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Numerical modeling and parametric sensitivity analysis of heat transfer and two-phase oil and water flow characteristics in horizontal and inclined flowlines using OpenFOAM 被引量:1
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作者 Nsidibe Sunday Abdelhakim Settar +1 位作者 Khaled Chetehouna Nicolas Gascoin 《Petroleum Science》 SCIE EI CAS CSCD 2023年第2期1183-1199,共17页
Estimating the oil-water temperatures in flowlines is challenging especially in deepwater and ultra-deepwater offshore applications where issues of flow assurance and dramatic heat transfer are likely to occur due to ... Estimating the oil-water temperatures in flowlines is challenging especially in deepwater and ultra-deepwater offshore applications where issues of flow assurance and dramatic heat transfer are likely to occur due to the temperature difference between the fluids and the surroundings. Heat transfer analysis is very important for the prediction and prevention of deposits in oil and water flowlines, which could impede the flow and give rise to huge financial losses. Therefore, a 3D mathematical model of oil-water Newtonian flow under non-isothermal conditions is established to explore the complex mechanisms of the two-phase oil-water transportation and heat transfer in different flowline inclinations. In this work, a non-isothermal two-phase flow model is first modified and then implemented in the InterFoam solver by introducing the energy equation using OpenFOAM® code. The Low Reynolds Number (LRN) k-ε turbulence model is utilized to resolve the turbulence phenomena within the oil and water mixtures. The flow patterns and the local heat transfer coefficients (HTC) for two-phase oil-water flow at different flowlines inclinations (0°, +4°, +7°) are validated by the experimental literature results and the relative errors are also compared. Global sensitivity analysis is then conducted to determine the effect of the different parameters on the performance of the produced two-phase hydrocarbon systems for effective subsea fluid transportation. Thereafter, HTC and flow patterns for oil-water flows at downward inclinations of 4°, and 7° can be predicted by the models. The velocity distribution, pressure gradient, liquid holdup, and temperature variation at the flowline cross-sections are simulated and analyzed in detail. Consequently, the numerical model can be generally applied to compute the global properties of the fluid and other operating parameters that are beneficial in the management of two-phase oil-water transportation. 展开更多
关键词 Flow assurance Flow pattern heat transfer Flowlines Two-phase flow Global sensitivity analysis
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Analysis of influence of heat exchangerfouling on heat transfer performancebased on thermal fluid coupling
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作者 HUANG Si MURAD Tariq +2 位作者 NIU Qifeng LIN Guangtang CHEN Jianxun 《排灌机械工程学报》 CSCD 北大核心 2023年第7期695-700,共6页
A study on heat transfer performance by thermal fluid coupling simulation for the fouling in a shell-tube heat exchanger used in engineering was presented. The coupling simulation was performed in a fluid and solid do... A study on heat transfer performance by thermal fluid coupling simulation for the fouling in a shell-tube heat exchanger used in engineering was presented. The coupling simulation was performed in a fluid and solid domains under three different fouling conditions: fouling inside the tube, fouling outside the tube, and fouling inside the shell. The flow field, temperature, and pressure distributions in the heat exchanger were solved numerically to analyze the heat transfer performance parameters, such as thermal resistance. It is found that the pressure drop of the heat exchanger and the thermal resistance of the tube wall increase by nearly 30% and 20%, respectively, when the relative fouling thickness reaches 10%. The fouling inside the tube has more impact on the heat transfer performance of the heat exchanger, and the fouling inside the shell has less impact. 展开更多
关键词 shell-tube heat exchanger thermal fluid coupling fouling thermal resistance heat transfer analysis
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NUMERICAL ANALYSIS OF THREE-DIMENSIONAL FLUID FLOW AND HEAT TRANSFER IN TIG WELD POOL WITH FULL PENETRATION WU Chuansong,CAO Zhenning,WU Lin Harbin Institute of Technology,Harbin,China 被引量:4
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作者 WU Chuansong,CAO Zhenning,WU Lin Harbin Institute of Technology,Harbin,China 《Acta Metallurgica Sinica(English Letters)》 SCIE EI CAS CSCD 1993年第8期130-136,共7页
A model is established to analyze three-dimensional fluid flow and heat transfer in TICweld pools with full penetration.It considers the deformation of the molten pool surfaceat the condition of full penetrated workpi... A model is established to analyze three-dimensional fluid flow and heat transfer in TICweld pools with full penetration.It considers the deformation of the molten pool surfaceat the condition of full penetrated workpieees,takes the are pressure as the drivingforce of the pool surface deformation,and determines the surface configuration of weldpool based on the dynamic balance of arc pressure,pool gravity and surface tension atdeformed weld pool surface. The SIMPLER algorithm is used to calculate the fluid flowfield and temperature distribution in TIG weld pools of stainless steel workpieces.TIGwelding experiments are made to verify the validity of the model.It shows the calculatedresults by the model are in good agreement with experimental measurements. professor,Dept of Welding Engineering,Harbin Institute of Technology,Harbin 150006,China 展开更多
关键词 TIG weld pool full penetration fluid flow heat transfer numerical analysis
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Flow of a Jeffery-Six Constant Fluid Between Coaxial Cylinders with Heat Transfer Analysis 被引量:1
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作者 Muhammad Yousaf Malik Azad Hussain Sohail Nadeem 《Communications in Theoretical Physics》 SCIE CAS CSCD 2011年第8期345-351,共7页
In the present investigation we have discussed the flow of a Jeffrey-six constant incompressible fluid betweentwo infinite coaxial cylinders in the presence of heat transfer analysis.The governing equations of Jeffrey... In the present investigation we have discussed the flow of a Jeffrey-six constant incompressible fluid betweentwo infinite coaxial cylinders in the presence of heat transfer analysis.The governing equations of Jeffrey-six constant fluidalong with energy equation have been derived in cylindrical coordinates.The highly nonlinear equations are simplifiedwith the help of non-dimensional parameters and then solved analytically with the help of homotopy analysis method(HAM) for two fundamental flows namely Couette and Generalized Couette Bow.The effects of emerging parametersare discussed through graphs.The convergence of the HAM solution has been discussed by plotting h-curves. 展开更多
关键词 不可压缩流体 传热分析 COUETTE流动 恒定 同轴 圆柱坐标系 无量纲参数 非线性方程
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Lie group analysis for thermophoretic and radiative augmentation of heat and mass transfer in a Brinkman-Darcy flow over a flat surface with heat generation
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作者 Faiza A.Salama 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2011年第4期531-540,共10页
A boundary layer analysis is presented to investigate numerically the effects of radiation, thermophoresis and the dimensionless heat generation or absorption on hydromagnetic flow with heat and mass transfer over a f... A boundary layer analysis is presented to investigate numerically the effects of radiation, thermophoresis and the dimensionless heat generation or absorption on hydromagnetic flow with heat and mass transfer over a flat surface in a porous medium. The boundary layer equations are transformed to non-linear ordinary differential equations using scaling group of transformations and they are solved numerically by using the fourth order Runge-Kutta method with shooting technique for some values of physical parameters. Comparisons with previously published work are performed and the results are found to be in very good agreement. Many results are obtained and a representative set is displayed graphically to illustrate the influence of the various parameters on the dimensionless velocity, temperature and concentration profiles as well as the local skin-friction coefficient, wall heat transfer, particle deposition rate and wall thermophoretic deposition velocity. The results show that the magnetic field induces acceleration of the flow, rather than deceleration (as in classical magnetohydrodynamics (MHD) boundary layer flow) but to reduce temperature and increase concentration of particles in boundary layer. Also, there is a strong dependency of the concentration in the boundary layer on both the Schmidt number and mass transfer parameter. 展开更多
关键词 Lie group analysis Brinkman-Darcy flowBoundary layer heat and mass transfer
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Comprehensive Molten Salt Storage Shell and Supporting Structure Design and Analysis-Part I:A Conductive and Convective Theoretical Heat Transfer Analysis for Molten Salt Cylindrical Shells at 565℃ and 700℃
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作者 Nathan Loyd Samaan Ladkany William Culbreth 《Journal of Energy and Power Engineering》 2022年第2期33-51,共19页
In this paper a full theoretical thermal analysis of a large molten salt container,80-foot in diameter and 46-foot high,including a four-foot elliptic shell roof,is presented for two temperatures,the standard 565℃ an... In this paper a full theoretical thermal analysis of a large molten salt container,80-foot in diameter and 46-foot high,including a four-foot elliptic shell roof,is presented for two temperatures,the standard 565℃ and a futuristic 700℃,which substantially improves the efficiency of the molten salt containers through the use of a highly stable chloride salt called SS700(SaltStream 700).The theoretical analysis includes conductive and convective heat transfer analysis in the steel container,elliptic roof shell,the fiberglass insulation,and firebrick insulation,and includes thermal insulation designs to safeguard against energy losses at high temperatures.The underlying soil and the high temperature concrete foundation were analyzed theoretically using conductive heat transfer,however the area surrounding the soil surface around the bottom of the molten salt storage tank had convective heat transfer analysis included.The final designs presented in this paper seek to limit heat losses to a maximum of 250 W/m^(2) while being able to operate at a minimum external ambient temperature of-10℃,which determines the thicknesses of the fiberglass and firebrick insulation. 展开更多
关键词 Molten salts storage tank design solar energy CONDUCTIVE CONVECTIVE heat transfer INSULATION theoretical analysis.
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A Turbine Blade Parametric Modeling Method Considering 1-D Heat Transfer Analysis
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作者 LI Ji-xing XI Ping +1 位作者 GUO Yan-fei ZHANG Jian-qi 《Computer Aided Drafting,Design and Manufacturing》 2015年第3期1-9,共9页
Traditional feature-based turbine blade models can match the needs of geometric modeling but could hardly meet the requirement of data extraction in 1-D heat transfer analysis. In this paper, the requirements of data ... Traditional feature-based turbine blade models can match the needs of geometric modeling but could hardly meet the requirement of data extraction in 1-D heat transfer analysis. In this paper, the requirements of data extraction in 1-D heat transfer analysis are taken into consideration as well as geometric representation in parametric design process. An improved turbine blade parametric modeling method is proposed. Based on the modeling method proposed, a system structure of blade modeling process considering 1-D heat transfer analysis is devised. Eventually, a turbine blade parametric modeling system is constructed to test and verify the feasibility of the proposed modeling method and system structure. Experiments show that the blade parametric modeling method proposed can make geometric models better adapt to the specific requirements of 1-D heat transfer analysis and has certain reference value to the creation of high quality digital models. 展开更多
关键词 turbine blade parametric modeling 1-D heat transfer analysis data extraction
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Analysis of Film-Boiling Heat Transfer on a High Temperature Sphere Immersed into Liquid Sodium
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作者 Alix Le Belguet Georges Berthoud Magali Zabiego 《Journal of Energy and Power Engineering》 2014年第4期628-635,共8页
关键词 液态钠 膜沸腾 传热分析 浸入 过冷液体 实验数据 高温 沸腾传热
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Heat transfer analysis of Williamson fluid over exponentially stretching surface 被引量:2
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作者 S.NADEEM S.T.HUSSAIN 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2014年第4期489-502,共14页
This study explores the effects of heat transfer on the Williamson fluid over a porous exponentially stretching surface. The boundary layer equations of the Williamson fluid model for two dimensional flow with heat tr... This study explores the effects of heat transfer on the Williamson fluid over a porous exponentially stretching surface. The boundary layer equations of the Williamson fluid model for two dimensional flow with heat transfer are presented. Two cases of heat transfer are considered, i.e., the prescribed exponential order surface temperature (PEST) case and the prescribed exponential order heat flux (PEHF) case. The highly nonlinear partial differential equations are simplified with suitable similar and non-similar variables, and finally are solved analytically with the help of the optimal homotopy analysis method (OHAM). The optimal convergence control parameters are obtained, and the physical fea- tures of the flow parameters are analyzed through graphs and tables. The skin friction and wall temperature gradient are calculated. 展开更多
关键词 optimal homotopy analysis method (OHAM) Williamson fluid expo-nential stretching permeable wall heat transfer prescribed exponential order surfacetemperature (PEST) prescribed exponential order heat flux (PEHF)
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Techno-economic analysis of single U-tube and double U-tube heat exchangers in Chongqing area 被引量:1
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作者 王勇 郭凯生 +3 位作者 田荣 韩传璞 赖道新 徐峰 《Journal of Central South University》 SCIE EI CAS 2009年第S1期244-248,共5页
On the basis of practical projects in Chongqing,the thermal performance of heat exchangers (single U-tube type and double U-tube type) of the ground-source heat pump (GSHP) system in the hot summer was obtained and an... On the basis of practical projects in Chongqing,the thermal performance of heat exchangers (single U-tube type and double U-tube type) of the ground-source heat pump (GSHP) system in the hot summer was obtained and analyzed. The data obtained from test could match with the result deduced from theoretical calculation. From the test results,the cooling capacity of double U-tube is 1.6 times that of single U-tube. Taking cost per depth per watt Clq as the evaluation standard,Clq of single U-tube is 4.69 RMB$/W,and Clq of double U-tube is 3.14 RMB$/W. The double U-tube heat exchangers usage should be prioritized. 展开更多
关键词 ground-source heat pump heat transfer performance SINGLE U-TUBE DOUBLE U-TUBE TECHNO-ECONOMIC analysis
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Conjugate Heat Transfer Analysis of an Ultrasonic Molten Metal Treatment System 被引量:1
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作者 ZHU Youli BIAN Feilong +1 位作者 WANG Yanli ZHAO Qian 《Chinese Journal of Mechanical Engineering》 SCIE EI CAS CSCD 2014年第5期986-991,共6页
In piezoceramic ultrasonic devices,the piezoceramic stacks may fail permanently or function improperly if their working temperatures overstep the Curie temperature of the piezoceramic material.While the end of the hor... In piezoceramic ultrasonic devices,the piezoceramic stacks may fail permanently or function improperly if their working temperatures overstep the Curie temperature of the piezoceramic material.While the end of the horn usually serves near the melting point of the molten metal and is enclosed in an airtight chamber,so that it is difficult to experimentally measure the temperature of the transducer and its variation with time,which bring heavy difficulty to the design of the ultrasonic molten metal treatment system.To find a way out,conjugate heat transfer analysis of an ultrasonic molten metal treatment system is performed with coupled fluid and heat transfer finite element method.In modeling of the system,the RNG model and the SIMPLE algorithm are adopted for turbulence and nonlinear coupling between the momentum equation and the energy equation.Forced air cooling as well as natural air cooling is analyzed to compare the difference of temperature evolution.Numerical results show that,after about 350 s of working time,temperatures in the surface of the ceramic stacks in forced air cooling drop about 7 K compared with that in natural cooling.At 240 s,The molten metal surface emits heat radiation with a maximum rate of about 19 036 W/m2,while the heat insulation disc absorbs heat radiation at a maximum rate of about 7922 W/m2,which indicates the effectiveness of heat insulation of the asbestos pad.Transient heat transfer film coefficient and its distribution,which are difficult to be measured experimentally are also obtained through numerical simulation.At 240 s,the heat transfer film coefficient in the surface of the transducer ranges from–17.86 to 20.17 W/(m2?K).Compared with the trial and error method based on the test,the proposed research provides a more effective way in the design and analysis of the temperature control of the molten metal treatment system. 展开更多
关键词 conjugate heat transfer finite element analysis ultrasonic molten metal treatment computational fluid dynamics
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Analysis of Heat Transfer Performance of Oscillating Heat Pipes Based on a Central Composite Design 被引量:12
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作者 马永锡 张红 《Chinese Journal of Chemical Engineering》 SCIE EI CAS CSCD 2006年第2期223-228,共6页
Oscillating heat pipes (OHPs) are very promising cooling devices. Their heat transfer performance is af- fected by many factors, and the form of the relationship between the performance and the factors is complex and ... Oscillating heat pipes (OHPs) are very promising cooling devices. Their heat transfer performance is af- fected by many factors, and the form of the relationship between the performance and the factors is complex and non-linear. In this paper, the effects of charging ratio, inclination angle, and heat input and their interaction effects on heat transfer performance of a looped copper-water OHP are analyzed. First, suppose that the relationship between the response and the variables approximates a second-order model. And use the central composite design to arrange the ex- periment. Then, the method of least squares is used to estimate the parameters in the second-order model. Finally, multi- variate variance analysis is used to analyze the model. The results show that the assumption is right, that is to say, the re- lationship is well modeled by a second-order function. Among the three main effect variables, the effect of inclination angle is the most significant, but their interaction effects are not significant. In the range of the considered factors, both the optimum charging ratio and the optimum inclination angle increase as the heating water flow rate increases. 展开更多
关键词 基于中心复合设计 振荡热管 传热 性能 方差分析
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Function chain neural network prediction on heat transfer performance of oscillating heat pipe based on grey relational analysis 被引量:11
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作者 鄂加强 李玉强 龚金科 《Journal of Central South University》 SCIE EI CAS 2011年第5期1733-1737,共5页
As for the factors affecting the heat transfer performance of complex and nonlinear oscillating heat pipe (OHP),grey relational analysis (GRA) was used to deal with the relationship between heat transfer rate of a loo... As for the factors affecting the heat transfer performance of complex and nonlinear oscillating heat pipe (OHP),grey relational analysis (GRA) was used to deal with the relationship between heat transfer rate of a looped copper-water OHP and charging ratio,inner diameter,inclination angel,heat input,number of turns,and the main influencing factors were defined.Then,forecasting model was obtained by using main influencing factors (such as charging ratio,interior diameter,and inclination angel) as the inputs of function chain neural network.The results show that the relative average error between the predicted and actual value is 4%,which illustrates that the function chain neural network can be applied to predict the performance of OHP accurately. 展开更多
关键词 函数链神经网络 灰色关联分析 神经网络预测 传输性能 振荡热管 影响因素 平均相对误差 传热性能
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Numerical analysis of factors affecting the range of heat transfer in earth surrounding three subways 被引量:13
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作者 HU Zeng-hui LI Xiao-zhao ZHAO Xiao-bao XIAO Lin WU Wei 《Journal of China University of Mining and Technology》 EI 2008年第1期67-71,共5页
In order to examine the factors which affect the range of heat transfer in earth surrounding subways, FLAC3D was adopted in this study to analyze these factors, under different conditions, in a systematic manner. When... In order to examine the factors which affect the range of heat transfer in earth surrounding subways, FLAC3D was adopted in this study to analyze these factors, under different conditions, in a systematic manner. When we compare these numerical tests, the results show that the main factors, affecting the heat transfer range are the thermal properties of the surrounding earth, the initial ground temperature and the temperature in the tunnel. The heat transfer coefficient between air and linings has little effect on the temperature distribution around the tunnel. The current results can provide a reference for improving the thermal environment in subways and optimizing the design of subway ventilation and air conditioning. 展开更多
关键词 数字分析技术 热传递 土壤 隧道 通风系统
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Analysis of Unsteady Heat Transfer Problems with Complex Geometries Using Isogeometric Boundary Element Method 被引量:1
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作者 Weihua Fang Zhilin An +1 位作者 Tiantang Yu Tinh Quoc Bui 《Computers, Materials & Continua》 SCIE EI 2020年第2期929-962,共34页
Numerical analysis of unsteady heat transfer problems with complex geometries by the isogeometric boundary element method(IGABEM)is presented.The IGABEM possesses many desirable merits and features,for instance,(a)exa... Numerical analysis of unsteady heat transfer problems with complex geometries by the isogeometric boundary element method(IGABEM)is presented.The IGABEM possesses many desirable merits and features,for instance,(a)exactly represented arbitrarily complex geometries,and higher-order continuity due to non-uniform rational B-splines(NURBS)shape functions;(b)using NURBS for both field approximation and geometric description;(c)directly utilizing geometry data from computer-aided design(CAD);and(d)only boundary discretization.The formulation of IGABEM for unsteady heat transfer is derived.The domain discretization in terms of IGABEM for unsteady heat transfer is required as that in traditional BEM.The internal values however are obtained with the analytical formula according to the values on the boundaries,and its computations are therefore mainly dependent on the discretization of the boundaries.The coordinates of internal control points are obtained with the coordinates of control points on the boundaries using Coons body interpolation method.The developed approach is tested with several numerical examples from simple to complicated geometries.Good agreement is gained with reference solutions derived from either analytical or finite element methods. 展开更多
关键词 Unsteady heat transfer BEM isogeometric analysis NURBS
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Thermal Analysis of Organic Light Emitting Diodes Based on Basic Heat Transfer Theory 被引量:1
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作者 张稳稳 吴朝新 +3 位作者 刘迎文 董军 严学文 侯洵 《Chinese Physics Letters》 SCIE CAS CSCD 2015年第8期139-143,共5页
We investigate the thermal characteristics of standard organic light-emitting diodes (OLEDs) using a simple and clear 1D thermal model based on the basic heat transfer theory. The thermal model can accurately estima... We investigate the thermal characteristics of standard organic light-emitting diodes (OLEDs) using a simple and clear 1D thermal model based on the basic heat transfer theory. The thermal model can accurately estimate the device temperature, which is linearly with electrical input power. The simulation results show that there is almost no temperature gradient within the OLED device working under steady state conditions. Furthermore, thermal analysis simulation results show that the surface properties (convective heat transfer coetficient and surface emissivity) of the substrate or cathode can significantly affect the temperature distribution of the OLED. 展开更多
关键词 OLEDS Thermal analysis of Organic Light Emitting Diodes Based on Basic heat transfer Theory EML
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AN ANALYSIS OF HEAT AND MASS TRANSFERPHENOMENON IN WOOD DURING DRYING
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作者 常建民 蔡力平 《Journal of Northeast Forestry University》 SCIE CAS CSCD 1996年第3期62-65,共4页
According to modeling simulation and experiments study, the heat and mass transtfer phenomenon.in wood during dring processes was analyzed. The results indicate: at initial stage of drying, moisture movement in wood i... According to modeling simulation and experiments study, the heat and mass transtfer phenomenon.in wood during dring processes was analyzed. The results indicate: at initial stage of drying, moisture movement in wood is due to capillary force, heat transfer is major effect, at end stage, moisture movement in wood is due to diffusive transport, heat transfer is less 展开更多
关键词 WOOD DRYING heat and MASS transfer analysis
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Consideration of transient heat conduction in a semi-infinite medium using homotopy analysis method
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作者 A. Rezania A. Ghorbali +1 位作者 G. Domairry H. Bararnia 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2008年第12期1625-1632,共8页
In the current work, transient heat conduction in a semi-infinite medium is considered for its many applications in various heat fields. Here, the homotopy analysis method (HAM) is applied to solve this problem and ... In the current work, transient heat conduction in a semi-infinite medium is considered for its many applications in various heat fields. Here, the homotopy analysis method (HAM) is applied to solve this problem and analytical results are compared with those of the exact and integral methods results. The results show that the HAM can give much better approximations than the other approximate methods: Changes in heat fluxes and profiles of temperature are obtained at different times and positions for copper, iron and aluminum. 展开更多
关键词 homotopy analysis method semi-infinite medium conduction transient heat transfer integral methods temperature profile
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Numerical analysis on solidification process and heat transfer of FGH95 superalloy droplets during PREP
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作者 HuanmingChen BenfuHu +2 位作者 YiwenZhang QuanmaoYu HuiyingLi 《Journal of University of Science and Technology Beijing》 CSCD 2003年第5期53-58,共6页
In order to understand the relation between microstructure of superalloypowders and its solidification progress, the processing parameters are optimized during plasmarotating electrode processing (PREP). It was predic... In order to understand the relation between microstructure of superalloypowders and its solidification progress, the processing parameters are optimized during plasmarotating electrode processing (PREP). It was predicted from the results that the droplet velocities,droplet temperature, and fractional solidification with flight time about FGH95 superalloy droplethave been carried out based on Newtonian heat transfer formulation coupled with the classicalheterogeneous nucleation and the specific solidification process. It has been found that the dropletdynamic and thermal behavior is strongly affected by the distribution of droplet diameters, theproportion of cooling atmosphere, but is relatively unaffected by the droplet superheat. 展开更多
关键词 plasma rotating electrode processing (PREP) heat transfer FGH95 superalloypowder numerical analysis
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The fast method and convergence analysis of the fractional magnetohydrodynamic coupled flow and heat transfer model for the generalized second-grade fluid
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作者 Xiaoqing Chi Hui Zhang Xiaoyun Jiang 《Science China Mathematics》 SCIE CSCD 2024年第4期919-950,共32页
In this paper,we first establish a new fractional magnetohydrodynamic(MHD)coupled flow and heat transfer model for a generalized second-grade fluid.This coupled model consists of a fractional momentum equation and a h... In this paper,we first establish a new fractional magnetohydrodynamic(MHD)coupled flow and heat transfer model for a generalized second-grade fluid.This coupled model consists of a fractional momentum equation and a heat conduction equation with a generalized form of Fourier law.The second-order fractional backward difference formula is applied to the temporal discretization and the Legendre spectral method is used for the spatial discretization.The fully discrete scheme is proved to be stable and convergent with an accuracy of O(τ^(2)+N-r),whereτis the time step-size and N is the polynomial degree.To reduce the memory requirements and computational cost,a fast method is developed,which is based on a globally uniform approximation of the trapezoidal rule for integrals on the real line.The strict convergence of the numerical scheme with this fast method is proved.We present the results of several numerical experiments to verify the effectiveness of the proposed method.Finally,we simulate the unsteady fractional MHD flow and heat transfer of the generalized second-grade fluid through a porous medium.The effects of the relevant parameters on the velocity and temperature are presented and analyzed in detail. 展开更多
关键词 fractional MHD coupled flow and heat transfer model generalized second-grade fuid fast method convergence analysis numerical simulation
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