Boundary layer flow and heat transfer of a Casson fluid past a symmetric porous wedge with surface heat flux

The aim of this paper is to investigate numerically the boundary layer forced convection flow of a Casson fluid past a symmetric porous wedge. Similarity transformations are used to convert the governing partial differential equations into ordinary ones. With the help of the shooting method, the reduced equations are then solved numerically. Comparisons are made with the previously published results in some special cases and they are found to be in excellent agreement with each other. The results obtained in this study are illustrated graphically and discussed in detail. The velocity is found to increase with an increasing Falkner-Skan exponent whereas the temperature decreases. With the rise of the Casson fluid parameter, the fluid velocity increases but the temperature is found to decrease in this case. Fluid velocity is suppressed with the increase of suction. The skin friction decreases with the increasing value of Casson fluid parameter. It is found that the temperature decreases as the Prandtl number increases and thermal boundary layer thickness decreases with the increasing value of Prandtl number. A significant finding of this investigation is that flow separation can be controlled by increasing the value of the Casson fluid parameter as well as by increasing the amount of suction.

Variable fluid properties and variable heat flux effects on the flow and heat transfer in a non-Newtonian Maxwell fluid over an unsteady stretching sheet with slip velocity

The effects of variable fluid properties and variable heat flux on the flow and heat transfer of a non-Newtonian Maxwell fluid over an unsteady stretching sheet in the presence of slip velocity have been studied. The governing differential equations are transformed into a set of coupled non-linear ordinary differential equations and then solved with a numerical technique using appropriate boundary conditions for various physical parameters. The numerical solution for the governing non-linear boundary value problem is based on applying the fourth-order Runge-Kutta method coupled with the shooting technique over the entire range of physical parameters. The effects of various parameters like the viscosity parameter, thermal conductivity parameter, unsteadiness parameter, slip velocity parameter, the Deborah number, and the Prandtl number on the flow and temperature profiles as well as on the local skin-friction coefficient and the local Nusselt number are presented and discussed. Comparison of numerical results is made with the earlier published results under limiting cases.

Analytical study of Cattaneo–Christov heat flux model for a boundary layer flow of Oldroyd-B fluid

We investigate the Cattaneo-Christov heat flux model for a two-dimensional laminar boundary layer flow of an incompressible Oldroyd-B fluid over a linearly stretching sheet. Mathematical formulation of the boundary layer problems is given. The nonlinear partial differential equations are converted into the ordinary differential equations using similarity transformatioris. The dimensionless velocity and temperature profiles are obtained through optimal homotopy analysis method （OHAM）. The influences of the physical parameters on the velocity and the temperature are pointed out. The results show that the temperature and the thermal boundary layer thickness are smaller in the Cattaneo-Christov heat flux model than those in the Fourier＇s law of heat conduction.

3D Casson nanofluid flow over slendering surface in a suspension of gyrotactic microorganisms with Cattaneo-Christov heat flux

A mathematical model is proposed to execute the features of the non-uniform heat source or sink in the chemically reacting magnetohydrodynamic （MHD） Casson fluid across a slendering sheet in the presence of microorganisms and Cattaneo-Christov heat flux. Multiple slips （diffusion, thermal, and momentum slips） are applied in the modeling of the heat and mass transport processes. The Runge-Kutta based shooting method is used to find the solutions. Numerical simulation is carried out for various values of the physical constraints when the Casson index parameter is positive, negative, or infinite with the aid of plots. The coefficients of the skin factors, the local Nusselt number, and the Sherwood number are estimated for different parameters, and discussed for engineering interest. It is found that the gyrotactic microorganisms are greatly encouraged when the dimensionless parameters increase, especially when the Casson fluid parameter is negative. It is worth mentioning that th~ velocity profiles when the Casson fluid parameter is positive are higher than those when the Casson fluid parameter is negative or infinite, whereas the temperature and concentration fields show exactly opposite phenomena.

Carreau fluid flow due to nonlinearly stretching sheet with thermal radiation, heat flux, and variable conductivity

A sophisticated theoretical and mathematical model is proposed.It is verified that this model can estimate and monitor the detailed behavior for the steady Carreau fluid flow past a nonlinear stretching surface and the predicted phenomena due to the presence of heat flux,thermal radiation,and viscous dissipation.Despite the fact that some properties of the fluid do not depend on the temperature,the fluid thermal conductivity is assumed to depend on the temperature.Based on accelerating the fluid elements,some of the kinetic energy for the fluid can be turned to the internal heating energy in the form of viscous dissipation phenomena.The contribution in this study is that a similar solution is obtained,in spite of the high nonlinearity of the Carreau model,especially,with the heat flux,variable conductivity,and viscous dissipation phenomena.Some of the major significant findings of this study can be observed from the reduction in the fluid velocity with enhancing the Weissenberg number.Likewise,the increase in the sheet temperature is noted with increasing the Eckert number while the reverse behavior is observed for increasing both the radiation parameter and the conductivity parameter.Finally,the accuracy and trust in the proposed numerical method are validated after benchmarking for our data onto the earlier results.

Cattaneo-Christov heat flux model for third-grade fluid flow towards exponentially stretching sheet

The Cattaneo-Christov heat flux in the two-dimensional （2D） flow of a third- grade fluid towards an exponentially stretching sheet is investigated. The energy equation is considered through thermal relaxation. Similarity transformations are accounted to obtain the ordinary differential systems. The converted non-dimensional equations are solved for the series solutions. The convergence analysis of the computed solutions is reported. The graphical results of the velocity and temperature profiles are plotted and elaborated in detail. The results show that the thermal relaxation enhances the temper- ature gradient while reduces the temperature profile.

Jeffrey fluid flow due to curved stretching surface with Cattaneo-Christov heat flux

The two-dimensional(2D) motion of the Jeffrey fluid by the curved stretching sheet coiled in a circle is investigated. The non-Fourier heat flux model is used for the heat transfer analysis. Feasible similarity variables are used to transform the highly nonlinear ordinary equations to partial differential equations(PDEs). The homotopy technique is used for the convergence of the velocity and temperature equations. The effects of the involved parameters on the physical properties of the fluid are described graphically.The results show that the curvature parameter is an increasing function of velocity and temperature, and the temperature is a decreasing function of the thermal relaxation time.Besides, the Deborah number has a reverse effect on the pressure and surface drag force.

西藏南部新生代东西向伸展作用的深部岩浆作用响应

随着新生代喜马拉雅山链的崛起,西藏南部经历了显著的东西向伸展作用,形成一系列近南北向展布的裂谷。伴随着增厚岩石圈的对流减薄或者拆沉,软流圈上涌,藏南岩石圈地幔和中下地壳发生顺次部分熔融作用,形成岩石学和地球化学特征各异的岩浆岩,具体表现为:1)富集岩石圈地幔部分熔融,形成碳酸质、煌斑质和超钾质岩浆岩;2)增厚基性下地壳部分熔融,形成高Sr/Y比值的花岗岩;3)中-下地壳变沉积岩发生白云母脱水/含水部分熔融,形成典型淡色花岗岩。这些新发现限定了藏南裂谷系的启动时限不晚于~30 Ma,为解译世界上造山带和陆内伸展作用过程中大陆岩石圈深部熔融的精细模式提供了典型实例。

Soret and Dufour Effects on Unsteady Free Convection Fluid Flow in the Presence of Hall Current and Heat Flux

Unsteady MHD natural convective heat and mass transfer flow through a semi-infinite vertical porous plate in a rotating system have been investigated with the combined Soret and Dufour effects in the presence of Hall current and constant heat flux. It is considered that the porous plate is subjected to constant heat flux. The obtained non-dimensional, non-similar coupled non-linear and partial differential equations have been solved by explicit finite difference technique. Numerical solutions for velocities, temperature and concentration distributions are obtained for various parameters by the above mentioned technique. The local and average shear stresses, Nusselt number as well as Sherwood number are also investigated. The stability conditions and convergence criteria of the explicit finite difference scheme are established for finding the restriction of the values of various parameters to get more accuracy. The obtained results are illustrated with the help of graphs to observe the effects of various legitimate parameters.

流体黏性对盐指型双扩散对流扩散通量影响的试验研究

为研究盐指型双扩散对流过程中流体黏性对通量的影响,使用中间有移动挡板的试验水箱形成初始为静止状态的糖-盐双层系统,并通过调整糖、盐组分质量分数设计了一系列密度稳定比相同而流体黏性不同的试验工况,进行了双扩散对流扩散通量变化规律的试验研究。试验结果表明:流体黏性对盐指型双扩散对流扩散通量的影响不可忽略,在双扩散对流强度相同的条件下,试验流体黏性越大,盐指型双扩散对流扩散通量越小;当试验流体的运动黏滞系数均小于1.15 mm2/s时,糖和盐这两种组分跨界面的双扩散对流扩散通量随流体黏性增大而减小的趋势相近,当两种组分的质量分数持续增大时,盐溶液的黏性仍缓慢增大,而糖溶液的黏性迅速变大,此时糖组分的跨界面双扩散对流扩散通量仍会随糖溶液黏性的增大而减小,但盐组分的跨界面双扩散对流扩散通量不再变化;Stern数与流体黏性呈负相关关系。

含氟流体助熔华南基底片麻岩的实验研究:对稀土成矿花岗岩成因的制约

为了明确含氟流体对花岗岩源区岩浆过程中稀土元素地球化学行为的影响,本文采用华南代表性的高稀土片麻岩和低稀土片麻岩作为初始物质,与~4%的流体(纯水、1.5 mol/L HF、1.0 mol/L NaF)在0.8 GPa、1000℃的条件下开展了流体助熔的部分熔融实验。实验结果表明,所有片麻岩的熔融程度达到40%以上,残余矿物组合主要为斜长石+石英+斜方辉石±单斜辉石+钛铁矿+磷灰石±黑云母。部分熔融产生的熔体的成分主要为花岗闪长质‒花岗质,总体具有高氟(0.11%~0.27%)、高水(0.38%~1.86%)和A2型花岗岩的特征;其中,高稀土片麻岩部分熔融形成的熔体为钾玄质和准铝质,而低稀土片麻岩熔融形成的熔体偏高钾钙碱性和强过铝质。在微量元素蛛网图上,两者均表现为富集K、Rb、Th、Ce、Sm、Y、Yb等元素,亏损Ba、Nb、Ta、Zr、Hf、Ti等元素;稀土元素配分曲线则表现为右倾、负Eu异常的特征。相对于原岩,含氟流体助熔会强化熔体中Si、K、Na、Rb、Sr、Ba、Th、U、LREE和F的富集,并增加熔体的La_(N)/Yb_(N)值。同时,实验也证实片麻岩部分熔融形成的熔体的稀土元素含量主要受原岩控制,高稀土片麻岩更易于熔出稀土元素初始富集的熔体;相对于原岩,各类流体助熔均会造成稀土元素在熔体中不同程度的富集,其中,含HF流体助熔最高可富集稀土46%~49%(近1.5倍富集)。我们因此认为在华南LREE型和HREE型成矿花岗岩形成过程中,含F流体发挥重要的作用。此外,本文也提出了一种新的A2型花岗岩形成机制,即含F流体助熔地壳基底岩石,这很好地解释了华南晚中生代大规模分布的与稀土、稀有金属及氟成矿相关的陆内A2型花岗岩的形成。

电磁磨粒检测中气泡对铜颗粒信号的影响特性分析

三线圈式电磁磨粒传感器在油液在线监测中应用广泛,而油液中的气泡对铜颗粒的检测极易造成干扰,定量分析气泡在颗粒检测时的影响规律将有助于提高电磁磨粒传感器的检测精度。基于电磁磨粒检测中的磁耦合效应,分别研究了气泡间隙、气泡大小、气泡位置以及气泡数量对铜颗粒检测的影响特性,并以大管径通道(?38 mm)电磁磨粒传感器为对象进行仿真和试验。结果表明,气泡与铜颗粒间隙越大,铜颗粒信号幅值越小,影响范围(0.52~10.31)%;气泡尺寸增大铜颗粒信号幅值也增大,气泡直径为20 mm和25 mm时影响分别是3.07%和5.47%;气泡与铜颗粒中心连线与传感器中心轴线的夹角越大,检测影响越小,影响范围(0.4~5.6)%;气泡数量越多干扰越大,单气泡和双气泡的影响程度分别是5.66%和8.74%。

非均匀热流影响超临界二氧化碳流动换热数值研究

针对部分极端工况下表面热流密度高、分布不均匀的特点,采用数值计算分析方法研究非均匀热流对超临界二氧化碳流动与换热特性的影响。针对内径为4 mm水平圆管内超临界压力二氧化碳的流动传热,依次在相同总热流不同变化斜率、不同总热流相同变化斜率的2组线性非均匀热流工况下进行数值模拟,得到线性非均匀热流工况下热物性分布、浮升力影响对流换热特性规律。仿真结果表明:相较于均匀热流,非均匀热流工况下加热段入口处附近上壁面传热恶化更严重,线性非均匀热流分布下该处管壁温度可达均匀热流工况下的1.85倍;对给定的实际表面热流边界条件下的超临界二氧化碳流动换热进行数值仿真,加热段入口处上壁面最大温度达出口温度的3.41倍,改变流动方向后这一比值降低到1.50,据此对采取超临界二氧化碳为工质的相关冷却方案给出了建议。

复杂固-液介质的速度应力方程三角形单元间断伽辽金地震波模拟算法

间断伽辽金法可用于存在复杂边界条件的模型,同时具有高阶精度和易于并行计算的优点,因此近年来在地震波传播模拟研究中得到了快速发展.数值通量是间断伽辽金法的关键组成部分之一.相比于其他通量,基于Rankine-Hugoniot跳跃条件的通量(RH-condition通量)在固体和液体介质边界具有更宽的稳定性,可以使用更大的时间步长,尤其是液体和固体之间的波阻抗差异较大时.它已被用于基于四边形网格和速度-应变方程的间断伽辽金地震波固液介质模拟.本文为了模拟陆地自然水体等存在复杂固-液界面形状的地震波传播,并在未来与其他数值方法耦合,发展了基于三角形网格的RH-condition通量间断伽辽金方法,使用一阶速度-压力声波和一阶速度-应力弹性波方程模拟复杂固-液介质中地震波的传播.通过水平层状和sin型起伏固-液模型,验证了该方法模拟结果的准确性.通过数值模拟展示了所提出的间断伽辽金法在不同网格大小和阶数下的准确性和效率.最后通过一个复杂模型的例子表明存在复杂固-液界面时该方法可以准确施加固-液边界条件.

轴向磁通永磁电机混合冷却结构设计与分析

针对轴向磁通永磁电机损耗大和散热困难的问题,提出了风冷结构和混合冷却结构,其中混合冷却结构由端盖风冷结构和定子水冷结构组成。建立了电机的三维模型,采用流固耦合法对电机进行仿真分析,通过对比两种冷却结构的冷却效果,选择了混合冷却结构作为电机的冷却系统。通过仿真分析了流速对电机温升的影响,并根据仿真结果确定了混合冷却结构最佳的入口风速以及水速,证明了混合冷却结构的有效性,为轴向磁通永磁电机的冷却系统设计提供了一定的参考。

Flux vector splitting solutions for coupling hydraulic transient of gas-liquid-solid three-phase flow in pipelines

The gas-liquid-solid three-phase mixed flow is the most general in multiphase mixed transportation. It is significant to exactly solve the coupling hydraulic transient problems of this type of multiphase mixed flow in pipelines. Presently, the method of characteristics is widely used to solve classical hydraulic transient problems. However, when it is used to solve coupling hydraulic transient problems, excessive interpolation errors may be introduced into the results due to unavoidable multiwave interpolated calculations. To deal with the problem, a finite difference scheme based on the Steger- Warming flux vector splitting is proposed. A flux vector splitting scheme is established for the coupling hydraulic transient model of gas-liquid-solid three-phase mixed flow in the pipelines. The flux subvectors are then discretized by the Lax-Wendroff central difference scheme and the Warming-Beam upwind difference scheme with second-order precision in both time and space. Under the Rankine-Hugoniot conditions and the corresponding boundary conditions, an effective solution to those points located at the boundaries is developed, which can avoid the problem beyond the calculation region directly induced by the second-order discrete technique. Numerical and experimental verifications indicate that the proposed scheme has several desirable advantages including high calculation precision, excellent shock wave capture capability without false numerical oscillation, low sensitivity to the Courant number, and good stability.

Thermodynamic analysis and simulation for gas baffle entrance collimator of EAST-NBI system based on thermo-fluid coupled method

The world's first full Experimental Advanced Superconducting Tokamak(EAST) is designed with the auxiliary heating method of neutral beam injection(NBI)system. Beam collimators are arranged on both sides of the beam channel for absorbing the divergence beam during the beam transmission process in the EAST-NBI system.The gas baffle entrance collimator(GBEC) is a typical high-heat-flux component located at the entrance of gas baffle. An efficient and accurate analysis of its thermodynamic performance is of great significance to explore the working limit and to ensure safe operation of the system under a high-parameter steady-state condition. Based on the thermo-fluid coupled method, thermodynamic analysis and simulation of GBEC is performed to get the working states and corresponding operating limits at different beam extraction conditions. This study provides a theoretical guidance for the next step to achieve long pulse with highpower experimental operation and has an important reference to ensure the safe operation of the system.

Shear-thinning behavior of the CaO–SiO2–CaF2–Si3N4 system mold flux and its practical application

Satisfying the mold-flux performance requirements for high-speed continuous casting necessitates the development of a new non-Newtonian-fluid mold flux with shear-thinning behavior, i.e., a mold flux whose viscosity is relatively high under lower shear rates and relatively low under higher shear rates. In this work, a mold flux that exhibits shear-thinning behavior was developed by adding different amounts of Si_3N_4 to the CaO–SiO_2–CaF_2 mold flux. The shear-thinning behavior was investigated using a rotational viscometer. In addition, the microstructure of the newly prepared slags was studied by high-temperature Raman spectroscopy and X-ray photoelectron spectroscopy. The results showed that the mechanism of shear-thinning was attributable to a temporary viscosity loss caused by the one-way shear stress, whereas the corresponding magnitude of shear-thinning was closely related to the degree of polymerization(DP). Finally, the non-Newtonian fluid mold flux was used for laboratory casting tests, which revealed that the mold flux could reduce slag entrapment and positively affect the continuous casting optimization.

Heat Transfer with Viscous Dissipation in Couette-Poiseuille Flow under Asymmetric Wall Heat Fluxes

Analytical solutions of temperature distributions and the Nusselt numbers in forced convection are reported for flow through infinitely long parallel plates, where the upper plate moves in the flow direction with constant velocity and the lower plate is kept stationary. The flow is assumed to be laminar, both hydro-dynamically and thermally fully developed, taking into account the effect of viscous dissipation of the flowing fluid. Both the plates being kept at specified and at different constant heat fluxes are considered as thermal boundary conditions. The solutions obtained from energy equation are in terms of Brinkman number, dimensionless velocity and heat flux ratio. These parameters greatly influence and give complete understanding on heat transfer rates that has potentials for designing and analyzing energy equipment and processes.

Numerical Simulation of Subcooled Boiling Inside High-Heat-Flux Component with Swirl Tube in Neutral Beam Injection System

In order to realize steady-state operation of the neutral beam injection（NBI） system with high beam energy,an accurate thermal analysis and a prediction about working conditions of heat-removal structures inside high-heat-flux（HHF） components in the system are key issues.In this paper,taking the HHF ion dump with swirl tubes in NBI system as an example,an accurate thermal dynamic simulation method based on computational fluid dynamics（CFD） and the finite volume method is presented to predict performance of the HHF component.In this simulation method,the Eulerian multiphase method together with some empirical corrections about the inter-phase transfer model and the wall heat flux partitioning model are considered to describe the subcooled boiling.The reliability of the proposed method is validated by an experimental example with subcooled boiling inside swirl tube.The proposed method provides an important tool for the refined thermal and flow dynamic analysis of HHF components,and can be extended to study the thermal design of other complex HHF engineering structures in a straightforward way.The simulation results also verify that the swirl tube is a promising heat removing structure for the HHF components of the NBI system.