UNSTEADY PLANE MHD BOUNDARY LAYER FLOW OF A FLUID OF VARIABLE ELECTRICAL CONDUCTIVITY

Abstract

This paper is devoted to the analysis of unsteady plane laminar magnetohydrodynamic (MHD) boundary layer flow of incompressible and variable electrical conductivity fluid. The present magnetic field is homogenous and perpendicular to the body surface. Outer electric filed is neglected and magnetic Reynolds number is significantly lower then one i.e. considered problem is in induction-less approximation. Free stream velocity is an arbitrary differentiable function. Fluid electrical conductivity is decreasing function of velocity ratio. In order to solve the described problem multiparametric (generalized similarity) method is used and so-called universal equations are obtained. Obtained universal equations are solved numerically in appropriate approximation and a part of obtained results is given in the form of figures and corresponding conclusions.

Keywords

Dates

  • Submission Date2010-05-22
  • Revision Date2010-07-05
  • Acceptance Date2010-07-06

DOI Reference

10.2298/TSCI100522024B

References

  1. Schlichting, H., Boundary layer-Theory, Verlag G., Braun-Karlsruhe, 1958.
  2. Blum, E.J. Mihailov, J. A., Heat transfer in electroconductive fluid in presence of transversal magnetic field, Magnetohydrodynamics, 5 (1966), pp.2-18.
  3. Gupta, A. S., Laminar free convection flow of an electrically conducting fluid from a vertical plate with uniform surface heat flux and variable wall temperature in the presence of a magnetic field, Zeitschrift fur Angewandte Mathematik und Physik, 13 (1962), 4, pp. 324-333.
  4. Pop, I., Kumari, M., Nath, G., Conjugate MHD flow past a flat plate, Acta Mechanica 106 (1994), 3-4, pp. 215-220.
  5. Pop, I., Na, T.-Y., A note on MHD flow over a stretching permeable surface, Mechanics Research Communications 25 (1998), 3, pp. 263-269.
  6. Takhar, H. S., Chamkha, A. J., Nath, G., Unsteady flow and heat transfer on a semi-infinite flat plate with an aligned magnetic field, International Journal of Engineering Science 37 (1999), 13, pp. 1723-1736.
  7. Sharma, P.R., Singh, G., Effects of ohmic heating and viscous dissipation on steady MHD flow near a stagnation point on an isothermal stretching sheet, Thermal Science 13 (2009), 1, pp. 5-12.
  8. Lojcjanski, L.G., Universal equation and parametric approximation in theory of laminar boundary layer, Scientific Academy of SSSR, Mathematics and Mechanic, 29 (1965), 1, pp. 70-87.
  9. V.N. Saljnikov, A contribution to universal solutions of the boundary layer theory, Theoretical and Applied Mechanics, 4 (1978), pp. 139-163.
  10. O.N.Busmarin, J.V.Saraev, Parametric method in theory of unsteady boundary layer, Eng. Physic journal, 27, (1972), 1, pp. 110-118.
  11. Boricic, Z., Nikodijevic, D., Milenkovic, D., Unsteady MHD boundary layer on a porous surface, Facta Universitatis, series Mechanics, Automatic control and Robotics, 1 (1995), 5, pp. 631-643.
  12. Boricic, Z., Nikodijevic, D., Milenkovic, D., Stamenkovic Z., A form of MHD universal equations of unsteady incompressible fluid flow with variable electroconductivity on heated moving plate, Theoretical and Applied Mechanics, 32 (2004), 4, pp. 65-77.
  13. Obrović, B., Nikodijević, D., Savić, S., Boundary-layer of dissociated gas on bodies of revolution of a porous contour, Strojniški vestnik - Journal of Mechanical Engineering, 55 (2009) 4, pp 244-253.
  14. Boricic, Z., Nikodijevic, D., Obrović, B., Stamenković Z., Universal equations of unsteady two-dimensional MHD boundary-layer on the body along temperature vary with time, Theoretical and Applied Mechanics, 36 (2009), 2, pp. 119-235.
  15. Simuni, M.L., Terentev, M.N., Equations solution in ''ratio-parametric'' theory of boundary layer, Tr. Leningrad, Multitech. Eng. 248, (1965), pp.129-145.
  16. Nikodijevic, D., Boricic, Z., Milenkovic, D., Stamenkovic, Z., Generalized similarity method in unsteady two-dimensional MHD boundary layer on the body which temperature varies with time, International Journal of Engineering, Science and Technology, 1 (2009), 1, pp. 206-215.
  17. Boricic, Z., Nikodijevic, D., Blagojevic, B., Stamenkovic, Z., Universal Solutions of Unsteady Two-Dimensional MHD Boundary Layer on the Body with Temperature Gradient along Surface, WSEAS Transactions on Fluid Mechanics, 4 (2009), 3, pp. 97-106.
  18. Rossow, J.V., On flow of electrically conducting fluid over a flat plate in the presence of a transverse magnetic field, Report No. 1358, NASA, USA, 1958
Volume 14, Issue 11, Pages171 -182