Hydromagnetic convective heat transfer in vertical pipes

In the present analysis, the effect of radial magnetic field on the steady flow produced by the combined free and forced convection in an annulus between two coaxial vertical cylinders is considered. A numerical solution of the problem is obtained by using Runge-Kutta-Merson method. For Rayleigh number less than 0, that is, when the temperature of the pipes decreases as their height increases, the velocity increases with the absolute value of the Rayleigh number. However, it reduces as the Hartmann number M increases. On the other hand, when the Rayleigh number is positive, there occurs back flow controlled by the effect of the magnetic field. Further, the influence of Rayleigh number and Hartmann number on the temperature is also discussed.