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Explicit Analytical Solutions of Radial Permeable Power Rate Flow

Chinese Journal of Mechanical Engineering 2011年第2期24卷 220-223页

作者： LI Yuanyuan cai ruixian Institute of Engineering Thermophysics Chinese Academy of Sciences Beijing 100190 China

The research of different kinds of permeable non-Newtonian fluid flow is increasing day by day owing to the development of science,technology and production *** is most common to use power rate equation to describe such ***,this equation is nonlinear and very difficult to derive explicit exact analytical ***,people can only derive approximate solutions with numerical ***,an advanced separating variables method which can derive exact analytical solutions easier is developed by Academician cai ruixian（the method of separating variables with addition）.It is assumed that the unknown variable may be indicated as the sum of one-dimensional functions rather than the product in the common method of separating *** method is used to solve the radial permeable power rate flow unsteady nonlinear equations on account of making the process *** concise（no special functions and infinite series） exact analytical solutions is derived with the new method about this flow to develop the theory of non-Newtonian permeable fluid,which are exponential solution,two-dimensional function with time and radius,logarithmic solution,and double logarithmic solution,*** addition,the method of separating variables with addition is developed and applied instead of the conventional multiplication *** is proven to be promising and encouraging by the *** solutions yielded will be valuable to the theory of the permeable power rate flow and can be used as standard solutions to check numerical methods and their differencing schemes,grid generation ways,*** also can be used to verify the accuracy,convergency and stability of the numerical solutions and to develop the numerical computational approaches.

关键词： non-Newtonian fluid analytical solution permeable power rate flow method of separating variables with addition

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Unsteady 3D algebraically explicit analytical solutions for bio-heat transfer equations

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Science China(Technological Sciences) 2011年第2期54卷 362-368页

作者： LI YuanYuan cai ruixian Institute of Engineering Thermophysics Chinese Academy of Sciences Beijing 100190 China Graduate University of Chinese Academy of Sciences Beijing 100039 China

Reasonable unsteady three-dimensional explicit analytical solutions are derived with different methods for the widely used bio-heat transfer equation–Pennes *** condition to decide temperature oscillation is obtained in this *** other cases the temperature would vary monotonously along geometric coordinates as time goes *** have been very few open reports of explicit unsteady multidimensional exact analytical solutions published in *** its irreplaceable theoretical value,the analytical solution can also serve as standard solution to check numerical calculation,and therefore promote the development of numerical method of computational heat *** addition,some new special methods have been given originally and deserved further attention.

关键词： Pennes equation temperature oscillation three-dimensional unsteady analytical solutions

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A new method for deriving analytical solutions of partial differential equations-Algebraically explicit analytical solutions of two-buoyancy natural convection in porous media

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Science China(Physics,Mechanics & Astronomy) 2008年第11期51卷 1733-1744页

作者： cai ruixian LIU QiBin Institute of Engineering Thermophysics Chinese Academy of SciencesBeijing 100190China

Analytical solutions of governing equations of various phenomena have their irre-placeable theoretical meanings. In addition, they can also be the benchmark solu-tions to verify the outcomes and codes of numerical solutions, and even to develop various numerical methods such as their differencing schemes and grid generation skills as well. A hybrid method of separating variables for simultaneous partial differential equation sets is presented. It is proposed that different methods of separating variables for different independent variables in the simultaneous equa-tion set may be used to improve the solution derivation procedure, for example, using the ordinary separating method for some variables and using extraordinary methods of separating variables, such as the separating variables with addition promoted by the first author, for some other variables. In order to prove the ability of the above-mentioned hybrid method, a lot of analytical exact solutions of two-buoyancy convection in porous media are successfully derived with such a method. The physical features of these solutions are given.

关键词： analytical solution hybrid method of separating variables two-buoyancy natural convection porous me-dium

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An analytical solution of non-Fourier Chen-Holmes bioheat transfer equation

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Chinese Science Bulletin 2005年第23期50卷 2791-2792页

作者： GOU Chenhua cai ruixian Institute of Engineering Thermophysics Chinese Academy of Sciences Beijing 100080 China Graduate School Chinese Academy of Sciences Beijing 100080China

An algebraically explicit analytical solution with heat wave effect is derived for the non-Fourier bioheat transfer Chen-Holmes model. Besides its important theoreti-cal meaning (for example, to expand the understanding of heat wave phenomena in living tissues), this analytical solu-tion is also valuable as the benchmark solution to check the numerical calculation and to develop various numerical computational approaches.

关键词： Chen-Holmes方程生物热传递模型非傅立叶效应解析解

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Explicit analytical solutions of non-Fourier heat conduction equation for IC chip

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Chinese Science Bulletin 1998年第13期43卷 1080-1084页

作者： ruixian cai Na Zhang Chinese Acad Sci Inst Engn Thermophys Beijing 100080 Peoples R China

Four basic explicit analytical solutions of non_Fourier heat conduction equation simulating IC chip thermal condition are derived. Some other analytical series solutions can also be derived with the above_mentioned basic solutions. Analytical solution has its own irreplaceable important meaning in theory. In addition, as the standard solution to check the accuracy, convergence and effectiveness of various numerical computational methods and their differencing schemes, grid generation ways and so on, the analytical solution is very useful also for the newly rapidly developing computational heat transfer.

关键词： Non_Fourier heat conduction analytical solution IC chip.

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热力机械基本方程的严格解析解

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机械工程学报 2009年第3期45卷 5-9页

作者：蔡睿贤中国科学院工程热物理研究所北京100190

对各学科基本方程的生成与发展,给出简明的表达。重点说明历史上对基本方程的求解有两大阶段:开始是以解析解为核心的时代,找不到解析解就想法以近似解代替。在电子计算机与计算方法飞速发展后,就基本都用数值计算解决问题。但原来的严... 详细信息

对各学科基本方程的生成与发展,给出简明的表达。重点说明历史上对基本方程的求解有两大阶段:开始是以解析解为核心的时代,找不到解析解就想法以近似解代替。在电子计算机与计算方法飞速发展后,就基本都用数值计算解决问题。但原来的严格解析解仍有其重大意义。一是在理论上的价值,而且所得的解析解多少总比具体的数值解包含有更广泛的可用范围。尤其更重要的是对基本方程,解析解是绝对准确的,可以作为标准解来校验、判断数值解的准确度,同时也可以用来考核计算程序的收敛度、稳定性等。并且启发研究人员如何去提高各种计算方法的水平,如差分格式、网络生成的技术等。因此近半个世纪以来,对热力机械仍有数以百计的求解析解的论文。其中国内学者的成绩处于领先地位,因此对他们一些著名的简明严格解析解给出了简单的介绍,并且还介绍了新的求得简明严格解析解的一条途径。

关键词：严格解析解热力机械基本方程加法分离变量法

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工程热物理学科中的若干解析解

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西安交通大学学报 2000年第2期34卷 1-6页

作者：蔡睿贤蔡档中国科学院工程热物理研究所北京100080 西安交通大学

介绍了蔡睿贤给出的工程热物理学科中典型的2组基本方程的解析解,即完全气体无粘可压流动的显式解析解和球体内不定常非Fourier导热的一维代数显式解析解.应用加法分离变量法。

关键词：解析解热波效应非傅里叶导热工程热物理学

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单轴燃气轮机联合循环变工况典型解析特性

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工程热物理学报 2000年第5期21卷 529-532页

作者：张娜蔡睿贤中国科学院工程热物理研究所!北京100080

本文对余热锅炉型联合循环给出其变工况特性解析解并加以规律性的总结，它虽不能严格表达某一具体机组的准确特性，但可将其视为这类动力装置通用特性的典型表达。

关键词：联合循环变工况解析特性

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锅炉受热面动态过程的一套显式解析特解

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机械工程学报 2000年第7期36卷 11-13页

作者：蔡睿贤张娜中国科学院工程热物理研究所北京100080

对锅炉省煤器受热面的动态过程偏微分方程组导出了一套代数显式解析特解。它仅由时间与几何坐标的常数项、线性项与负指数项组成 ,比较简单明了 ,而且有典型的物理意义。另外 ,在推导这些解时用了作者建议的一些新的办法 ,例如加法分离... 详细信息

对锅炉省煤器受热面的动态过程偏微分方程组导出了一套代数显式解析特解。它仅由时间与几何坐标的常数项、线性项与负指数项组成 ,比较简单明了 ,而且有典型的物理意义。另外 ,在推导这些解时用了作者建议的一些新的办法 ,例如加法分离变量法。它把未知多元变量视为多个单元变量之和 ,而非如经典办法那样视为单元变量之积。

关键词：锅炉受热面动态过程解析解省煤器

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One-dimensional unsteady general solution for Wang bioheat transfer equation with heat source proportional to temperature

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Progress in Natural Science:Materials International 2006年第7期16卷 766-768页

作者： GOU Chenhua and cai ruixian ( Institute of Engineering Thermophysics, Chinese Academy of Sciences, Beijing 100080, China Graduate School, Chinese Academy of Sciences, Beijing 100080, China) Chinese Acad Sci Inst Engn Thermophys Beijing 100080 Peoples R China Chinese Acad Sci Grad Sch Beijing 100080 Peoples R China

An analytical general solution is derived for the non-Fourier Wang bioheat transfer model with special internal heat production. It is valuable for finding the special solutions with specified conditions and for expanding the understanding of the non-Fourier heat conduction phenomena in living tissues, for example, the controversial temperature fluctuation effects. This analytical solution can also be used as the benchmark solution to check the numerical calculations and to develop various numerical computational approaches. Because there is an arbitrary function in the expression of internal heat production, this solution can actually be applied to many types of internal heat production distributions.

关键词： bioheat transfer model non-fourier effect analytical solution

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