Steady and transient free convection of an electrically conducting fluid from a vertical plate in the presence of a magnetic field

  • A. S. Gupta


An analysis is made for the laminar free convection and heat transfer of a viscous electrically conducting fluid from a hot vertical plate in the case when the induced field is negligible compared to the imposed magnetic field. It is found that similar solutions for velocity and temperature exist when the imposed magnetic field (acting perpendicular to the plate) varies inversely as the fourth root of the distance from the lowest end of the plate. Explicit expressions for velocity, temperature, boundary layer thickness and Nusselt number are obtained and the effect of a magnetic field on them is studied. It is found that the effect of the magnetic field is to decrease the rate of heat transfer from the wall. In the second part, the method of characteristics is employed to obtain solutions of the time-dependent hydromagnetic free convection equations (hyperbolic) of momentum and energy put into integral form. The results yield the time required for the steady flow to be established, and the effect of the magnetic field on this time is studied.


  1. 1).
    Meyer, R. C., J. Aero. Sci. 25 (1958) 561.Google Scholar
  2. 2).
    Lykoudis, P. S., Proc. IXth Int. Astronautical Congr. 1958, p. 168.Google Scholar
  3. 3).
    Schmidt, E. and W. Beckmann, Tech. Mech. Thermodyn. 1 (1930) 1.CrossRefGoogle Scholar
  4. 4).
    Ostrach, S., NACA Report 1952, TN 2635.Google Scholar
  5. 5).
    Sparrow, E. M. and J. L. Gregg, Trans. Amer. Soc. Mech. Engrs 80 (1958) 379.Google Scholar
  6. 6).
    Eckert, E. R. G., Heat and Mass Transfer, McGraw Hill Book Co Inc. New York 1959.Google Scholar
  7. 7).
    Siegel, R., Trans. Amer. Soc. Mech. Engrs 80 (1958) 347.Google Scholar
  8. 8).
    Rossow, V. J., NACA Report 1957, TN 3971.Google Scholar
  9. 9).
    Resler, E. L. and W. R. Sears, J. Aero. Sci. 25 (1958) 235.MathSciNetGoogle Scholar
  10. 10).
    Touloukian, G. A., G. A. Hawkins and M. Jacob, Trans. Amer. Soc. Mech. Engrs. 70 (1948) 13.Google Scholar
  11. 11).
    Courant, R. and K. O. Friedrichs, Supersonic flow and shock waves, Interscience Publishers Inc., New York 1948.MATHGoogle Scholar

Copyright information

© Martinus Nijhoff 1960

Authors and Affiliations

  • A. S. Gupta
    • 1
  1. 1.Department of Applied MathematicsIndian Institute of TechnologyKharagpurIndia

Personalised recommendations