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The Improved Element-Free Galerkin Method for Anisotropic Steady-State Heat Conduction Problems
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作者 Heng Cheng Zebin Xing Miaojuan Peng 《Computer Modeling in Engineering & Sciences》 SCIE EI 2022年第9期945-964,共20页
In this paper,we considered the improved element-free Galerkin(IEFG)method for solving 2D anisotropic steadystate heat conduction problems.The improved moving least-squares(IMLS)approximation is used to establish the ... In this paper,we considered the improved element-free Galerkin(IEFG)method for solving 2D anisotropic steadystate heat conduction problems.The improved moving least-squares(IMLS)approximation is used to establish the trial function,and the penalty method is applied to enforce the boundary conditions,thus the final discretized equations of the IEFG method for anisotropic steady-state heat conduction problems can be obtained by combining with the corresponding Galerkin weak form.The influences of node distribution,weight functions,scale parameters and penalty factors on the computational accuracy of the IEFG method are analyzed respectively,and these numerical solutions show that less computational resources are spent when using the IEFG method. 展开更多
关键词 Improved element-free Galerkin method penalty method weak form anisotropic steady-state heat conduction improved moving least-squares approximation
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Meshless analysis of three-dimensional steady-state heat conduction problems 被引量:3
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作者 程荣军 葛红霞 《Chinese Physics B》 SCIE EI CAS CSCD 2010年第9期36-41,共6页
Steady-state heat conduction problems arisen in connection with various physical and engineering problems where the functions satisfy a given partial differential equation and particular boundary conditions, have attr... Steady-state heat conduction problems arisen in connection with various physical and engineering problems where the functions satisfy a given partial differential equation and particular boundary conditions, have attracted much attention and research recently. These problems are independent of time and involve only space coordinates, as in Poisson's equation or the Laplace equation with Dirichlet, Neuman, or mixed conditions. When the problems are too complex, it is difficult to find an analytical solution, the only choice left is an approximate numerical solution. This paper deals with the numerical solution of three-dimensional steady-state heat conduction problems using the meshless reproducing kernel particle method (RKPM). A variational method is used to obtain the discrete equations. The essential boundary conditions are enforced by the penalty method. The effectiveness of RKPM for three-dimensional steady-state heat conduction problems is investigated by two numerical examples. 展开更多
关键词 reproducing kernel particle method meshless method steady-state heat conduction problem
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Differential Quadrature Method for Steady Flow of an Incompressible Second-Order Viscoelastic Fluid and Heat Transfer Model 被引量:1
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作者 A.S.J.AL-SAIF 朱正佑 《Journal of Shanghai University(English Edition)》 CAS 2005年第4期298-305,共8页
The two-dimensional steady flow of an incompressible second-order viscoelastic fluid between two parallel plates was studied in terms of vorticity, the stream function and temperature equations. The governing equation... The two-dimensional steady flow of an incompressible second-order viscoelastic fluid between two parallel plates was studied in terms of vorticity, the stream function and temperature equations. The governing equations were expanded with respect to a snmll parameter to get the zeroth- and first-order approximate equations. By using the differenl2al quadrature method with only a few grid points, the high-accurate numerical results were obtained. 展开更多
关键词 differential quadrature method(DQM) second-order viscoelastic fluid steady flow heat transfer.
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Interval finite difference method for steady-state temperature field prediction with interval parameters 被引量:5
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作者 Chong Wang Zhi-Ping Qiu 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2014年第2期161-166,共6页
A new numerical technique named interval finite difference method is proposed for the steady-state temperature field prediction with uncertainties in both physical parameters and boundary conditions. Interval variable... A new numerical technique named interval finite difference method is proposed for the steady-state temperature field prediction with uncertainties in both physical parameters and boundary conditions. Interval variables are used to quantitatively describe the uncertain parameters with limited information. Based on different Taylor and Neumann series, two kinds of parameter perturbation methods are presented to approximately yield the ranges of the uncertain temperature field. By comparing the results with traditional Monte Carlo simulation, a numerical example is given to demonstrate the feasibility and effectiveness of the proposed method for solving steady-state heat conduction problem with uncertain-but-bounded parameters. 展开更多
关键词 steady-state heat conduction Interval finite dif-ference Temperature field prediction Parameter perturba-tion method Interval uncertainties
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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 被引量:1
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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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Accurate solutions for viscoelastic boundary layer flow and heat transfer over stretching sheet 被引量:3
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作者 A.MASTROBERARDINO 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2014年第2期133-142,共10页
In this article, we present accurate analytical solutions for boundary layer flow and heat transfer of an incompressible and electrically conducting viscoelastic fluid over a linearly stretching surface subject to a t... In this article, we present accurate analytical solutions for boundary layer flow and heat transfer of an incompressible and electrically conducting viscoelastic fluid over a linearly stretching surface subject to a transverse uniform magnetic field using the homotopy analysis method (HAM) for two general types of non-isothermal boundary conditions. In addition, we demonstrate that the previously reported analytical solutions for the temperature field given in terms of Kummer's function do not converge at the boundary. We provide a graphical and numerical demonstration of the convergence of the HAM solutions and tabulate the effects of various parameters on the skin friction coefficient and wall heat transfer. 展开更多
关键词 viscoelastic fluid nonuniform heat source/sink stretching sheet magneto-hydrodynamic (MHD) flow homotopy analysis method (HAM)
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Second-order slip MHD flow and heat transfer of nanofluids with thermal radiation and chemical reaction 被引量:2
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作者 Jing ZHU Liu ZHENG +1 位作者 Liancun ZHENG Xinxin ZHANG 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2015年第9期1131-1146,共16页
The effects of the second-order velocity slip and temperature jump boundary conditions on the magnetohydrodynamic (MHD) flow and heat transfer in the presence of nanoparticle fractions are investigated. In the model... The effects of the second-order velocity slip and temperature jump boundary conditions on the magnetohydrodynamic (MHD) flow and heat transfer in the presence of nanoparticle fractions are investigated. In the modeling of the water-based nanofluids containing Cu and A1203, the effects of the Brownian motion, thermophoresis, and thermal radiation are considered. The governing boundary layer equations are transformed into a system of nonlinear differential equations, and the analytical approximations of the solutions axe derived by the homotopy analysis method (HAM). The reliability and efficiency of the HAM solutions are verified by the residual errors and the numerical results in the literature. Moreover, the effects of the physical factors on the flow and heat transfer are discussed graphically. 展开更多
关键词 NANOFLUID velocity slip temperature jump homotopy analysis method(HAM) heat and mass transfer magnetohydrodynamic (MHD) flow
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Series solutions of annular axisymmetric stagnation flow and heat transfer on moving cylinder 被引量:1
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作者 A.MASTROBERARDINO 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2013年第9期1043-1054,共12页
The steady, laminar, incompressible flow and heat transfer of a viscous fluid between two circular cylinders for two different types of thermal boundary conditions are investigated. The governing Navier-Stokes and the... The steady, laminar, incompressible flow and heat transfer of a viscous fluid between two circular cylinders for two different types of thermal boundary conditions are investigated. The governing Navier-Stokes and thermal equations of the flow are reduced to a nonlinear system of ordinary differential equations. The equations are solved analyt- ically using the homotopy analysis method (HAM). Convergence of the HAM solutions is discussed in detail. These solutions are then compared with recently obtained numericM and perturbative solutions. Plots of the velocity and temperature profiles are provided for various values of the relevant parameters. 展开更多
关键词 stagnation flow heat transfer moving cylinder boundary value problem homotopy analysis method (HAM)
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Delaware Method Improvement for the Shell and Tubes Heat Exchanger Design 被引量:1
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作者 Miguel Toledo-Velázquez Pedro Quinto-Diez +3 位作者 Juan C. Alzelmetti-Zaragoza Sergio R. Galvan Juan Abugaber-Francis Arturo Reyes-León 《Engineering(科研)》 2014年第4期193-201,共9页
In this paper the Delaware Method published in 1963 is analyzed and upgraded with using correction factors which take into account the undesirable currents of the mean flow. However, this method presents graphically t... In this paper the Delaware Method published in 1963 is analyzed and upgraded with using correction factors which take into account the undesirable currents of the mean flow. However, this method presents graphically these correction factors which imply an impediment to fulfill the software calculations. Thus, the equations corresponding to the correction factor equations and a Fortran 77 numerical program were established. This system is given to explore different design alternatives in order to find the optimal solution to each proposed problem. The results of this work was a simple software that can perform calculations with the introduction of parameters depending only on the geometry of the heat exchanger, i.e., geometry, temperature and fluid characteristics eliminating the human errors and increasing the calculations speed and accuracy. 展开更多
关键词 DELAWARE method flow CORRECTION FACTOR heat EXCHANGER
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Numerical Simulation and Control of Two-Phase Flow with Evaporation in a Vertical Tube Submitted to a Conjugate Heat Transfer 被引量:2
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作者 Ghazali Mebarki Samir Rahal 《Journal of Energy and Power Engineering》 2013年第7期1282-1292,共11页
A better understanding of two-phase flows with evaporation allows leading to an optimal design of evaporators. For that purpose, numerical simulations are very useful. In this paper, a numerical study has been carried... A better understanding of two-phase flows with evaporation allows leading to an optimal design of evaporators. For that purpose, numerical simulations are very useful. In this paper, a numerical study has been carried out in order to model and simulate the combination of a two-phase flow with evaporation in a vertical tube. The VOF (volume-of-fluid) multiphase flow method and a phase-change model for the mass transfer have been used. For an accurate modeling, the effect of axial conduction has been also taken into account using a conjugate heat transfer model. Since thermal oscillations are undesirable as they can lead to the failure of the tube, flow instabilities have also been analyzed, using FFT (fast Fourier transforms), in order to comprehend their behavior and influence. A control study of the flow instabilities in the tube is also presented. For that purpose tube inlet temperature has been varied using a gain control parameter. 展开更多
关键词 Two-phase flow EVAPORATION VOF method conjugate heat transfer flow instabilities control of instabilities.
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Flow and heat transfer over hyperbolic stretching sheets
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作者 A. AHMAD S. ASGHAR 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2012年第4期445-454,共10页
The boundary layer flow and heat transfer analysis of an incompressible viscous fluid for a hyperbolically stretching sheet is presented. The analytical and numer- ical results are obtained by a series expansion metho... The boundary layer flow and heat transfer analysis of an incompressible viscous fluid for a hyperbolically stretching sheet is presented. The analytical and numer- ical results are obtained by a series expansion method and a local non-similarity (LNS) method, respectively. The analytical and numerical results for the skin friction and the Nusselt number are calculated and compared with each other. The significant observation is that the momentum and the thermal boundary layer thickness decrease as the distance from the leading edge increases. The well-known solution of linear stretching is found as the leading order solution for the hyperbolic stretching. 展开更多
关键词 hyperbolic stretching sheet boundary layer flow heat transfer seriesexpansion method local non-similarity method
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Prediction of hypersonic boundary layer transition on sharp wedge flow considering variable specific heat
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作者 毛旭 曹伟 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2014年第2期143-154,共12页
When the air temperature reaches 600 K or higher, vibration is excited. The specific heat is not a constant but a function of temperature. Under this condition, the transition position of hypersonic sharp wedge bounda... When the air temperature reaches 600 K or higher, vibration is excited. The specific heat is not a constant but a function of temperature. Under this condition, the transition position of hypersonic sharp wedge boundary layer is predicted by using the improved eN method considering variable specific heat. The transition positions with different Mach numbers of oncoming flow, half wedge angles, and wall conditions are computed condition, the nearer to the Mach number The results show that for the same oncoming flow condition and wall transition positions of hypersonic sharp wedge boundary layer move much leading edge than those of the flat plate. The greater the oncoming flow the closer the transition position to the leading edge. 展开更多
关键词 hypersonic flow wedge boundary layer variable specific heat transitionprediction improved eN method
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Numerical simulation of boundary heat flow effects on directional solidification microstructure of a binary alloy
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作者 Xue Xiang Tang Jinjun 《China Foundry》 SCIE CAS 2010年第3期253-258,共6页
The boundary heat flow has important significance for the microstructures of directional solidified binary alloy.Interface evolution of the directional solidified microstructure with different boundary heat flow was d... The boundary heat flow has important significance for the microstructures of directional solidified binary alloy.Interface evolution of the directional solidified microstructure with different boundary heat flow was discussed.In this study, only one interface was allowed to have heat flow, and Neumann boundary conditions were imposed at the other three interfaces.From the calculated results, it was found that different boundary heat flows will result in different microstructures.When the boundary heat flow equals to 20 W·cm-2, the growth of longitudinal side branches is accelerated and the growth of transverse side branches is restrained, and meanwhile, there is dendritic remelting in the calculation domain.When the boundary heat flow equals to 40 W·cm-2, the growths of the transverse and longitudinal side branches compete with each other, and when the boundary heat flow equals to 100-200 W·cm-2, the growth of transverse side branches dominates absolutely.The temperature field of dendritic growth was analyzed and the relation between boundary heat flow and temperature field was also investigated. 展开更多
关键词 numerical simulation directional solidification phase field method boundary heat flow
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Numerical Study for Magnetohydrodynamic(MHD)Unsteady Maxwell Nanofluid Flow Impinging on Heated Stretching Sheet
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作者 Muhammad Shoaib Arif Muhammad Jhangir +3 位作者 Yasir Nawaz Imran Abbas Kamaleldin Abodayeh Asad Ejaz 《Computer Modeling in Engineering & Sciences》 SCIE EI 2022年第11期303-325,共23页
The numerous applications of Maxwell Nanofluid Stagnation Point Flow,such as those in production industries,the processing of polymers,compression,power generation,lubrication systems,food manufacturing and air condit... The numerous applications of Maxwell Nanofluid Stagnation Point Flow,such as those in production industries,the processing of polymers,compression,power generation,lubrication systems,food manufacturing and air conditioning,among other applications,require further research into the effects of various parameters on flow phenomena.In this paper,a study has been carried out for the heat andmass transfer of Maxwell nanofluid flow over the heated stretching sheet.A mathematical model with constitutive expressions is constructed in partial differential equations(PDEs)through obligatory basic conservation laws.A series of transformations are then used to take the system into an ordinary differential equation(ODE).The boundary conditions(BCs)are also treated similarly for transforming into first-order ordinary differential equations(ODEs).Then these ODEs are computed by using the Shooting Method.The effect of factors on the skin friction coefficient,the local Nusselt number,and the local Sherwood number are explored,and the results are displayed graphically.The obtained results demonstrate that by increasing the values of the Maxwell and slip velocity parameters,velocity deescalates.For investigators tasked with addressing unresolved difficulties in the realm of enclosures used in industry and engineering,we thought this work would serve as a guide. 展开更多
关键词 Maxwell fluid stagnation point flow heat and mass transfer thermal radiations shooting method
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Algebraic Calculation Method of One-Dimensional Steady Compressible Gas Flow
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作者 Andrey Tolmachev 《Open Journal of Fluid Dynamics》 2017年第1期83-88,共6页
This paper describes a new method of calculation of one-dimensional steady compressible gas flows in channels with possible heat and mass exchange through perforated sidewalls. The channel is divided into small elemen... This paper describes a new method of calculation of one-dimensional steady compressible gas flows in channels with possible heat and mass exchange through perforated sidewalls. The channel is divided into small elements of a finite size for which mass, energy and momentum conservation laws are written in the integral form, assuming linear distribution of the parameters along the length. As a result, the calculation is reduced to finding the roots of a quadratic algebraic equation, thus providing an alternative to numerical methods based on differential equations. The advantage of this method is its high tolerance to coarse discretization of the calculation area as well as its good applicability for transonic flow calculations. 展开更多
关键词 method of Calculation STEADY COMPRESSIBLE flow Channel with Perforated Sidewalls heat and Mass EXCHANGE FINITE Size Elements ONE-DIMENSIONAL Approach
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Radiative Heat Transfer and Thermocapillary Effects on the Structure of the Flow during Czochralski Growth of Oxide Crystals
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作者 Reza Faiez Yazdan Rezaei 《Advances in Chemical Engineering and Science》 2015年第3期389-407,共19页
A numerical study was carried out to describe the flow field structure of an oxide melt under 1) the effect of internal radiation through the melt (and the crystal), and 2) the impact of surface tension-driven forces ... A numerical study was carried out to describe the flow field structure of an oxide melt under 1) the effect of internal radiation through the melt (and the crystal), and 2) the impact of surface tension-driven forces during Czochralski growth process. Throughout the present Finite Volume Method calculations, the melt is a Boussinnesq fluid of Prandtl number 4.69 and the flow is assumed to be in a steady, axisymmetric state. Particular attention is paid to an undulating structure of buoyancy-driven flow that appears in optically thick oxide melts and persists over against forced convection flow caused by the externally imposed rotation of the crystal. In a such wavy pattern of the flow, particularly for a relatively higher Rayleigh number , a small secondary vortex appears nearby the crucible bottom. The structure of the vortex which has been observed experimentally is studied in some details. The present model analysis discloses that, though both of the mechanisms 1) and 2) end up in smearing out the undulating structure of the flow, the effect of thermocapillary forces on the flow pattern is distinguishably different. It is shown that for a given dynamic Bond number, the behavior of the melt is largely modified. The transition corresponds to a jump discontinuity in the magnitude of the flow stream function. 展开更多
关键词 Numerical Simulation Fluid flow RADIATIVE heat Transfer THERMOCAPILLARY Forces CZOCHRALSKI method OXIDES
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Numerical Solution of MHD Flow of Micropolar Fluid with Heat and Mass Transfer towards a Stagnation Point on a Vertical Plate
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作者 N. T. El-Dabe A. Y. Ghaly +2 位作者 R. R. Rizkallah K. M. Ewis A. S. Al-Bareda 《American Journal of Computational Mathematics》 2015年第2期158-174,共17页
The paper investigates the numerical solution of problem of magnetohydrodynamic (MHD) micropolar fluid flow with heat and mass transfer towards a stagnation point on a vertical plate. In this study, we consider both s... The paper investigates the numerical solution of problem of magnetohydrodynamic (MHD) micropolar fluid flow with heat and mass transfer towards a stagnation point on a vertical plate. In this study, we consider both strong concentrations (n = 0) and weak concentrations (n = 1/2). The governing equations have been transformed into nonlinear ordinary differential equations by applying the similarity transformation and have been solved numerically by using the finite difference method (FDM) and analytically by using (DTM). The effects of various governing parameters, namely, material parameter, radiation parameter, magnetic parameter, Prandtl number, Schmidt number, chemical reaction parameter and Soret number on the velocity, microrotation, temperature and concentration have been computed and discussed in detail through some figures and tables. In order to verify the accuracy of the present results, we have compared these results with the analytical solutions by using the differential transform method (DTM) and the multi-step differential transform method (MDTM). It is observed that this approximate numerical solution is in good agreement with the analytical solution. 展开更多
关键词 Finite Difference method (FDM) Differential Transform method (DTM) MICROPOLAR Fluid MHD heat and Mass Transfer STAGNATION flow Chemical Reaction Radiation
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Magneto Hydrodynamics Stagnation Point Flow of a Nano Fluid over an Exponentially Stretching Sheet with an Effect of Chemical Reaction, Heat Source and Suction/Injunction
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作者 Ch. Achi Reddy B. Shankar 《World Journal of Mechanics》 2015年第11期211-221,共11页
A numerical investigation is carried out on the effects of heat source suction and viscous dissipation on Magneto hydrodynamics boundary layer flow of a viscous, steady and incompressible fluid. The flow is assumed to... A numerical investigation is carried out on the effects of heat source suction and viscous dissipation on Magneto hydrodynamics boundary layer flow of a viscous, steady and incompressible fluid. The flow is assumed to be over on exponentially stretching sheet. The governing system of partial differential equations has been transformed into ordinary differential equation using similarity transformation. Keller box method is simulated on the dimensionless system of differential equations. The skin friction coefficient and the heat and mass transfer rates are very significant parameters that are computed, analysed discussed in detail. 展开更多
关键词 Boundary Layer flow EXPONENTIALLY STRETCHING Sheet Keller Box method heat Source SUCTION Chemical Reaction and Viscous Dissipation
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Modal and Thermal Analysis of a Modified Connecting Rod of an Internal Combustion Engine Using Finite Element Method
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作者 Nkrumah Jacob Kwaku Baba Ziblim +1 位作者 Sulemana Yahaya Sherry Kwabla Amedorme 《Modeling and Numerical Simulation of Material Science》 2023年第3期29-49,共21页
The connecting rod is one of the most important moving components in an internal combustion engine. The present work determined the possibility of using aluminium alloy 7075 material to design and manufacture a connec... The connecting rod is one of the most important moving components in an internal combustion engine. The present work determined the possibility of using aluminium alloy 7075 material to design and manufacture a connecting rod for weight optimisation without losing the strength of the connecting rod. It considered modal and thermal analyses to investigate the suitability of the material for connecting rod design. The parameters that were considered under the modal analysis were: total deformation, and natural frequency, while the thermal analysis looked at the temperature distribution, total heat flux and directional heat flux of the four connecting rods made with titanium alloy, grey cast iron, structural steel and aluminium 7075 alloy respectively. The connecting rod was modelled using Autodesk inventor2017 software using the calculated parameters. The steady-state thermal analysis was used to determine the induced heat flux and directional heat flux. The study found that Aluminium 7075 alloy deformed more than the remaining three other materials but has superior qualities in terms of vibrational natural frequency, total heat flux and lightweight compared to structural steel, grey cast iron and titanium alloy. 展开更多
关键词 Connecting Rod steady-state Thermal Analysis DEFORMATION heat Flux Thermal and Modal Finite Element method
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基于恒热流法和恒温法的岩土热物性试验分析研究
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作者 张志尧 孙林娜 +2 位作者 魏俊辉 刘启明 褚赛 《建筑节能(中英文)》 CAS 2024年第7期22-28,共7页
目前岩土热物性测试仪采用的方法包括两种:恒热流法和恒温法,通过介绍两种测试方法的区别及模型算法,以北京市某公建项目岩土热物性测试结果为基准,利用TRNSYS软件分别模拟了恒热流法和恒温法的测试工况,针对模拟结果展开分析研究。经对... 目前岩土热物性测试仪采用的方法包括两种:恒热流法和恒温法,通过介绍两种测试方法的区别及模型算法,以北京市某公建项目岩土热物性测试结果为基准,利用TRNSYS软件分别模拟了恒热流法和恒温法的测试工况,针对模拟结果展开分析研究。经对比,试验时间至48 h时,两种测试方法利用软件模拟出的延米换热量与现场测试结果的误差在10%以内,表明若已知项目周边的地层热物性参数如地层的导热系数、热扩散率等,可将软件模拟结果作为前期地埋管系统设计的依据,并作为后续热物性勘察结果验证的参考数据。此外,根据模拟结果,由于夏季地埋管流体在设计工况下与土壤的温差值较大,为了使流体尽快达到设计工况点,恒温法测试时应选用较大的功率,否则48 h内的测试值结果与实际值偏差较大。 展开更多
关键词 地源热泵系统 热物性试验 TRNSYS 恒热流法 恒温法
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