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Galerkin-based quasi-smooth manifold element(QSME)method for anisotropic heat conduction problems in composites with complex geometry
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作者 Pan WANG Xiangcheng HAN +2 位作者 Weibin WEN Baolin WANG Jun LIANG 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2024年第1期137-154,共18页
The accurate and efficient analysis of anisotropic heat conduction problems in complex composites is crucial for structural design and performance evaluation. Traditional numerical methods, such as the finite element ... The accurate and efficient analysis of anisotropic heat conduction problems in complex composites is crucial for structural design and performance evaluation. Traditional numerical methods, such as the finite element method(FEM), often face a trade-off between calculation accuracy and efficiency. In this paper, we propose a quasi-smooth manifold element(QSME) method to address this challenge, and provide the accurate and efficient analysis of two-dimensional(2D) anisotropic heat conduction problems in composites with complex geometry. The QSME approach achieves high calculation precision by a high-order local approximation that ensures the first-order derivative continuity.The results demonstrate that the QSME method is robust and stable, offering both high accuracy and efficiency in the heat conduction analysis. With the same degrees of freedom(DOFs), the QSME method can achieve at least an order of magnitude higher calculation accuracy than the traditional FEM. Additionally, under the same level of calculation error, the QSME method requires 10 times fewer DOFs than the traditional FEM. The versatility of the proposed QSME method extends beyond anisotropic heat conduction problems in complex composites. The proposed QSME method can also be applied to other problems, including fluid flows, mechanical analyses, and other multi-field coupled problems, providing accurate and efficient numerical simulations. 展开更多
关键词 anisotropic heat conduction quasi-smooth manifold element(QSME) composite with complex geometry numerical simulation finite element method(FEM)
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CALCULATING METHOD OF AERODYNAMIC HEATING FOR HYPERSONIC AIRCRAFTS 被引量:1
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作者 季卫栋 王江峰 《Transactions of Nanjing University of Aeronautics and Astronautics》 EI 2013年第3期237-242,共6页
A new calculating method of aerodynamic heating for unsteady hypersonic aircrafts with complex configuration is presented.This method,which considers the effects of high temperature chemical non-equilibrium and the he... A new calculating method of aerodynamic heating for unsteady hypersonic aircrafts with complex configuration is presented.This method,which considers the effects of high temperature chemical non-equilibrium and the heat transfer process in thermal protection structure,is based on the combination of the inviscid outerflow solution and the engineering method,where the Euler solver provides the flow parameters on boundary layer edge for engineering method in aerodynamic heating calculation.A high efficient interpolation technique,which can be applied to the fast computation of longtime aerodynamic heating for hypersonic aircraft,is developed for flying trajectory.In this paper,three hypersonic test cases are calculated,and the heat flux and temperature distribution of thermo-protection system are shown.The numerical results show the high efficiency of the developed method and the validation of thermal characteristics analysis on hypersonic aerodynamic heating. 展开更多
关键词 hypersonic aircraft aerodynamic heating fluid-structure coupled analysis chemical non-equilibrium effects coupling of numerical and engineering methods
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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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Simulations of the Boiling Process on a Porous Heater by Lattice Boltzmann Method
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作者 Alexander Fedoseev Mikhail Salnikov 《Frontiers in Heat and Mass Transfer》 EI 2024年第6期1679-1694,共16页
In order to research the process of boiling occurring on a porous surface,a model of multiple blocks was developed.The mathematical basis of these blocks is the lattice Boltzmann method in combination with heat transf... In order to research the process of boiling occurring on a porous surface,a model of multiple blocks was developed.The mathematical basis of these blocks is the lattice Boltzmann method in combination with heat transfer equation.The reported complex allows one to obtain the boiling curves for various wall superheats and to find the optimal parameters of a porous heater in terms of heat transfer enhancement.The porous heater structure is specified as a skeleton of square metal heaters located in the lower part of the computational domain.The calculations were performed for the following parameters of the porous heater structure:different number and size of the metal heaters,different distances between them in horizontal and vertical directions,regular and asymmetric packing of the heaters.Using the developed numerical model,parametric studies of the boiling process on porous heaters with different parameters of the porous skeleton were carried out and phase pictures of such a process were obtained.It was shown that the heat transfer coefficient on a porous heater is 3–7 times greater than that on a smooth heater,and depends on the number of heater elements,their size,and location.The results showed a significant advantage of the porous heaters with greater critical heat flux at higher wall superheats compared to that on the smooth surface. 展开更多
关键词 Pool boiling heat transfer enhancement porous heater lattice Boltzmann method
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Experimental Study of Heat Transfer in an Insulated Local Heated fromBelow and Comparison with Simulation by Lattice Boltzmann Method
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作者 Noureddine Abouricha Ayoub Gounni Mustapha El Alami 《Frontiers in Heat and Mass Transfer》 EI 2024年第1期359-375,共17页
In this paper,experimental and numerical studies of heat transfer in a test local of side H=0.8 m heated from below are presented and compared.All the walls,the rest of the floor and the ceiling are made from plywood ... In this paper,experimental and numerical studies of heat transfer in a test local of side H=0.8 m heated from below are presented and compared.All the walls,the rest of the floor and the ceiling are made from plywood and polystyrene in sandwich form(3 mmplywood-3 cm polystyrene-3 mmplywood)just on one of the vertical walls contained a glazed door(2 H/3×0.15 m).This local is heated during two heating cycles by a square plate of iron the width L=0.6 H,which represents the heat source,its temperature Th is controlled.The plate is heated for two cycles by an adjustable set-point heat source placed just down the center of it.For each cycle,the heat source is switched“on”for 6 h and switched“off”for 6 h.The outdoor air temperature is kept constant at a low temperature Tc<Th.All measurements are carried out with k-type thermocouples and with flux meters.Results will be qualitatively presented for two cycles of heating in terms of temperatures and heat flux densitiesϕfor various positions of the test local.The temperature evolution of the center and the profile of the temperature along the vertical centerline are compared by two dimensions simulation using the lattice Boltzmann method.The comparison shows a good agreement with a difference that does not exceed±1℃. 展开更多
关键词 Experimental study numerical study lattice Boltzmann method heat transfer building insulation thermal comfort
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Amplitude and Period Effect on Heat Transfer in an Enclosure with Sinusoidal Heating from Below Using Lattice Boltzmann Method 被引量:1
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作者 Noureddine Abouricha Chouaib Ennawaoui Mustapha El Alami 《Frontiers in Heat and Mass Transfer》 EI 2023年第1期523-537,共15页
This work presents a simulation of the phenomena of natural convection in an enclosure with a variable heating regime by the lattice Boltzmann method(LBM).We consider a square enclosure of side H filled with air(Pr=0.... This work presents a simulation of the phenomena of natural convection in an enclosure with a variable heating regime by the lattice Boltzmann method(LBM).We consider a square enclosure of side H filled with air(Pr=0.71)and heated from below,with a hot portion of length L=0.8 H,by imposing a sinusoidal temperature.The unheated segments of the bottom wall are treated as adiabatic,and one of the vertical walls features a cold region,while the remaining walls remain adiabatic.The outcomes of the two-dimensional(2D)problem are depicted through isotherms,streamlines,the temperature evolution within the enclosure,and the Nusselt number.These visualizations span various amplitude values“a”in the interval[0.2,0.8],and of the period T0 for Ra=107.The amplitude and period effect on the results is evaluated and discussed.The amplitude of the temperature at the heart of the enclosure increases with the increase in amplitude.This also increases with the period(T0)of the imposed temperature,something that is not observable on the global Nusselt number. 展开更多
关键词 Sinusoidal heating square cavity lattice Boltzmann method natural convection heat transfer under floor heating
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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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A Full Predictor-Corrector Finite Element Method for the One-Dimensional Heat Equation with Time-Dependent Singularities
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作者 Jake L. Nkeck 《Journal of Applied Mathematics and Physics》 2024年第4期1364-1382,共19页
The energy norm convergence rate of the finite element solution of the heat equation is reduced by the time-regularity of the exact solution. This paper presents an adaptive finite element treatment of time-dependent ... The energy norm convergence rate of the finite element solution of the heat equation is reduced by the time-regularity of the exact solution. This paper presents an adaptive finite element treatment of time-dependent singularities on the one-dimensional heat equation. The method is based on a Fourier decomposition of the solution and an extraction formula of the coefficients of the singularities coupled with a predictor-corrector algorithm. The method recovers the optimal convergence rate of the finite element method on a quasi-uniform mesh refinement. Numerical results are carried out to show the efficiency of the method. 展开更多
关键词 SINGULARITIES Finite Element methods heat Equation Predictor-Corrector Algorithm
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Catalytic CVD Growth of Carbon Nanotubes by Electric Heating Method
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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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PROPERTIES OF (Y.Gd) BO_3: Eu^(3+)PHOSPHORS SYNTHESIZED BY MICROWAVE HEATING METHOD
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作者 Yuan Ying LI Ming LI PENG(Department of Chehemistry, Zhongshan University, GuangZhou, 510275)Shou Hua FENG(Department of Chemistry, Jilin University, Changchun. 130023) 《Chinese Chemical Letters》 SCIE CAS CSCD 1996年第4期387-388,共2页
In this peper we have synthesized powder crystal form (Y,Gd) BO3:Eu(3+)Phosphors by microwave heating method. ItS structure belongs to hexagonal system with lattice parameters a=0.3796,c=0. 8835. Its excitation spetra... In this peper we have synthesized powder crystal form (Y,Gd) BO3:Eu(3+)Phosphors by microwave heating method. ItS structure belongs to hexagonal system with lattice parameters a=0.3796,c=0. 8835. Its excitation spetra peaks at 239.0nm and 240. 0nm monitored at the emission of 589nm and 612nm respectively, the half peak width is 40nm. Under 240nm excitation the phosphors show a strons oranse-red luminescence, the fluorescent intensity ratio for I589/I612 is 1.9/1 展开更多
关键词 GD OF PROPERTIES heating MICROWAVE method PHOSPHORS SYNTHESIZED EU BO3
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Synthesis strategies of covalent organic frameworks: An overview from nonconventional heating methods and reaction media
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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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Development of Contactless Method of the DUT Heating during Single-Event Effect Tests
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作者 Vasily S.Anashin Eugeny V.Mitin +1 位作者 Aleksandr E.Koziukov Ekaterina N.Nekrasova 《Journal of Physical Science and Application》 2018年第2期22-27,共6页
This paper presents two approaches to perform the electronic device heating during radiation hardness assurance tests.Commonly used conductive heating approach is compared with contactless laser-based approach,charact... This paper presents two approaches to perform the electronic device heating during radiation hardness assurance tests.Commonly used conductive heating approach is compared with contactless laser-based approach,characteristics and limitations of these methods are described.Experimental results for temperature dependence of single-event latchup(SEL)cross-section during heavy ion irradiation along with some aspects of physics-based numerical simulation of heat transfer processes are presented. 展开更多
关键词 Single-event effect(SEE)tests HEAVY ions radiation hardness heating methods SEL
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Program for Solar Water Heating Systems Based on the F-Chart Method
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作者 Felix do Rego Barros Adriano Gatto Lemos +1 位作者 Sildenir Alves Ribeiro Manoel Antonio da Fonseca Costa Filho 《Journal of Mechanics Engineering and Automation》 2014年第9期752-762,共11页
This paper aims at presenting an application developed in Java for optimizing the design of centralized solar water heating systems with forced circulation, based on the f-chart method. The program uses data from the ... This paper aims at presenting an application developed in Java for optimizing the design of centralized solar water heating systems with forced circulation, based on the f-chart method. The program uses data from the Brazilian Solar Atlas, performance data of flat plate collectors and thermal reservoirs from the standardized tests run within the Brazilian Labeling Program, and values of water consumption of appliances defined by the ABNT. The program finds the inclination of the collector that maximizes the annual solar fraction, or for the winter, and enables the use of arrays in series and parallel collectors. From the investment costs and O & M (operations and maintenance) of solar heating systems, the program carries out economical analysis using classical parameters as net present value, discounted payback and internal rate of return. The program was validated through examples from the book of Duffle & Beckman and also by comparison with the results from a project developed at UFRGS, having obtained good agreement. 展开更多
关键词 Solar water heating f-chart method solar collectors.
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Finite element modeling of heating phenomena of cracks excited by high-intensity ultrasonic pulses 被引量:10
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作者 陈赵江 郑江 +2 位作者 张淑仪 米小兵 郑凯 《Chinese Physics B》 SCIE EI CAS CSCD 2010年第11期678-690,共13页
A three-dimensional thermo-mechanical coupled finite element model is built up to simulate the phenomena of dynamical contact and frictional heating of crack faces when the plate containing the crack is excited by hig... A three-dimensional thermo-mechanical coupled finite element model is built up to simulate the phenomena of dynamical contact and frictional heating of crack faces when the plate containing the crack is excited by high-intensity ultrasonic pulses. In the finite element model, the high-power ultrasonic transducer is modeled by using a piezoelectric thermal-analogy method, and the dynamical interaction between both crack faces is modeled using a contact-impact theory. In the simulations, the frictional heating taking place at the crack faces is quantitatively calculated by using finite element thermal-structural coupling analysis, especially, the influences of acoustic chaos to plate vibration and crack heating are calculated and analysed in detail. Meanwhile, the related ultrasonic infrared images are also obtained experimentally, and the theoretical simulation results are in agreement with that of the experiments. The results show that, by using the theoretical method, a good simulation of dynamic interaction and friction heating process of the crack faces under non-chaotic or chaotic sound excitation can be obtained. 展开更多
关键词 ultrasonic infrared imaging frictional heating of cracks acoustic chaos finite element method
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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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FEM Simulation of Large Diameter Pipe Bending Using Local Heating 被引量:5
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作者 LI Xue-tong WANG Min-ting DU Feng-shan XU Zhi-qiang 《Journal of Iron and Steel Research International》 SCIE EI CAS CSCD 2006年第5期25-29,共5页
With the aid of elastic plastic large deformation finite element method (FEM), an elastic plastic and cou pling thermo-mechanical model was built to calculate the bending process of the bent pipe, combining with loc... With the aid of elastic plastic large deformation finite element method (FEM), an elastic plastic and cou pling thermo-mechanical model was built to calculate the bending process of the bent pipe, combining with local heating or cooling of the bent pipe. Based on the FEM simulation, the metal deformation during the bending process was analyzed in detail. The thinning and thickening ratio of the pipe wall thickness, the ovality of the cross section of the pipe and the spring back angle, etc. , are presented. 展开更多
关键词 bent pipe finite element method local heating simulation
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Fast precise integration method for hyperbolic heat conduction problems 被引量:6
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作者 吴峰 高强 钟万勰 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2013年第7期791-800,共10页
A fast precise integration method is developed for the time integral of the hyperbolic heat conduction problem. The wave nature of heat transfer is used to analyze the structure of the matrix exponential, leading to t... A fast precise integration method is developed for the time integral of the hyperbolic heat conduction problem. The wave nature of heat transfer is used to analyze the structure of the matrix exponential, leading to the fact that the matrix exponential is sparse. The presented method employs the sparsity of the matrix exponential to improve the original precise integration method. The merits are that the proposed method is suitable for large hyperbolic heat equations and inherits the accuracy of the original version and the good computational efficiency, which are verified by two numerical examples. 展开更多
关键词 hyperbolic heat conduction sparse matrix precise integration method matrix exponential fast algorithm
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A Numerical Method on Inverse Determination of Heat Transfer Coefficient Based on Thermographic Temperature Measurement 被引量:6
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作者 范春利 孙丰瑞 杨立 《Chinese Journal of Chemical Engineering》 SCIE EI CAS CSCD 2008年第6期901-908,共8页
The heat transfer coefficient in a multidimensional heat conduction problem is obtained from the solution of the inverse heat conduction problem based on the thermographic temperature measurement. The modified one-dim... The heat transfer coefficient in a multidimensional heat conduction problem is obtained from the solution of the inverse heat conduction problem based on the thermographic temperature measurement. The modified one-dimensional correction method (MODCM), along with the finite volume method, is employed for both two- and three-dimensional inverse problems. A series of numerical experiments are conducted in order to verify the effectiveness of the method. In addition, the effect of the temperature measurement error, the ending criterion of the iteration, etc. on the result of the inverse problem is investigated. It is proved that the method is a simple, stable and accurate one that can solve successfully the inverse heat conduction problem. 展开更多
关键词 inverse heat conduction problem heat transfer coefficient finite volume method modified one-dimensional correction method measurement error
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A new complex variable meshless method for transient heat conduction problems 被引量:5
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作者 王健菲 程玉民 《Chinese Physics B》 SCIE EI CAS CSCD 2012年第12期42-50,共9页
In this paper, based on the improved complex variable moving least-square (ICVMLS) approximation, a new complex variable meshless method (CVMM) for two-dimensional (2D) transient heat conduction problems is pres... In this paper, based on the improved complex variable moving least-square (ICVMLS) approximation, a new complex variable meshless method (CVMM) for two-dimensional (2D) transient heat conduction problems is presented. The variational method is employed to obtain the discrete equations, and the essential boundary conditions are imposed by the penalty method. As the transient heat conduction problems are related to time, the Crank-Nicolson difference scheme for two-point boundary value problems is selected for the time discretization. Then the corresponding formulae of the CVMM for 2D heat conduction problems are obtained. In order to demonstrate the applicability of the proposed method, numerical examples are given to show the high convergence rate, good accuracy, and high efficiency of the CVMM presented in this paper. 展开更多
关键词 meshless method improved complex variable moving least-square approximation com-plex variable meshless method transient heat conduction problem
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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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