Controlling instabilities, bifurcations and chaos in a thermo-nanofluid porous layer

This study reports controlling the onset of thermal convection and bifurcations of a horizontal nanofluid layer embedded in an isotropic porous medium under gravity subject to heating from below. The inclusion of nanoparticles with clear fluid is considered to maintain a single-phase nanofluid model. First, a linear stability analysis is performed through normal modes and obtain critical Rayleigh number of base fluid, which depends on the physical properties of the materials in the layer and its value increases with increasing the volumes of nanofragments. The principle of exchange of stability holds for the present model. Adopting low-order Galerkin approximations for velocity and temperature fields, we obtain a three dimensional nonlinear system. The linear stability and bifurcations are analyzed. Studies discourse that stationary convection emerges through supercritical pitchfork bifurcation, whereas oscillatory convection takes place via supercritical Hopf bifurcation. The critical value for Hopf bifurcation is non-monotonic with respect to porous medium characteristics. Also, there appears homoclinic bifurcation before Hopf bifurcation. The model exhibits basically two transitional routes to chaos, viz., (i) homoclinic explosion, and (ii) supercritical Hopf bifurcation. The enhancement of linear and weakly nonlinear stability thresholds are obtained. Further, chaotic motion is suppressed by increasing values of nanoparticles volume fractions. The convective mode is suppressed while the conductive mode of heat transfer strengthens resulting in the enhancement of overall heat transfer. In essence, nanofragments serve as passive stabilizer in the system and offer a powerful strategy for mitigating chaos and enhancing stability in heat driven engineering devices.