection,” Communication in Non-linear science and numerical simulation, vol. 13, pp. 1571-1580, 2008.
[15] Sunil, and A. Mahajan, "A nonlinear stability analysis of a double-diffusive magnetized ferrofluid with magnetic field-dependent viscosity,” Journal of Magnetism and Magnetic Materials, vol. 321, pp. 2810-2820, 2009.
[16] P. Ram, A. Bhandari, and K. Sharma, "Effect of magnetic field-dependent viscosity on revolving ferrofluid,” Journal of Magnetism and Magnetic Materials, vol. 322, pp. 3476-3480, 2010.
[17] P. Ram, K. Sharma, and A. Bhandari, "Effect of porosity on ferrofluid flow with rotating disk,” International Journal of Applied Mathematics and Mechanics, vol. 6, pp. 67-76, 2010.
[18] G. Komurgoz, A. Arikoglu, and I. Ozkol, "Analysis of the magnetic effect on entropy generation in an inclined channel partially filled with a porous medium,” Numerical Heat Transfer, Part A: Application: An International Journal of Computation and Methodology, vol. 61, pp. 786-799, 2012.
[19] P. Ram, and V. Kumar, "Ferrofluid flow with magnetic field dependent viscosity due to a rotating disk in porous medium,” International Journal of Applied Mechanics, vol. 4, pp. 1250041 (18 pages), 2012.
[20] P. Ram, and V. Kumar, "FHD flow with heat transfer over a stretchable rotating disk,” Multidiscipline Modeling in Materials and Structures, vol. 9, pp. 524-537.
[21] H. Schlichting, Boundary Layer Theory. New York: McGraw-Hill Book Company, 1960.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:65750", author = "Paras Ram and Vikas Kumar", title = "Revolving Ferrofluid Flow in Porous Medium with Rotating Disk", abstract = "An attempt has been made to study the effect of rotation on incompressible, electrically non-conducting ferrofluid in porous medium on Axi-symmetric steady flow over a rotating disk excluding thermal effects. Here, we solved the boundary layer equations with boundary conditions using Neuringer-Rosensweig model considering the z-axis as the axis of rotation. The non linear boundary layer equations involved in the problem are transformed to the non linear coupled ordinary differential equations by Karman's transformation and solved by power series approximations. Besides numerically calculating the velocity components and pressure for different values of porosity parameter with the variation of Karman's parameter we have also calculated the displacement thickness of boundary layer, the total volume flowing outward the z-axis and angle between wall and ferrofluid. The results for all above variables are obtained numerically and discussed graphically.
", keywords = "Ferrofluid, magnetic field porous medium, rotating disk.", volume = "7", number = "12", pages = "1664-6", }
