Thermal nonlinear oscillator in mixed convection

Abstract

A detailed numerical simulation is carried out for transient laminar flow opposing mixed convection in a downward vertical channel flow with both walls suddenly subjected to isothermal heat sources over a finite portion of the channel walls, by solving the unsteady two-dimensional Navier-Stokes and energy equations. The dynamical behavior of the system is influenced by, in addition to the geometrical parameters, three nondimensional parameters: the Reynolds, Richardson, and Prandtl numbers. Numerical experiments were performed for fixed values of the geometrical parameters, the Reynolds number (Re=100) and the Prandtl number (Pr=7). With variation in the value of the buoyancy (Richardson number), the nonlinear dynamical response of the system can reach (i) a stationary solution, (ii) a local and then a global periodic solution where the system executes self-sustained relaxation oscillations, or (iii) a solution in which the relaxation oscillation is destroyed leading to a chaotic state. In this study, bifurcations between different states, phase-space plots of the self-oscillatory system, characteristic times of temperature oscillations, and an exact description of the oscillations are presented quantitatively for a range of values of the buoyancy parameter. The results include the effects of the Reynolds and Prandtl numbers on the evolution of the different transitions.