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首页> 外文期刊>Journal of Heat Transfer >Nonlinear Rayleigh-Benard Convection With Variable Heat Source
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Nonlinear Rayleigh-Benard Convection With Variable Heat Source

机译：可变热源的非线性Rayleigh-Benard对流

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Linear and nonlinear Rayleigh-Benard convections with variable heat source (sink) are studied analytically using the Fourier series. The strength of the heat source is characterized by an internal Rayleigh number, R_1, whose effect is to decrease the critical external Rayleigh number. Linear theory involving an autonomous system (linearized Lorenz model) further reveals that the critical point at pre-onset can only be a saddle point. In the postonset nonlinear study, analysis of the generalized Lorenz model leads us to two other critical points that take over from the critical point of the pre-onset regime. Classical analysis of the Lorenz model points to the possibility of chaos. The effect of R_1 is shown to delay or advance the appearance of chaos depending on whether R_1 is negative or positive. This aspect is also reflected in its effect on the Nusselt number. The Lyapunox exponents provide useful information on the closing in and opening out of the trajectories of the solution of the Lorenz model in the cases of heat sink and heat source, respectively. The Ginzburg-Landau models for the problem are obtained via the 3-mode and 5-mode Lorenz models of the paper.
机译：使用傅立叶级数分析研究了具有可变热源（沉）的线性和非线性Rayleigh-Benard对流。热源的强度由内部瑞利数R_1表征，其作用是降低临界外部瑞利数。涉及自治系统的线性理论（线性洛伦兹模型）进一步表明，预发病的临界点只能是一个鞍点。在发病后的非线性研究中，对广义Lorenz模型的分析将我们引向其他两个临界点，这些临界点取代了发病前机制的临界点。 Lorenz模型的经典分析指出了混乱的可能性。根据R_1是负还是正，R_1的作用可以延迟或增加混沌的出现。这方面也反映在它对Nusselt数的影响上。 Lyapunox指数分别提供了有关在散热器和热源情况下Lorenz模型解的轨迹的内开和外开的有用信息。该问题的Ginzburg-Landau模型是通过论文的3模和5模Lorenz模型获得的。

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