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Detailed numerical analysis is presented for natural convection heat transfer in internally finned horizontal annuli. Governing equations are discretized using the finite volume method, and solved using SIMPLE algorithm with Quick scheme. The results show that the flow and heat transfer can reach steady state when the Rayleigh number is below 2×10 4. When the Rayleigh number is greater than 3×10 4 , two different types of numerical solutions under the same parameters can be obtained for different initial conditions. The critical Rayleigh numbers with two different initial conditions are different from steady to unsteady solutions. The oscillatory flow undergoes several bifurcations and ultimately evolves to a chaotic flow as the Rayleigh numbers increase.

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With the developing of manufacturing technique and the lack of material in recent years, the elliptic tube-fin bank heat exchangers have been paid more and more attentions. The numerical simulation has become an important mean and effective way for studying the flow and heat transfer. The heat transfer capacity of the heat exchanger is affected by multiple factors, among which the cross sections of the elliptic tube is a major factor. In this article, we take numerical analysis methods and SIMPLE algorithm in body-fitted coordinate system to analyze the effect of the different elliptic cross sections on heat transfer characteristics, the results will provide basis for designing and manufacturing compact heat exchangers.

In this paper, the periodic motion, bifurcation and chatter of two-degree-of-freedom vibratory system with dry friction and clearance were studied. Slip-stick motion and the impact of system motions were analyzed and numerical simulations were also carried out. The results showed that the system possesses rich dynamics characterized by periodic motion, stick-slip-impact motion, quasi-periodic motion and chaotic attractors, and the routs from periodic motions to chaos observed via Hof bifurcation or period-doubling bifurcation. Furthermore, it was found that there exists the chatter phenomena induced by dry friction in low frequency, and the windows of chaotic motion are broadened in the area of higher excitation frequencies as the dry friction increases.