Transitions and Bifurcations to Chaos in Combined Radiation and Natural Convection in a Two-Dimensional Participating Medium

Combined radiation and natural convection in a square cavity with emitting and absorbing participating medium is studied numerically. The equation of radiation transfer is analyzed by the P-1 approximation. The momentum and energy balance equations are calculated using spectral methods. The presence of a radiation source increases the bulk temperature of the fluid, and has a significant influence on the flow pattern and temperature distribution. In this work, the flow is initially stationary, and is simulated from transition to chaos by varying with Rayleigh numbers of 10⁴, 10⁵, 10⁶, 10⁷, and 10⁸. The conduction-radiation parameter ranges from 100 to 0.1, and optical thickness ranges from 10 to 0.01. Comparisons are made with some existing results. The influence of the conduction-radiation parameter, Rayleigh numbers and optical thickness on flow instabilities and bifurcations is discussed.