Numerical Simulation Of The Rayleigh-Bénard Convection Of Nanofluids In Rectangular Enclosure

The flows existed widely in natural phenomena, such as airflow and ocean current,are driven by buoyancy, which is cased by the temperature gradients. Rayleigh-Bénardconvection is one of the typical models for studying those kinds of phenomena.However, the research on the Rayleigh-Bénard convection of nanofluids in enclosure isvery limited. Thus, investigating the unsteady flow and heat transfer on theRayleigh-Bénard convection, obtaining the critical condition of the flow transition andanalysing the physical mechanism of the bifurcation sequence will not only enrich theRayleigh-Bénard convection theory, but also provide important theory base to industries(electronics refrigeration, phase change for cold storage and air conditioning technology,for example). Therefore, this research is of great theoretical significance and practicalvalue.Physical and mathematical models of the Rayleigh-Bénard convection ofnanofluids in rectangular enclosure are established. A three-dimensional numericalsimulation is systematically conducted. The distributions of the temperature and theflow fields are obtained and the effects of parameters, such as the Rayleigh number, thePrandtl number, the initial condition, the aspect ratio of the enclosure, and the solidvolume fraction of nanoparticles, on the Rayleigh-Bénard convection are analyzed. Theflow pattern and the transition among them, the basic characteristics of bifurcationsequences are ascertained. The critical conditions for the bifurcation are alsodetermined.The simulation results indicate that,(1) Comparing with the results from theconductive state, there exists wider range of Rayleigh number for the flow pattern fromthe stable state flow. It hints that the tendency of the flow pattern can keep memory ofitself in the steady state.(2) It is shown that the critical Rayleigh numbers both for theonset of convection and time-dependent flow increase with the increase of the volumefraction of the nanoparticles and decrease of the aspect ratio.(3) For an enclosure withunity aspect ratio, the average Nusselt number of CuO-water nanofluid is enhanced byincreasing the volume fraction of nanoparticles. However, the velocity at the enclosurereduced by increasing the volume fraction of nanoparticles. It hints that nanoparticlesmake the nanofluid more stable than base fluid.(4) The bifurcation sequence is alsosensitive to the aspect ratio of the enclosure, the range of Rayleigh number for each flow pattern become narrower with the increase of the aspect ratio.(5) There aredifferent modes of periodic oscillation; each variation of mode is accompanied by amore or less pronounced step-change in the Nusselt number and the frequency.(6)Although the critical Rayleigh numbers for the onset of time-dependent flow are notidentical for different condition, one common feature is that the first bifurcation fromsteady flow to oscillations through a supercritical Hopf bifurcation. After bifurcation toperiodic oscillation, different conditions may have different route to chaos. At anestablished condition, flow field either experience quasi-periodic or direct into chaos.There are four types of bifurcation sequences in the article: steady→periodic→chaos,steady→periodic→steady→periodic→chaos, steady→periodic→quasi-periodic→periodic→chaos, steady→periodic→quasi-periodic→chaos.