Analytical solution for the time-fractional heat conduction equation in spherical coordinate system by the method of variable separation

In this paper,using the fractional Fourier law,we obtain the fractional heat conduction equation with a time-fractional derivative in the spherical coordinate system.The method of variable separation is used to solve the timefractional heat conduction equation.The Caputo fractional derivative of the order 0 〈 α≤ 1 is used.The solution is presented in terms of the Mittag-Leffler functions.Numerical results are illustrated graphically for various values of fractional derivative.

Ionic Conduction and Fuel Cell Performance of Ba0.98Ce0.8Tm0.2O3-α Ceramic

The perovskite-type oxide solid solution Ba0.98Ce0.8Tm0.2O3-α was prepared by high temperature solid-state reaction and its single phase character was confirmed by X-ray diffraction. The conduction property of the sample was investigated by alternating current impedance spectroscopy and gas concentration cell methods under different gases atmospheres in the temperature range of 500-900 ℃. The performance of the hydrogen-air fuel cell using the sample as solid electrolyte was measured. In wet hydrogen, the sample is a pure protonic conductor with the protonic transport number of 1 in the range of 500-600 ℃, a mixed conductor of proton and electron with the protonic transport number of 0.945-0.933 above 600 ℃. In wet air, the sample is a mixed conductor of proton, oxide ion, and electronic hole. The protonic transport numbers are 0.010-0.021, and the oxide ionic transport numbers are 0.471-0.382. In hydrogen-air fuel cell, the sample is a mixed conductor of proton, oxide ion and electron, the ionic transport numbers are 0.942 0.885. The fuel cell using Ba0.98Ce0.8Tm0.2O3-α as solid electrolyte can work stably. At 900 ℃, the maximum power output density is 110,2 mW/cm2, which is higher than that of our previous cell using Ba0.98Ce0.8Tm0.2O3-α （x〈≤1, RE=Y, Eu, Ho） as solid electrolyte.

Ionic Conduction and Fuel Cell Performance of Ba0.97Ce0.8Ho0.2O3-α Ceramic

The perovskite-type-oxide solid solution Ba0.97Ce0.8Ho0.2O3-α was prepared by high temperature solidstate reaction and its single-phase character was confirmed by X-ray diffraction. The ionic conduction of the sample was investigated using electrical methods at elevated temperatures, and the performance of the hydrogen-air fuel cell using the sample as solid electrolyte was measured, which were compared with those of BaCe0.8Ho0.2O3-α. In wet hydrogen, BaCe0.8Ho0.2O3-α almost exhibits pure protonic conduction at 600-1000℃, and its protonic transport number is 1 at 600-900 ℃ and 0.99 at 1000 ℃. Similarly, Ba0.97Ce9.8Ho0.2O3-α exhibits pure protonic conduction with the protonic transport number of 1 at 600- 700℃, but its protonic conduction is slightly lower than that of BaCe0.8Ho0.2O3-α, and the protonic transport number are 0.99-0.96 at 800-1000 ℃. In wet air, the two samples both show low protonic and oxide ionic conduction. For Ba0.97Ce0.8Ho0.2O3-α, the protonic and oxide ionic transport numbers are 0.01-0.11 and 0.30-0.31 respectively, and for BaCe0.8Ho0.2O3-α, 0.01-0.09 and 0.27-0.33 respectively. Ionic conductivities of Ba0.97Ce0.8Ho0.2O3-α are higher than those of BaCe0.8Ho0.2O3-α under wet hydrogen and wet air. The performance of the fuel cell using Ba0.97Ce0.8Ho0.2O3-α as solid electrolyte is better than that of BaCe0.8Ho0.2O3-α. At 1000 ℃, its maximum short-circuit current density and power output density are 465 mA/cm^2 and 112 mW/cm^2, respectively.

Mixed Conduction in BaCe0.8Pr0.2O3-α Ceramic

BaCe0.8Pr0.2O3-α ceramic was synthesized by high temperature solid-state reaction. The structural characteristics and the phase purity of the crystal were determined using powder X-ray diffraction analysis. By using the methods of AC impedance spectroscopy, gas concentration cell and electrochemical pumping of hydrogen, the conductivity and ionic transport number of BaCe0.8Pr0.2O3-α were measured, and the electrical conduction behavior of the material was investigated in different gases in the temperature range of 500-900℃. The results indicate that the material was of a single perovskite-type orthorhombic phase. From 500℃ to 900 ℃, electronic-hole conduction was dominant in dry and wet oxygen, air or nitrogen, and the total conductivity of the material increased slightly with increasing oxygen partial pressure in the oxygen partial pressure range studied. Ionic conduction was dominant in wet hydrogen, and the total conductivity was about one or two orders of magnitude higher than that in hydrogen-free atmosphere （oxygen, air or nitrogen）

Ionic conduction in Ba_xCe_(0.8)Pr_(0.2)O_(3–α)

BaxCe0.8Pr0.2O3-α (x=0.98-1.03) ceramics were prepared by high temperature solid-state reaction. X-ray diffraction (XRD) patterns showed that the materials were perovskite-type orthorhombic single phase. By using gas concentration cell and AC impedance spectroscopy methods, the electrical conduction behavior of the materials was investigated in different gases at 500-900 °C. The influence of non-stoichiometry in the materials with x≠1 on conduction properties was studied and compared with that in the material with x=1. The results indicated that Ba1.03Ce0.8Pr0.2O3-α was a pure protonic conductor, and Ba0.98Ce0.8Pr0.2O3-α was a mixed conductor of protons and electrons in wet hydrogen at 500-900 °C. BaCe0.8Pr0.2O3-α was a pure protonic conductor in 500-600 °C, and a mixed conductor of protons and electrons above 600 °C in wet hydrogen. In 500-900 °C, they were all mixed conductors of oxide ions and electronic holes in dry air, and mixed conductors of protons, oxide ions and electronic holes in wet air. Both the protonic and oxide ionic conductivities increased with increasing barium content in the materials in wet hydrogen, dry air and wet air, respectively.

氧化栲胶溶液电导率的测定

用电导率的方法测出了氧化栲胶溶液的临界胶束浓度。结果表明,氧化栲胶溶液具有离子型高分子溶液的特征。测定了不同浓度的氧化栲胶溶液在293K～343K温度范围内的电导率,讨论了其电导率在293K～343K温度范围内服从VTF方程。利用电导率与温度的关系,估算了氧化栲胶溶液的电导活化能。

弱电解质溶液无限稀时的摩尔电导测定

通常认为 ,弱电解质溶液无限稀时的摩尔电导Λ0 不能直接测定 ,它只能通过相关强电解质溶液无限稀时的摩尔电导及离子独立移动定律计算得出 .事实上 ,通过弱电解质溶液的电导率测定 ,不仅可以确定弱电解质的电离平衡常数 ,而且可以确定弱电解质无限稀时的摩尔电导 .与此同时 。

基于MATLAB仿真模拟炼油厂尾气燃烧模型的优化

基于数学物理思想和热传导理论,对炼油厂尾气燃烧模型进行优化。假设为连续性火源,利用粒子经典的扩散方程,得到了炼油厂的火势蔓延函数N(r,t)及在t时刻距离井曹底部r处的烟雾扩散密度随时间的变化规律。最后,假定烟雾扩散是以烟团为基本状态的方式进行,并对烟雾扩散进行了必要的简化,从而建立了高斯扩散模型,并利用MATLAB软件进行仿真模拟,得到了烟雾在近地面扩散的浓度随时间的分布函数图。

离子独立运动定律在火电厂水汽指标监控中的应用

以离子独立运动定律及离子摩尔电导率的相关概念为依据，推导了极稀氨水的电导率-pH方程、极稀盐酸、极稀氢氧化钠的电导率——浓度方程，并应用于电厂水汽质量监督及品质控制。