MHD TWO-PHASE FLUID FLOW AND HEAT TRANSFER WITH PARTIAL SLIP IN AN INCLINED CHANNEL

Abstract

The aim of this paper is to investigate the velocity and thermal slip effects in MHD flow and heat transfer of two-phase viscous fluid. It is assumed that both the phases have different densities, viscosities and electrical conductivities. The fully developed flow governed by a constant pressure gradient is passing through an inclined channel having inclination Φ with horizontal axis. The electrical conductivity in phase I is assumed to be zero so that the constant applied magnetic field of strength B0 in the transverse direction only effect the fluid in phase II. The method of successive approximation is used to develop the analytic solution of order 1 for the developed dimensionless coupled ordinary differential equations. The main focus is to discuss the influence of velocity and thermal slip parameters and Hartmann number on the velocity and temperature profiles.

Keywords

Dates

  • Submission Date2013-03-27
  • Revision Date2014-01-13
  • Acceptance Date2014-04-25
  • Online Date2014-05-04

DOI Reference

10.2298/TSCI130327049A

References

  1. Packham, B. A., Shail, R., Stratified laminar flow of two immiscible fluids., Proc. Camb. Phil. Soc., 69 (1971), pp. 443-448.
  2. Shail, R., On laminar two-phase flow in magnetohydrodynamics., Int. J. Engng. Sci., 11 (1973), pp. 1103-1108.
  3. Saffman, P.G., On the stability of laminar flow of a dusty gas, J. Fluid. Mech., 13 (1962), pp. 120- 128.
  4. Datta, N., Mishra, S. K., Boundary layer flow of a dusty fluid over a semi-infinite flat plate, Acta. Mech., 42, (1982), pp. 71-83.
  5. Marble, F. E., Proc. V. AGARD Combustion and Propulsion Colloquim, 175 (1963).
  6. Soo, S. l., The Fluid Dynamics of Multiphase Systems. Blaisdell, New York, (1968).
  7. Ottermann, B., Lee, S. L., Particle migrations in laminar mixing of a suspension with a clean fluid, Z. Angew. Math. Phys., 20 (1969), pp. 730-749.
  8. Tabakoff , W., Hameed, A., The boundary layer of particulate gas flow, Z. Flugwiss, 20 (1972), pp. 373-379.
  9. Peddieson, J., Jr, Proc. Ninth South Eastern Seminar on Thermal Science, Norfolk, VA, (1973).
  10. Fenandez, D. L. M. J., Physio Chemical Hydrodynamic, 2 (1981), 1.
  11. Kumar, S. K., Sharma, L. V. K. V., Fluid-particle suspension flow past a stretching sheet, Int. J. Engng Sci. 29 (1991), pp. 123-132.
  12. Charkrabarti, A., Gupta, A. S., Hydromagnetic flow and heat transfer over a stretching sheet, Quart. appl. Math., 37 (1979), pp. 73-78.
  13. Vajravelu, K., Nayfeh, J., Hydromagnetic flow of a dusty fluid over a stretching sheet, Int. J. Nonlinear Mech., 6 (1992), pp. 937-945.
  14. Ezzat, M. A., et al., Space approach to the hydro-magnetic flow of a dusty fluid through a porous medium, Comput. Math. Appli., 59 (2010), pp. 2868-2879.
  15. Gireesha, B. J., et al., Boundary layer flow and heat transfer of a dusty fluid flow over a stretching sheet with non-uniform heat source/sink, Int. J. Multiphase flow, 37 (2011), pp. 977-982.
  16. B Gireesha, B. J., et al., Three-dimensional Couette flow of a dusty fluid with heat transfer, Appl. Math. Model., 36 (2012), pp. 683-701
  17. Raithby, G. D., Hollands, K. G. T., Natural convection. In Handbook of Heat transfer, eds W. M. Rohsnow, J. P. Hartnett and E. Genic, 2nd edn. McGraw-Hill, NewYork, (1984).
  18. Catton, I., Natural convection in enclosures. 6th National Heat Transfer Conf., Toronto, 6 (1978), pp. 13-43.
  19. Malashetty, M. S., Umavathi, J. C., Two-phase magnetohydrodynamic flow and heat transfer in an inclined channel, Int. J. Multiphase Flow, 23 (1997), pp. 545-560.
  20. Malashetty, M. S., et al., Convective magnetrohydrodynamic two fluid flow and heat transfer in an inclined channel, Heat and Mass Transfer, 37 (2001), pp. 259-264.
  21. Umavathi, J. C., et al., Unsteady oscillatory flow and heat transfer in a horizontal composite porous medium channel, Nonlinear Analysis: Model. Cont. 14 (2009), pp. 397-415.