The Stability Analysis Of Heat Transfer By Transitional Natural Convection In Cavity

Heat transfer of transition flow is relevant to many industrial and environmental applications, such as aerospace heat exchangers, high voltage motor systems and even the flow of blood through arteries. The range of transition flow is comparatively narrow and the heat transfer in this range is much more unsteady with periodic oscillations, which is different from that in laminar flow and turbulent flow. The changing amplitude and frequency of periodic oscillations have significant influence on the characteristics of transitional flow and heat transfer. Many studies have been done on the transitional dynamics characteristics of the vortex structure, however, very few investigated the characteristics of heat transfer in transition flow. And there has been no numerical study of the heat transfer by transitional convection and radiation with participating media.Numerical investigations are carried out for stability analysis of heat transfer in transitional convection and coupled radiation and convection using Multiple-Relaxation-Time lattice Boltzmann method(MRT-LBM) and the combination of lattice Boltzmann and direct collocation meshless method(LB-DCM) respectively. The effects of various influencing parameters on the stability of heat transfer in transitional convection, such as Rayleigh number(Ra), Prandtl number(Pr), the parameter of geometric characteristics(A) and the position of internal heat source, has been considered in the present work. And the corresponding ranges of transition flow in different conditions are also summarized in this paper. The flow bifurcations with different dynamic flow structures under different initial states are also investigated to explain the unsteady heat transfer of transition flow. The figures of critical Prandtl number(Prc) in the transition flow region and the critical Rayleigh number(Rac) of pitchfork bifurcation are shown in this paper. As Pr is reduced to less than Prc, the system is observed to undergo a supercritical Hopf bifurcation with a sustained periodic oscillatory behaviour, and the Prc increases with the increase of Ra. As Ra is increased to over Rac, there will be two stable dissipative structure of the system and also two different heat exchange processes with different initial conditions. In addition, stability analysis of heat transfer in transitional coupled radiation and convection is also presented, and the influence of the parameter of coupled radiation and convection(Rc) and optical thickness(τ) has been analyzed emphatically. The results indicate that the thermal radiation effect causes an expansion of the transition flow range and makes it easier to arise a periodic oscillatory behaviour. The decrease of Rc and τ also makes a larger range of transition flow, and the effect of thermal radiation enhanced, while the effect of convection weakened, and as a result, the total intensity of heat transfer increases.