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Measurement of boiling heat transfer coefficient in liquid nitrogen bath by inverse heat conduction method 被引量:8
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作者 Tao JIN Jian-ping HONG +2 位作者 Hao ZHENG Ke TANG Zhi-hua GAN 《Journal of Zhejiang University-Science A(Applied Physics & Engineering)》 SCIE EI CAS CSCD 2009年第5期691-696,共6页
Inverse heat conduction method (IHCM) is one of the most effective approaches to obtaining the boiling heat transfer coefficient from measured results. This paper focuses on its application in cryogenic boiling heat t... Inverse heat conduction method (IHCM) is one of the most effective approaches to obtaining the boiling heat transfer coefficient from measured results. This paper focuses on its application in cryogenic boiling heat transfer. Experiments were conducted on the heat transfer of a stainless steel block in a liquid nitrogen bath, with the assumption of a 1D conduction condition to realize fast acquisition of the temperature of the test points inside the block. With the inverse-heat conduction theory and the explicit finite difference model, a solving program was developed to calculate the heat flux and the boiling heat transfer coefficient of a stainless steel block in liquid nitrogen bath based on the temperature acquisition data. Considering the oscillating data and some unsmooth transition points in the inverse-heat-conduction calculation result of the heat-transfer coefficient, a two-step data-fitting procedure was proposed to obtain the expression for the boiling heat transfer coefficients. The coefficient was then verified for accuracy by a comparison between the simulation results using this expression and the verifying experimental results of a stainless steel block. The maximum error with a revised segment fitting is around 6%, which verifies the feasibility of using IHCM to measure the boiling heat transfer coefficient in liquid nitrogen bath. 展开更多
关键词 Inverse heat conduction method (IHCM) Liquid nitrogen bath Boiling heat transfer coefficient
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Synthesis strategies of covalent organic frameworks: An overview from nonconventional heating methods and reaction media 被引量:2
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作者 Jing Xiao Jia Chen +2 位作者 Juewen Liu Hirotaka Ihara Hongdeng Qiu 《Green Energy & Environment》 SCIE EI CAS CSCD 2023年第6期1596-1618,共23页
Covalent organic frameworks(COFs), as an emerging class of porous crystalline materials constructed by covalent links between the building monomers, have gained tremendous attention. Over the past 15 years, COFs have ... Covalent organic frameworks(COFs), as an emerging class of porous crystalline materials constructed by covalent links between the building monomers, have gained tremendous attention. Over the past 15 years, COFs have made rapid progress and substantial development in the chemistry and materials fields. However, the synthesis of COFs has been dominated by solvothermal methods for a long time and it usually involves high temperature, high pressure and toxic organic solvents, which created many challenges for environmental considerations. Recently,the exploration of new approaches for facile fabrication of COFs has aroused extensive interest. Hence, in this review, we comprehensively describe the synthetic strategies of COFs from the aspects of nonconventional heating methods and reaction media. In addition, the advantages,limitations and properties of the preparation methods are compared. Finally, we outline the main challenges and development prospects of the synthesis of COFs in the future and propose some possible solutions. 展开更多
关键词 Covalent organic frameworks heating methods Reaction media Synthesis strategy Formation mechanism
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A new hybrid method—combined heat flux method with Monte-Carlo method to analyze thermal radiation 被引量:2
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作者 Zengwu Zhao Daqiang Cang +2 位作者 Wenfei Wu Yike Li Baowei Li 《Journal of University of Science and Technology Beijing》 CSCD 2006年第1期25-28,共4页
A new hybrid method, Monte-Carlo-Heat-Flux (MCHF) method, was presented to analyze the radiative heat transfer of participating medium in a three-dimensional rectangular enclosure using combined the Monte-Carlo meth... A new hybrid method, Monte-Carlo-Heat-Flux (MCHF) method, was presented to analyze the radiative heat transfer of participating medium in a three-dimensional rectangular enclosure using combined the Monte-Carlo method with the heat flux method. Its accuracy and reliability was proved by comparing the computational results with exact results from classical "Zone Method". 展开更多
关键词 radiation heat transfer SCATTERING numerical simulation Monte-Carlo method heat flux method
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Catalytic CVD Growth of Carbon Nanotubes by Electric Heating Method 被引量:1
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作者 徐先锋 欧阳甜 +3 位作者 CHAI Lingzhi ZENG Lingsheng LI Gang CHEN Yue 《Journal of Wuhan University of Technology(Materials Science)》 SCIE EI CAS 2017年第1期136-139,共4页
Carbon nanotubes(CNTs) were synthesized by the electric heating catalytic chemical deposition method(CCVD) using acetylene(C2H2) as the carbon source and nitrogen(N2) as carrier gas,and nickel catalyst was loa... Carbon nanotubes(CNTs) were synthesized by the electric heating catalytic chemical deposition method(CCVD) using acetylene(C2H2) as the carbon source and nitrogen(N2) as carrier gas,and nickel catalyst was loaded by electroplating.The electric heating method,as a new method,electrifies the carbon fiber directly by using its conductivity.The morphology and structure of CNTs were characterized by SEM and TEM,and the surface properties of carbon fibers before and after the growth of CNT were characterized by Raman spectroscopy.The experimental results show that the electric heating method is a new method to produce CNT,and can grow a large number of CNTs in a short time,the crystallization degree and surface average crystallite size of carbon fiber increased after the growth of CNT on it.In addition,electroplating loading catalyst can also be used as an ideal loading way,which can control the number,shape,and distribution of nickel particles by controlling the plating time. 展开更多
关键词 electric heating method catalytic CVD nickel plating carbon nanotubes
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Application of heat absorption method to reduce macrosegregation during solidification of bearing steel ingot 被引量:2
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作者 Sheng Yu Long-qiang Zhu +6 位作者 Jin-hu Lai Ming-xu Pan Yue-yun Liu Wei-dong Xuan Jiang Wang Chuan-jun Li Zhong-ming Ren 《Journal of Iron and Steel Research International》 SCIE EI CAS CSCD 2022年第12期1915-1926,共12页
The control of macrosegregation is still a difficult problem for the production of large steel ingots.In order to develop new techniques for producing low-macrosegregation and high-quality steel ingots,the effect of t... The control of macrosegregation is still a difficult problem for the production of large steel ingots.In order to develop new techniques for producing low-macrosegregation and high-quality steel ingots,the effect of the heat absorption method(HAM)used by the inorganic material rods to cool the liquid steel on the formation of macrosegregation during solidification of a 5-t GCr15SiMn bearing steel ingot was studied using experiment and mathematical simulation.The inorganic material was a mixture of CaF2 and CaO.The levels of macrosegregation in the longitudinal sections of two ingots with and without HAM were compared.Experimental results showed that the application of HAM reduced the positive segregation in the upper part of the ingot and the negative segregation in the lower part.The levels of carbon segregation along the longitudinal centerline and horizontal direction at different heights were all alleviated and the fluctuation of carbon segregation was significantly reduced.The simulation results confirmed that the melting and floating of the inorganic material could carry the sensible heat to the top of the liquid steel quickly.This leads to the acceleration of the cooling rate of the liquid steel,thereby alleviating the level of macrosegregation. 展开更多
关键词 Large steel ingot MACROSEGREGATION Inorganic material heat absorption method Mathematical simulation
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Chemical Oxygen Demand of Seawater Determined with a Microwave Heating Method 被引量:1
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作者 LIULi JIHongwei LIUYing XINHuizhen 《Journal of Ocean University of China》 SCIE CAS 2005年第2期152-156,共5页
This paper investigates a microwave heating method for the determination of chemical oxygen demand (COD) in seawater. The influences of microwave-power, heating time and standard substances on the results are studied.... This paper investigates a microwave heating method for the determination of chemical oxygen demand (COD) in seawater. The influences of microwave-power, heating time and standard substances on the results are studied. Using the proposed method, we analyzed the glucose standard solution, the coefficient of variation being less than 2%. Compared with the traditional electric stove heating method, the results of F-test and T-test showed that there was no significant difference between the two methods, but the microwave method had slightly higher precision and reproducibility than the electric stove method. With the microwave heating method, several seawater samples from Jiaozhou Bay and the South Yellow Sea were also analyzed. The recovery was between 97.5% and 104.3%. This new method has the advantages of shortening the heating time, improving the working efficiency and having simple operation and therefore can be used to analyze the COD in seawater. 展开更多
关键词 seawater COD alkalinity potassium permanganate microwave heating method
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Heat transfer study on solid and porous convective fins with temperature-dependent heat generation using efficient analytical method 被引量:10
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作者 S.E.Ghasemi P.Valipour +1 位作者 M.Hatami D.D.Ganji 《Journal of Central South University》 SCIE EI CAS 2014年第12期4592-4598,共7页
A simple and highly accurate semi-analytical method, called the differential transformation method(DTM), was used for solving the nonlinear temperature distribution equation in solid and porous longitudinal fin with t... A simple and highly accurate semi-analytical method, called the differential transformation method(DTM), was used for solving the nonlinear temperature distribution equation in solid and porous longitudinal fin with temperature dependent internal heat generation. The problem was solved for two main cases. In the first case, heat generation was assumed variable by fin temperature for a solid fin and in second heat generation varied with temperature for a porous fin. Results are presented for the temperature distribution for a range of values of parameters appearing in the mathematical formulation(e.g. N, εG, and G). Results reveal that DTM is very effective and convenient. Also, it is found that this method can achieve more suitable results in comparison to numerical methods. 展开更多
关键词 heat transfer convective fin solid and porous fin heat generation analytical method thermal analysis
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Streamline upwind finite element method for conjugate heat transfer problems 被引量:3
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作者 Niphon Wansophark Atipong Malatip Pramote Dechaumphai 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2005年第5期436-443,共8页
This paper presents a combined finite element method for solving conjugate heat transfer problems where heat conduction in a solid is coupled with heat convection in viscous fluid flow. The streamline upwind finite el... This paper presents a combined finite element method for solving conjugate heat transfer problems where heat conduction in a solid is coupled with heat convection in viscous fluid flow. The streamline upwind finite element method is used for the analysis of thermal viscous flow in the fluid region, whereas the analysis of heat conduction in solid region is performed by the Galerkin method. The method uses the three-node triangular element with equal-order interpolation functions for all the variables of the velocity components, the pressure and the temperature. The main advantage of the proposed method is to consistently couple heat transfer along the fluid-solid interface. Three test cases, i.e. conjugate Couette flow problem in parallel plate channel, counter-flow in heat exchanger, and conjugate natural convection in a square cavity with a conducting wall, are selected to evaluate the efficiency of the present method. 展开更多
关键词 Streamline upwind.Conjugate heat transfer.Finite element method
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Combining the complex variable reproducing kernel particle method and the finite element method for solving transient heat conduction problems 被引量:2
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作者 陈丽 马和平 程玉民 《Chinese Physics B》 SCIE EI CAS CSCD 2013年第5期67-74,共8页
In this paper, the complex variable reproducing kernel particle (CVRKP) method and the finite element (FE) method are combined as the CVRKP-FE method to solve transient heat conduction problems. The CVRKP-FE metho... In this paper, the complex variable reproducing kernel particle (CVRKP) method and the finite element (FE) method are combined as the CVRKP-FE method to solve transient heat conduction problems. The CVRKP-FE method not only conveniently imposes the essential boundary conditions, but also exploits the advantages of the individual methods while avoiding their disadvantages, then the computational efficiency is higher. A hybrid approximation function is applied to combine the CVRKP method with the FE method, and the traditional difference method for two-point boundary value problems is selected as the time discretization scheme. The corresponding formulations of the CVRKP-FE method are presented in detail. Several selected numerical examples of the transient heat conduction problems are presented to illustrate the performance of the CVRKP-FE method. 展开更多
关键词 complex variable reproducing kernel particle method finite element method combined method transient heat conduction
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Study on the Pyrolytic Carbon Generated by the Electric Heating CVD Method 被引量:1
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作者 徐先锋 欧阳甜 +1 位作者 ZENG Lingsheng CHAI Lingzhi 《Journal of Wuhan University of Technology(Materials Science)》 SCIE EI CAS 2018年第2期409-413,共5页
A new method of fabricating C/C composite materials, namely electric heating CVD method, was used, which electrified the carbon fiber directly by using the conductivity of itself. Acetylene was used as the carbon sour... A new method of fabricating C/C composite materials, namely electric heating CVD method, was used, which electrified the carbon fiber directly by using the conductivity of itself. Acetylene was used as the carbon source with nitrogen as dilution gas, and the pyrolytic carbon started to deposit on the carbon fiber surface when the deposition temperature was reached. The morphology of pyrolytic carbon was characterized by SEM, and the surface properties of carbon fibers before and after CVD were characterized by Raman spectroscopy. The experimental results show that the electric heating method is a novel method to fabricate C/C composite materials, which can form a dense C/C composite material in a short time. The order degree and the average crystallite size of the carbon fiber surface were decreased after the experiment. 展开更多
关键词 C/C composite materials electric heating method chemical vapor deposition pyrolytic carbon
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Optical and scintillation properties of Ce:Y_(3)Al_(5)O_(12) single crystal fibers grown by laser heated pedestal growth method 被引量:2
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作者 Xibin Wang Yun Dai +4 位作者 Zhonghan Zhang Liangbi Su Huamin Kou Yangxiao Wang Anhua Wu 《Journal of Rare Earths》 SCIE EI CAS CSCD 2021年第12期1533-1539,I0003,共8页
The single crystal scintillating optical fibers acting as the scintillators and light conductors show potential application in scintillating fiber array detectors with high spatial resolution.In this paper we report t... The single crystal scintillating optical fibers acting as the scintillators and light conductors show potential application in scintillating fiber array detectors with high spatial resolution.In this paper we report the growth of 0.2 at%Ce:Y_(3)Al_(5)O_(12) single crystal fiber.The crystalline phase,surface morphology of the axialsection and cro ss-section,optical and scintillation properties of the as-grown fiber were investigated.The Ce:Y_(3)Al_(5)O_(12) single crystal fiber has a pure YAG phase,a uniform distribution of cerium in the axialsection and cross-section surface.Emission spectrum is composed of broad bands ranging from 440 to700 nm.In addition,the single crystal fiber has a high light yield of 26115±2000 photons/MeV,low energy resolution of 9.44%@662 keV and decay time of a fast component of 78 ns and a slow component of 301 ns.The intensity ratio of fast to slow components is roughly 8:1. 展开更多
关键词 Ce:Y_(3)Al_(5)O_(12) Single crystal fiber Laser heated pedestal growth method Rare earth Scintillator
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Radiation heat transfer model for complex superalloy turbine blade in directional solidification process based on finite element method 被引量:5
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作者 Dun-ming Liao Liu Cao +4 位作者 Tao Chen Fei Sun Yong-zhen Jia Zi-hao Teng Yu-long Tang 《China Foundry》 SCIE 2016年第2期123-132,共10页
For the sake of a more accurate shell boundary and calculation of radiation heat transfer in the Directional Solidification(DS) process, a radiation heat transfer model based on the Finite Element Method(FEM)is develo... For the sake of a more accurate shell boundary and calculation of radiation heat transfer in the Directional Solidification(DS) process, a radiation heat transfer model based on the Finite Element Method(FEM)is developed in this study. Key technologies, such as distinguishing boundaries automatically, local matrix and lumped heat capacity matrix, are also stated. In order to analyze the effect of withdrawing rate on DS process,the solidification processes of a complex superalloy turbine blade in the High Rate Solidification(HRS) process with different withdrawing rates are simulated; and by comparing the simulation results, it is found that the most suitable withdrawing rate is determined to be 5.0 mm·min^(-1). Finally, the accuracy and reliability of the radiation heat transfer model are verified, because of the accordance of simulation results with practical process. 展开更多
关键词 directional solidification radiation heat transfer finite element method numerical simulation local matrix superalloy turbine blade
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Regularization Method to the Parameter Identification of Interfacial Heat Transfer Coefficient and Properties during Casting Solidification 被引量:4
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作者 隋大山 崔振山 《Journal of Shanghai Jiaotong university(Science)》 EI 2007年第4期511-516,共6页
The accurate material physical properties, initial and boundary conditions are indispensable to the numerical simulation in the casting process, and they are related to the simulation accuracy directly. The inverse he... The accurate material physical properties, initial and boundary conditions are indispensable to the numerical simulation in the casting process, and they are related to the simulation accuracy directly. The inverse heat conduction method can be used to identify the mentioned above parameters based on the temperature measurement data. This paper presented a new inverse method according to Tikhonov regularization theory. A regularization functional was established and the regularization parameter was deduced, the Newton-Raphson iteration method was used to solve the equations. One detailed case was solved to identify the thermal conductivity and specific heat of sand mold and interfacial heat transfer coefficient (IHTC) at the meantime. This indicates that the regularization method is very efficient in decreasing the sensitivity to the temperature measurement data, overcoming the ill-posedness of the inverse heat conduction problem (IHCP) and improving the stability and accuracy of the results. As a general inverse method, it can be used to identify not only the material physical properties but also the initial and boundary conditions' parameters. 展开更多
关键词 CASTING INVERSE heat conduction problem parameter identification REGULARIZATION method INTERFACIAL heat transfer COEFFICIENT
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Transient heat conduction analysis using the NURBS-enhanced scaled boundary finite element method and modified precise integration method 被引量:3
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作者 Gao Lin Peng Li +1 位作者 Jun Liu Pengchong Zhang 《Acta Mechanica Solida Sinica》 SCIE EI CSCD 2017年第5期445-464,共20页
The Non-uniform rational B-spline (NURBS) enhanced scaled boundary finite element method in combination with the modified precise integration method is proposed for the transient heat conduction problems in this pap... The Non-uniform rational B-spline (NURBS) enhanced scaled boundary finite element method in combination with the modified precise integration method is proposed for the transient heat conduction problems in this paper. The scaled boundary finite element method is a semi-analytical technique, which weakens the governing differential equations along the circumferential direction and solves those analytically in the radial direction. In this method, only the boundary is discretized in the finite element sense leading to a re- duction of the spatial dimension by one with no fundamental solution required. Neverthe- less, in case of the complex geometry, a huge number of elements are generally required to properly approximate the exact shape of the domain and distorted meshes are often un- avoidable in the conventional finite element approach, which leads to huge computational efforts and loss of accuracy. NURBS are the most popular mathematical tool in CAD industry due to its flexibility to fit any free-form shape. In the proposed methodology, the arbitrary curved boundary of problem domain is exactly represented with NURBS basis functions, while the straight part of the boundary is discretized by the conventional Lagrange shape functions. Both the concepts of isogeometric analysis and scaled boundary finite element method are combined to form the governing equations of transient heat conduction analy- sis and the solution is obtained using the modified precise integration method. The stiffness matrix is obtained from a standard quadratic eigenvalue problem and the mass matrix is determined from the low-frequency expansion. Finally the governing equations become a system of first-order ordinary differential equations and the time domain response is solved numerically by the modified precise integration method. The accuracy and stability of the proposed method to deal with the transient heat conduction problems are demonstrated by numerical examples. 展开更多
关键词 Transient heat conduction analysisScaled boundary finite elementmethodNURBSIsogeometric analysisModified precise integration method
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NUMERICAL SIMULATION OF FORGING AND SUBSEQUENT HEAT TREATMENT OF A ROD BY A FINITE VOLUME METHOD 被引量:6
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作者 P. R. Ding D. Y. Ju T. Lnouc and E. de Vries( 1) MSC Japan Ltd., Osaka,Japan 2) Saitama Institute of Technology,Saitama,Japan 3) Kyoto Universily, Kyoto, Japan 4) MacNeal - Schwendler (E. D. C. ) B. V., Gouda, The Netherlands) 《Acta Metallurgica Sinica(English Letters)》 SCIE EI CAS CSCD 2000年第1期270-280,共11页
A method to simulate processes of forging and subsequent heat treatment of an axial symmetric rod is formulated in eulerian description and the feasibility is investigated. This method uses finite volume mushes for t... A method to simulate processes of forging and subsequent heat treatment of an axial symmetric rod is formulated in eulerian description and the feasibility is investigated. This method uses finite volume mushes for troching material deformation and an automatically refined facet surface to accurately trace the free surface of the deforming material.In the method,the deforming work piece flows through fixed finite volume meshes using eulerian formulation to describe the conservation laws,Fixed finite volume meshing is particularly suitable for large three-dimensional deformation such as forging because remeshing techniques are not required, which are commonly considered to be the main bottelencek in the ssimulations of large defromation by using the finite element method,By means of this finite volume method, an approach has been developed in the framework of 'metallo-thermo-mechanics' to simulate metallic structure, temperature and stress/strain coupled in the heat treatment process.In a first step of simulation, the heat treatment solver is limited in small deformation hypothesis,and un- coupled with forging. The material is considered as elastic-plastic and takes into account of strain, strain rate and temperature effects on the yield stress.Heat generation due to deformation,heat con- duction and thermal stress are considered.Temperature - dependent phase transformation,stress-in- duced phase transformation,latent heat,transformation stress and strain are included.These ap- proaches are implemented into the commerical commercial computer program MSC/SuperForge and a verification example with experimental date is given as comparison. 展开更多
关键词 finite volume method forging heat treatment quenching phase transformation
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Nodeless variable finite element method for heat transfer analysis by means of flux-based formulation and mesh adaptation 被引量:1
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作者 Sutthisak Phongthanapanich Suthee Traivivatana Parinya Boonmaruth Pramote Dechaumphai 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2006年第2期138-147,共10页
Based on flux-based formulation, a nodeless variable element method is developed to analyze two-dimensional steady-state and transient heat transfer problems. The nodeless variable element employs quadratic interpolat... Based on flux-based formulation, a nodeless variable element method is developed to analyze two-dimensional steady-state and transient heat transfer problems. The nodeless variable element employs quadratic interpolation functions to provide higher solution accuracy without necessity to actually generate additional nodes. The flux-based formulation is applied to reduce the complexity in deriving the finite element equations as compared to the conventional finite element method, The solution accuracy is further improved by implementing an adaptive meshing technique to generaie finite element mesh that can adapt and move along corresponding to the solution behavior. The technique generates small elements in the regions of steep solution gradients to provide accurate solution, and meanwhile it generates larger elements in the other regions where the solution gradients are slight to reduce the computational time and the computer memory. The effectiveness of the combined procedure is demonstrated by heat transfer problems that have exact solutions. These problems tire: (a) a steady-state heat conduction analysis in a square plate subjected to a highly localized surface heating, and (b) a transient heat conduction analysis in a long plate subjected to moving heat source. 展开更多
关键词 Flux-based formulation Adaptive mesh movement Finite element method heat transfer
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ANALYSIS OF THE HEAT TRANSFER IN FIN ASSEMBLIES BY THE BOUNDARY ELEMENT METHOD
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作者 张平 王朝阳 《苏州大学学报(自然科学版)》 CAS 1991年第2期162-165,共4页
The special formulation that allows an accurate and efficient solution to the heat transfer problems within fin assemblies with very large aspect ratios has been developed in this paper Numerically,it consists of the ... The special formulation that allows an accurate and efficient solution to the heat transfer problems within fin assemblies with very large aspect ratios has been developed in this paper Numerically,it consists of the boundary element method in the wall region and the analytical solution in the fin region This modified BEM makes tractable a large class of heat transfer problems in the long and thin domains which are frequently encountered in practice. 展开更多
关键词 热传导 边界元法 解析解 圆筒管 翅片装配
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Fuzzy finite difference method for heat conduction analysis with uncertain parameters 被引量:3
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作者 Chong Wang Zhi-Ping Qiu 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2014年第3期383-390,共8页
A new numerical technique named as fuzzy finite difference method is proposed to solve the heat conduction problems with fuzzy uncertainties in both the phys- ical parameters and initial/boundary conditions. In virtue... A new numerical technique named as fuzzy finite difference method is proposed to solve the heat conduction problems with fuzzy uncertainties in both the phys- ical parameters and initial/boundary conditions. In virtue of the level-cut method, the difference discrete equations with fuzzy parameters are equivalently transformed into groups of interval equations. New stability analysis theory suited to fuzzy difference schemes is developed. Based on the parameter perturbation method, the interval ranges of the uncertain temperature field can be approximately predicted. Subsequently, fuzzy solutions to the original difference equations are obtained by the fuzzy resolution theorem. Two numerical examples are given to demonstrate the feasibility and efficiency of the presented method for solving both steady-state and transient heat conduction problems. 展开更多
关键词 heat conduction Fuzzy uncertainties Finitedifference method Parameter perturbation Stability analysis
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Determination of an Unknown Source in the Heat Equation by the Method of Tikhonov Regularization in Hilbert Scales 被引量:1
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作者 Zhenyu Zhao Ou Xie +1 位作者 Zehong Meng Lei You 《Journal of Applied Mathematics and Physics》 2014年第2期10-17,共8页
In this paper, we consider the problem for determining an unknown source in the heat equation. The Tikhonov regularization method in Hilbert scales is presented to deal with ill-posedness of the problem and error esti... In this paper, we consider the problem for determining an unknown source in the heat equation. The Tikhonov regularization method in Hilbert scales is presented to deal with ill-posedness of the problem and error estimates are obtained with a posteriori choice rule to find the regularization parameter. The smoothness parameter and the a priori bound of exact solution are not needed for the choice rule. Numerical tests show that the proposed method is effective and stable. 展开更多
关键词 ILL-POSED Problem UNKNOWN SOURCE heat Equation Regularization method DISCREPANCY Principle in HILBERT Scales
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Application of Mixed Differential Quadrature Method for Solving the Coupled Two-Dimensional Incompressible Navier-Stokes Equation and Heat Equation 被引量:2
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作者 A.S.J.AL-SAIF 朱正佑 《Journal of Shanghai University(English Edition)》 CAS 2003年第4期343-351,共9页
The traditional differential quadrature method was improved by using theupwind difference scheme for the convective terms to solve the coupled two-dimensionalincompressible Navier-stokes equations and heat equation. T... The traditional differential quadrature method was improved by using theupwind difference scheme for the convective terms to solve the coupled two-dimensionalincompressible Navier-stokes equations and heat equation. The new method was compared with theconventional differential quadrature method in the aspects of convergence and accuracy. The resultsshow that the new method is more accurate, and has better convergence than the conventionaldifferential quadrature method for numerically computing the steady-state solution. 展开更多
关键词 coupled N-S equation and heat equation differential quadrature method upwind difference scheme
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