Dynamical System Analysis of Thermal Convection in a Horizontal Layer of Nanofluids Heated from Below

Figure 2

Computational results for the evolution of trajectories over time in the state space for two values of Rayleigh number (𝑅 where the solution is limit cycle and the critical value of 𝑅). The graphs represent the projection of the solution data points onto 𝑋-𝑌-𝑍 plane for Pr=10,𝜆=8/3, and 𝜙=0.05.

(a)   Ag

(b) Cu

(c) Al₂O₃

(d) TiO₂