Effect of Perpendicular Magnetic Field on Chaos in a Rotating Cavity Heated from Side


Department of Mathematics, Banaras Hindu University, Varanasi, India-221005


This paper presents chaotic behavior due to an applied perpendicular magnetic field on a rotating cavity heated from side using the theory of dynamical system. The solution to the non-linear problem is obtained by using a truncated Galerkin method to find a set of ordinary differential equation for the time evolution of the Galerkin amplitudes. The system of differential equations is solved by using the fourth-order Runge Kutta method. Below a certain critical value of the scaled Rayleigh number the unique motionless conduction solution is obtained. At slightly super-critical values of scaled Rayleigh numbers transition to chaotic solutions occurs via a Hopf bifurcation. The chaotic behaviour can be obtained faster for decreasing Hartmann number as well as increasing scaled Rayleigh number. Also variation in Nusselt number increases with increasing scaled Rayleigh number and decreasing Hartmann number.