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 | | 为了更好的帮助您理解掌握查询词或其译词在地道英语中的实际用法，我们为您准备了出自英文原文的大量英语例句，供您参考。 | |
As applications, the wave equation on?+ × ?+ and the heat equation in a semi-infinite rod are considered in detail.
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In a much cited article, Yau [5] proved that when the Ricci curvature is bounded uniformly below, then the only bounded solution to the heat equation ?tμ=Δμ on [0, ∞) × M which vanishes at t=0 is the one which vanishes evarywhere.
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Well-posedness of a semilinear heat equation with weak initial data
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In the first part the initial value problem (IVP) of the semilinear heat equation with initial data in is studied.
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For the analogs of the heat and wave equation, we give algorithms for approximating the solution, and display the results of implementing these algorithms.
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| The method of calculation of saturated liquid density, based on the Hanson's method, has been proved theoretically from Haggenmacher's equation of state. A critical compressibility has been used as a parameter for dividing the compounds into groups to overcome the defeat of Hanson's method. The error of Saturated liquid density, calculated by this method, was within 1%. In this paper, a method for calculation of Saturated vapor densities and mixture liquid densities and a generalized equation of heat of... The method of calculation of saturated liquid density, based on the Hanson's method, has been proved theoretically from Haggenmacher's equation of state. A critical compressibility has been used as a parameter for dividing the compounds into groups to overcome the defeat of Hanson's method. The error of Saturated liquid density, calculated by this method, was within 1%. In this paper, a method for calculation of Saturated vapor densities and mixture liquid densities and a generalized equation of heat of vapolyzation was also given. These results proved that the theorem of corresponding state, could be applied to two phases region. | 本文证实了Hanson计算方法的可能性,并应用了跨界压缩因子解决了Hanson方法中存在的缺点.计算饱和液体的密度,其误差在1%以内,本文尚提供了计算饱和蒸气的密度和混合液体的密度的方法.导出了一个计算汽化热的普遍公式.这些结果证明了在两相区域内可以应用对比状态的规律. | An experimental investigation was made of temperature gradients in air streams being cooled while flowing through a cylinder of diameter 81 mm packed with high thermal conductivity (iron and copper) and low thermal conductivity solids of spheres, cylinders and Raschig rings. From the measured temperature gradients at various bed depths and radial posi-tions, and for the different particle sizes and flow rates, the effective thermal conductivity Ke, and the heat transfer coefficient of the wall hw, were... An experimental investigation was made of temperature gradients in air streams being cooled while flowing through a cylinder of diameter 81 mm packed with high thermal conductivity (iron and copper) and low thermal conductivity solids of spheres, cylinders and Raschig rings. From the measured temperature gradients at various bed depths and radial posi-tions, and for the different particle sizes and flow rates, the effective thermal conductivity Ke, and the heat transfer coefficient of the wall hw, were determined by the integral, graphical and the direct-current electric analog methods. | 作者用低导热系数(包括玻璃、磁)的球体、圆柱体、环柱体与高导热系数(包括铜、铁的球体,圆柱体为填充物,以空气为传热介质,使其在管径为81毫米之填充床层内冷却,改变流体流量,床层高度及填充物大小,通过试验测出在不同的条件下床层的径向温度分布,并应用积分法、直流电模拟计算法及图解法求得床层的有效导热系数及管壁薄膜传热系数.在试验范围:低导热系数填充物D_P/D_t自0.074—0.254;高导热系数填充物D_p/D_t自0.12—0.2,L/D_t自5—15,Re汇数自130—1400,即直线速度自0.5—1.6公尺/分,若以床层进出口平均温度之数学平均值为定性温度,则床层之有效导热系数及管壁薄膜传热系数可分别归纳于下式:低导热系数填充物:K_e=0.182(D_t/D_p)~(0.45)Re~(0.75),h_w=65e~(-4)(D_p/D_t)(K/D_t)((D_t/L))~(0.2)Re~(0.4)高导热系数填充物:K_e=0.3k(D_t/D_p)~(0.6)Re~(0.72),h_w=5.1(K/D_t)(D_t/D_p)~(0.8)(D_t/L)~(0.1)Re~(0.46)填充物形状对K_e及h... 作者用低导热系数(包括玻璃、磁)的球体、圆柱体、环柱体与高导热系数(包括铜、铁的球体,圆柱体为填充物,以空气为传热介质,使其在管径为81毫米之填充床层内冷却,改变流体流量,床层高度及填充物大小,通过试验测出在不同的条件下床层的径向温度分布,并应用积分法、直流电模拟计算法及图解法求得床层的有效导热系数及管壁薄膜传热系数.在试验范围:低导热系数填充物D_P/D_t自0.074—0.254;高导热系数填充物D_p/D_t自0.12—0.2,L/D_t自5—15,Re汇数自130—1400,即直线速度自0.5—1.6公尺/分,若以床层进出口平均温度之数学平均值为定性温度,则床层之有效导热系数及管壁薄膜传热系数可分别归纳于下式:低导热系数填充物:K_e=0.182(D_t/D_p)~(0.45)Re~(0.75),h_w=65e~(-4)(D_p/D_t)(K/D_t)((D_t/L))~(0.2)Re~(0.4)高导热系数填充物:K_e=0.3k(D_t/D_p)~(0.6)Re~(0.72),h_w=5.1(K/D_t)(D_t/D_p)~(0.8)(D_t/L)~(0.1)Re~(0.46)填充物形状对K_e及h_w的影响,仅需将D_p用 D’_p代替,同时把K_e式中之常数0182及03各改为0.22及0.38即可.直流电模拟计算法系利用电压表示温度,电阻表示传热阻力,电流表示热的流动,是简单的模拟计算机的一种,它在近代工程上的应用日渐广泛,有了传热数据应用它来求床层的温度分布异常方便. | In this paper the influence of Pr number, shape and thermal conductivity of the packing material and the bed height on the heat transfer coefficients of the packed beds have been thoroughly studied when air and water were cooled through packed tubes. In order to offer the data for the design of fixed bed, catalytic reactors and packed heat exchangers operated at high space velocity, high Re number was adopted. | 填充床层之传热系数包括二重阻力,即床层内部的传热阻力和床层与管壁界面间薄膜的传热阻力。本文以空气和水为传热介质,使其流过填充床层冷却,改变操作条件和床层构造,考察了Pr准数,床层高度、填充物的导热系数和形状对於传热系数的影响。由於高速固定床接触反应器和填充热交换器逐渐在工业上取得了应用,高线速下的传热数据需要迫切,因此试验的范围采用了较大的Re准数。 玻璃或磁质等低导热系数球状填充物的传热系数可归纳成: 试验范围: D_p/D_t=0.08～0.5; L/D_t=10～30; Re=250～6500; Pr=0.722～4.8 铜、铁等高导热系数球状填充物的传热系数可归纳成: 试验范围; D_p/D_t=0.1～0.5; Re=300～10,000; L/D_t=10～30 在此范围内所有试验皆经过二次以上的重复试验,误差一般不大於5%。 以圆柱体为填充物的传热系数,仅须将修正Re准数中的几何量D_p,改成与圆球具有相同的几何表面面积的球径D'_p即可。 以上二式说明流体的物理性质即Pr准数对传热系数的影响不很显著,床层高度对传热系数的影响:低导热系数填充... 填充床层之传热系数包括二重阻力,即床层内部的传热阻力和床层与管壁界面间薄膜的传热阻力。本文以空气和水为传热介质,使其流过填充床层冷却,改变操作条件和床层构造,考察了Pr准数,床层高度、填充物的导热系数和形状对於传热系数的影响。由於高速固定床接触反应器和填充热交换器逐渐在工业上取得了应用,高线速下的传热数据需要迫切,因此试验的范围采用了较大的Re准数。 玻璃或磁质等低导热系数球状填充物的传热系数可归纳成: 试验范围: D_p/D_t=0.08～0.5; L/D_t=10～30; Re=250～6500; Pr=0.722～4.8 铜、铁等高导热系数球状填充物的传热系数可归纳成: 试验范围; D_p/D_t=0.1～0.5; Re=300～10,000; L/D_t=10～30 在此范围内所有试验皆经过二次以上的重复试验,误差一般不大於5%。 以圆柱体为填充物的传热系数,仅须将修正Re准数中的几何量D_p,改成与圆球具有相同的几何表面面积的球径D'_p即可。 以上二式说明流体的物理性质即Pr准数对传热系数的影响不很显著,床层高度对传热系数的影响:低导热系数填充物的传热系数随L/D_t比率之减小而逐渐增大,L/D_t>30,影响甚微,L/D_t=20,误差约7%,L/D_t=10,误差可达15%;高导热系数填充物的传热系数随L/D_t的增大略有增大的趋势,但影响? | | | | << 更多相关文摘 |
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