Fluid flow coupled with heat transfer through a vertical cylindrical Collapsible tube in the presence of a magnetic field and an obstacle has been investigated. The governing equations for this flow are the equations of continuity, motion and energy. These are non linear partial differential equations and has been transformed into non-linear ordinary differential equations by introducing a similarity transformation. The resulting equations are solved simultenously in the bvp4c MATLAB library to obtain the profiles and also the rate of heat transfer has been calculated. The effects of varying the Reynolds number, Hartmann number, Eckert number, Unsteadiness parameter and Prandtl number on fluid temperature , fluid velocity and the rate of heat transfer are presented in the form of tables and graphs and has been discussed. Variation in the various parameters is observed to change the fluid primary velocity, temperature and the rate of heat transfer. This kind of result is important due to its widespread application in physical, biological and applied sciences.
Summary: In this paper, the regular and chaotic oscillations in a modified Rayleigh-Liénard system under parametric excitation are studied. Two subharmonic resonant states are generated using the multiple time scales method and the effects of the system parameters on the frequency-response curves are investigated. Bifurcation structures and transitions to chaos for the first subharmonic resonant state are numerically investigated via the fourth-order Runge-Kutta integration algorithm, and symmetry-breaking, period-doubling, period-windows, intermittency and antimonotonicity phenomena are obtained. The influences of the nonlinear damping coefficients, cubic nonlinearity coefficient and small dimensionless coefficient on the bifurcation sequences are also investigated. As results, it is found that the nonlinear damping coefficients and cubic nonlinearity coefficient can be used to control the presence of chaos in the system while decreasing of the small dimensionless parameter removes chaos from the system.
In this paper, we define Tetranacci and Tetranacci-Lucas matrix sequences and investigate their properties.
