Forced Oscillations of Electrical Conducting Fluid Under the Influence of Applied Magnetic Field on the Porous Boundary
Exact solution of an incompressible fluid of second order type by causing forced oscillations in the liquid of finite depth bounded by a porous bottom has been obtained in this paper. The results presented are in terms of non-dimensional elastic-viscosity parameter (β) which depends on the non-Newtonian coefficient and the frequency of excitation (σ) of the external disturbance while considering the porosity (K) and magnetic parameter (m) of the medium into account. The flow parameters are found to be identical with that of Newtonian case as β →0, m →0 and K→ ∞. It is seen that the effect of elastico viscosity parameter, magnetic parameter and the porosity of the bounding surface has significant effect on the velocity parameter, phase parameter, skin friction and mass flow rate. Further, the nature of the paths of the fluid particles have also been obtained with reference to the elastico viscosity parameter, magnetic parameter and the porosity of the bounding surface.
Sanjay B. Kulkarni,
Forced Oscillations of Electrical Conducting Fluid Under the Influence of Applied Magnetic Field on the Porous Boundary, American Journal of Software Engineering and Applications.
Vol. 5, No. 5,
2016, pp. 33-39.
K. R. Rajagopal, P. L. Koloni, “Continuum Mechanics and its Applications”, Hemisphere Press, Washington, DC, 1989.
K. Walters, “Relation between Coleman-Nall, Rivlin-Ericksen, Green-Rivlin and Oldroyd fluids”, ZAMP, 21, 1970 pp. 592-600.
J. E. Dunn, R. L. Fosdick, “Thermodynamics stability and boundedness of fluids of complexity 2 and fluids of second grade”, Arch. Ratl. Mech. Anal, 56, 1974, pp. 191-252.
J. E. Dunn, K. R. Rajagopal, “Fluids of differential type-critical review and thermodynamic analysis”, J. Eng. Sci., 33, 1995, pp. 689-729.
K. R. Rajagopal, “Flow of visco-elastic fluids between rotating discs”, Theor. Comput. Fluid Dyn., 3, 1992, pp. 185-206.
N. Ch. Pattabhi Ramacharyulu, “Exact solutions of two dimensional flows of second order fluid”, App. Sc Res, Sec-A, 15. 1964, pp. 41–50.
S. G. Lekoudis, A. H. Nayef and Saric., “Compressible boundary layers over wavy walls”, Physics of fluids, 19, 1976, pp. 514-19.
P. N. Shankar, U. N. Shina, “The Rayeigh problem for wavy wall”, J. Fluid Mech, 77, 1976, pp. 243–256.
M. Lessen, S. T. Gangwani, “Effects of small amplitude wall waviness upon the stability of the laminar boundary layer”, Physics of the fluids, 19, 1976, pp. 510-513.
K. Vajravelu, K. S. Shastri, “Free convective heat transfer in a viscous incompressible fluid confined between a long vertical wavy wall and a parallel flat plate”, J. Fluid Mech, 86, 1978, pp. 365–383.
U. N. Das, N. Ahmed, “Free convective MHD flow and heat transfer in a viscous incompressible fluid confined between a long vertical wavy wall and a parallel flat wall”, I. J. Pure & App. Math, 23, 1992, pp. 295-304.
R. P Patidar, G. N. Purohit, “Free convection flow of a viscous incompressible fluid in a porous medium between two long vertical wavy walls”, I. J. Math, 40, 1998, pp. 76-86.
R. Taneja, N. C. Jain, “MHD flow with slip effects and temperature dependent heat source in a viscous in compressible fluid confined between a long vertical wavy wall and a parallel flat wall”, J. Def. Sci., 2004, pp. 21-29.
Ch. V. R. Murthy, S. B. Kulkarni, “On the class of exact solutions of an incompressible fluid flow of second order type by creating sinusoidal disturbances”, J. Def. Sci, 57, 2, 2007, pp. 197-209.
S. B. Kulkarni, “Unsteady poiseuille flow of second order fluid in a tube of elliptical cross section on the porous boundary”, Special Topics & Reviews in Porous Media., 5, 2014, pp. 269–276.
W. Noll, “A mathematical theory of mechanical behaviour of continuous media”, Arch. Ratl. Mech. & Anal., 2, 1958, pp. 197–226.
B. D. Coleman, W. Noll, “An approximate theorem for the functionals with application in continuum mechanics”, Arch. Ratl. Mech and Anal, 6, 1960, pp. 355–376.
R. S. Rivlin, J. L. Ericksen, “Stress relaxation for isotropic materials”, J. Rat. Mech, and Anal, 4, 1955, pp. 350–362.
M. Reiner, “A mathematical theory of diletancy”, Amer. J. ofMaths, 64, 1964, pp. 350-362.
H. Darcy, “Les FontainesPubliques de la Ville de, Dijon, Dalmont, Paris” 1856.
E. M. Erdogan, E. Imrak, “Effects of the side walls on the unsteady flow of a Second-grade fluid in a duct of uniform cross-section”, Int. Journal of Non-Linear Mechanics, 39, 2004, pp. 1379-1384.
S. Islam, Z. Bano, T. Haroon and A. M. Siddiqui, “Unsteady poiseuille flow of second grade fluid in a tube of elliptical cross-section”, 12, 4, 2011. 291-295.
S. B. Kulkarni, “Unsteady flow of an incompressible viscous electrically conducting fluid in tub of elliptical cross section under the influence of magnetic field”, International Journal of Mathematical, Computational, Physical and Quantum Engineering, 8 (10), 2014, pp. 1311–1317.
S. B. Kulkarni, “Unsteady poiseuille flow of an incompressible viscous fluid in a tube of spherical cross section on a porous boundary”, International Journal of Mechanical Aero Space Industrial and Mechatronics Engineering, 9 (2), 2015, pp. 240–246.
S. B. Kulkarni, “Unsteady MHD flow of elastico–viscous incompressible fluid through a porous media between two parallel plates under the influence of magnetic field”, Defence Science Journal, 65 (2), 2015, pp. 119–125.
S. B. Kulkarni, “Unsteady MHD flow of elastic-viscous fluid in tube of spherical cross section on porous boundary”, International Journal of Mechanical Aero Space Industrial and Mechatronics Engineering, 9 (4), 2015, pp. 590–596.
S. B. Kulkarni, G. G. Bhide and G. S. Kulkarni, “On the class of exact solution of MHD fluid flow of second order type by creating forced oscillation on the porous boundary”, International Journal of Recent Advances in Engineering and Technplogy, 4 (8), 2016, pp, 1–8.