A three stages transition into chaos for mixed convection nanofluid inside a differentially-heated square ventilated cavity

Abstract

In this paper, we present a numerical study of an unsteady Al2O3 water nanofluid mixed convection in a differentially-heated square ventilated cavity. The routes from steady state to chaotic mixed convection state have been also studied for a constant Reynolds Number (Re), Re = 50 and Richardson number (Ri) ranging from Ri = 40 to Ri = 150. The governing equations are solved using an implicit finite-volume scheme and TDMA algorithm. Results are presented through streamlines, isotherms, mean temperature, average Nusselt number, pressure drop, etc. It is observed that the average Nusselt number and the mean cavity temperature values are all the higher as the Ri number is great. The pressure drop slightly decreases as Ri number increases. The fully chaotic flow regime is reached after three stages. The first stage is similar to the Ruelle-Takens-Newhouse scenario. At the end of this stage, apparition of periodicity interrupted the development of a full chaos initiating the second stage of the route to chaos where another series of three supercritical Hopf type bifurcations and a period doubling bifurcation takes place. The third stage starts by the emergence of intermittencies which interrupts the apparition of a full chaotic flow. A complete chaos is achieved at the end of this third stage.