多釜串联模型停留时间分布方差的推导

简要分析了理想反应器的特点,并指出现实反应器与理想反应器的区别,介绍了多釜串联模型描述实际反应器的思想.针对多釜串联模型的停留时间分布的计算函数进行逐步的推导,以阶跃法对模型进行分析,采用数学归纳法和分部积分法等方法推导出了多釜串联模型无因次停留时间分布函数表达式;根据停留时间分布密度函数定义,推导出了无因次停留时间分布密度函数的表达式;根据概率中方差的定义,推导出了无因次方差的表达式.     

Enhancement of microwave absorption of nanocomposite BaFe_(12)O_(19)/α-Fe microfibers

Nanocomposite BaFe12O19/α-Fe microfibers with diameters of about 1-5 μm are prepared by the organic gelthermal selective reduction process. The binary phase of BaFe12O19 and α-Fe is formed after reduction of the precursor BaFe12O19/α-Fe2O3 microfibers at 350℃ for 1 h. These nanocomposite microfibers are fabricated from α-Fe (16-22 nm in diameter) and BaFe12O19 particles (36-42 nm in diameter) and basically exhibit a single-phase-like magnetization behavior, with a high saturation magnetization and coercive force arising from the exchange-coupling interactions of soft α-Fe and hard BaFe12O19 . The microwave absorption characteristics in a 2-18 GHz frequency range of the nanocomposite BaFe12O19/α-Fe microfibers are mainly influenced by their mass ratio of α-Fe/BaFe12O19 and specimen thickness. It is found that the nanocomposite BaFe12O19/α-Fe microfibers with a mass ratio of 1:6 and specimen thickness of 2.5 mm show an optimal reflection loss (RL) of 29.7 dB at 13.5 GHz and the bandwidth with RL exceeding 10 dB covers the whole Ku-band (12.4-18.0 GHz). This enhancement of microwave absorption can be attributed to the heterostructure of soft, nano, conducting α-Fe particles embedded in hard, nano, semiconducting barium ferrite, which improves the dipolar polarization, interfacial polarization, exchange-coupling interaction, and anisotropic energy in the nanocomposite BaFe12O19/α-Fe microfibers.