UNSTEADY FLOWS OF A GENERALIZED SECOND GRADE FLUID WITH THE FRACTIONAL DERIVATIVE MODEL BETWEEN TWO PARALLEL PLATES

The fractional calculus approach in the constitutive relationship model of a generalized second grade fluid is introduced.Exact analytical solutions are obtained for a class of unsteady flows for the generalized second grade fluid with the fractional derivative model between two parallel plates by using the Laplace transform and Fourier transform for fractional calculus.The unsteady flows are generated by the impulsive motion or periodic oscillation of one of the plates.In addition,the solutions of the shear stresses at the plates are also determined.

Heat transfer on peristaltic flow of fourth grade fluid in inclined asymmetric channel with partial slip

In this paper, the effects of slip and heat transfer are studied on the peristaltic transport of a magnetohydrodynamic （MHD） fourth grade fluid. The governing equations are modeled and solved under the long wavelength approximation by using a regular perturbation method. Explicit expressions of solutions for the stream function, the velocity, the pressure gradient, the temperature, and the heat transfer coefficient are presented. Pumping and trapping phenomena are analyzed for increasing the slip parameter. Further, the temperature profiles and the heat transfer coefficient are observed for various increasing parameters. It is found that these parameters considerably affect the considered flow characteristics. Comparisons with published results for the no-slip case are found in close agreement.

Blasius flow and heat transfer of fourth-grade fluid with slip

This investigation deals with the effects of slip, magnetic field, and non- Newtonian flow parameters on the flow and heat transfer of an incompressible, electrically conducting fourth-grade fluid past an infinite porous plate. The heat transfer analysis is carried out for two heating processes. The system of highly non-linear differential equations is solved by the shooting method with the fourth-order Runge-Kutta method for moderate values of the parameters. The effective Broyden technique is adopted in order to improve the initial guesses and to satisfy the boundary conditions at infinity. An exceptional cross-over is obtained in the velocity profile in the presence of slip. The fourth-grade fluid parameter is found to increase the momentum boundary layer thickness, whereas the slip parameter substantially decreases it. Similarly, the non-Newtonian fluid parameters and the slip have opposite effects on the thermal boundary layer thickness.

Three-dimensional channel flow of second grade fluid in rotating frame

An analysis is performed for the hydromagnetic second grade fluid flow between two horizontal plates in a rotating system in the presence of a magnetic field. The lower sheet is considered to be a stretching sheet, and the upper sheet is a porous solid plate. By suitable transformations, the equations of conservation of mass and momentum are reduced to a system of coupled non-linear ordinary differential equations. A series of solutions to this coupled non-linear system are obtained by a powerful analytic technique, i.e., the homotopy analysis method （HAM）. The results are presented with graphs. The effects of non-dimensional parameters R, A, M2, a, and K2 on the velocity field are discussed in detail.

Series solutions for the stagnation flow of a second-grade fluid over a shrinking sheet

This study derives the analytic solutions of boundary layer flows bounded by a shrinking sheet. With the similarity transformations, the partial differential equations are reduced into the ordinary differential equations which are then solved by the homotopy analysis method （HAM）. Two-dimensional and axisymmetric shrinking flow cases are discussed.

Couette Flow Problem for an Unsteady MHD Fourth-Grade Fluid with Hall Currents

In this work, we analyze Couette flow problem for an unsteady magnetohydrodynamic (MHD) fourth-grade fluid in presence of pressure gradient and Hall currents. The existing literature on the topic shows that the effect of Hall current on Couette flow of an unsteady MHD fourth-grade fluid with pressure gradient has not been investigated so far. The arising non-linear problem is solved by the homotopy analysis method (HAM) and the convergence of the obtained complex series solution is carefully analyzed. The influence of pressure number, Hartmann number, Hall parameter and fourth-grade material parameters on the unsteady velocity is discussed through plots and on local skin-friction coefficient discussed through numerical values presented in tabular form.

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.

Hydromagnetic rotating flow of third grade fluid

This work investigates the flow of a third grade fluid in a rotating frame of reference. The fluid is incompressible and magnetohydrodynamic （MHD）. The flow is bounded between two porous plates, the lower of which is shrinking linearly. Mathematical modelling of the considered flow leads to a nonlinear problem. The solution of this nonlinear problem is computed by the homotopy analysis method （HAM）. Graphs are presented to demonstrate the effect of several emerging parameters, which clearly describe the flow characteristics.

Exact solutions for the flow of second grade fluid in annulus between torsionally oscillating cylinders

The velocity field and the associated shear stress corresponding to the torsional oscillatory flow of a second grade fluid, between two infinite coaxial circular cylinders, are determined by means of the Laplace and Hankel transforms. At time t = 0, the fluid and both the cylinders are at rest and at t = 0 ＋ , cylinders suddenly begin to oscillate around their common axis in a simple harmonic way having angular frequencies ω 1 and ω 2 . The obtained solutions satisfy the governing differential equation and all imposed initial and boundary conditions. The solutions for the motion between the cylinders, when one of them is at rest, can be obtained from our general solutions. Furthermore, the corresponding solutions for Newtonian fluid are also obtained as limiting cases of our general solutions.

MHD axisymmetric flow of third grade fluid between porous disks with heat transfer

The magnetohydrodynamic （MHD） flow of the third grade fluid between two permeable disks with heat transfer is investigated. The governing partial differential equa- tions are converted into the ordinary differential equations by suitable transformations. The transformed equations are solved by the homotopy analysis method （HAM）. The expressions for square residual errors are defined, and the optimal values of convergence- control parameters are selected. The dimensionless velocity and temperature fields are examined for various dimensionless parameters. The skin friction coefficient and the Nus- selt number are tabulated to analyze the effects of dimensionless parameters.

Oscillatory flow of second grade fluid in cylindrical tube

The unsteady oscillatory flow of an incompressible second grade fluid in a cylindrical tube with large wall suction is studied analytically. Flow in the tube is due to uniform suction at the permeable walls, and the oscillations in the velocity field are due to small amplitude time harmonic pressure waves. The physical quantities of interest are the velocity field, the amplitude of oscillation, and the penetration depth of the oscillatory wave. The analytical solution of the governing boundary value problem is obtained, and the effects of second grade fluid parameters are analyzed and discussed.

Exact analytical solutions for axial flow of a fractional second grade fluid between two coaxial cylinders

The velocity field and the adequate shear stress corresponding to the longitudinal flow of a fractional second grade fluid,between two infinite coaxial circular cylinders,are determined by applying the Laplace and finite Hankel transforms.Initially the fluid is at rest,and at time t=0^+, the inner cylinder suddenly begins to translate along the common axis with constant acceleration. The solutions that have been obtained are presented in terms of generalized G functions.Moreover, these solutions satisfy both the governing differential equations and all imposed initial and boundary conditions.The corresponding solutions for ordinary second grade and Newtonian fluids are obtained as limiting cases of the general solutions.Finally,some characteristics of the motion,as well as the influences of the material and fractional parameters on the fluid motion and a comparison between models,are underlined by graphical illustrations.

级配与拦挡位置对滑坡碎屑流运动影响研究

为了研究不同级配的高位滑坡碎屑流经多级偏转后冲击不同拦挡结构的运动特性以及致灾效应,结合自然地形构建固定坡度和偏转角度均为45°的离散元模型,并利用DEM软件进行数值模拟分析不同拦挡工况和不同级配对碎屑流颗粒运动过程中能量耗散、最终堆积形态,以及碎屑流冲击挡板的作用高度的影响,进而建立相关冲击力学模型。研究结果显示:(1)上下均设置挡板的工况能有效减缓碎屑流颗粒的平均动能和势能,且能有效降低颗粒流翻越挡板的数量,并降低颗粒流的最大运动距离从而减小致灾范围;随着颗粒组级配的增大,势能时程曲线分散点出现的时间越晚,颗粒流最终堆积面积中细颗粒组最大,粗颗粒组最小。(2)当滑槽底部反作用力位置取2/3静止堆积体长度时,计算所得碎屑流最大冲击作用高度与模拟试验结果相接近,力学模型计算的冲击作用高度在0.017~0.138 m。在实际工程中,可按研究相似比对此范围进行加强抗冲击防护。(3)由于侧板的切向力和“颗粒分选效应”,大颗粒会主要冲击挡板的中上部,小颗粒主要冲击挡板的下部,并受偏转角影响集中在一侧,因此工程设计可根据实际情况避免在沟道偏转方向的反向建设工程。研究结果可为高位滑坡碎屑流灾害的治理防护提供参考。

等扩展度条件下骨料包裹砂浆层的影响因素

水泥(砂)浆在混凝土中起胶凝和润滑的双重作用,其用量随着混凝土流动性要求的提高而增大,已有研究发现浆体过多会导致混凝土的体积稳定性问题,环保绿色程度低,但骨料级配等因素对混凝土中浆体合理用量的影响研究尚不多见。在粗骨料低空隙率前提下固定粗骨料用量不变,调整砂浆用量来控制混凝土扩展度,研究骨料级配和砂浆流变特性对粗骨料包裹砂浆层厚度及用量的影响。试验结果表明:粗骨料的几何平均粒径增大,包裹砂浆层厚度单调增加,包裹砂浆用量会呈现先减小后增大的趋势,存在最优几何平均粒径;扩展度要求越高,包裹砂浆层厚度及包裹砂浆用量越大,最优几何粒径越小;当粗骨料级配不变时,包裹砂浆层厚度和包裹砂浆用量均随砂浆屈服应力和塑性黏度的增大而增大。

隧道弃渣级配碎石细观力学参数研究

隧道弃渣级配碎石作为道路基层填料,能有效避免资源浪费与环境污染。有限元方法将其视为连续介质进行研究时存在一定局限性,而采用离散元对颗粒材料进行模拟时,细观参数对其宏观力学性质的影响并不明确。基于三轴压缩试验和数值模拟,通过正交控制参数变化分析,揭示了颗粒间细观参数与宏观力学参数之间的关联性,明确了细观参数对隧道弃渣级配碎石路用力学性能的影响。结果表明:细观参数中,切向黏结强度对黏聚力值的影响最大,而摩擦系数与内摩擦角值变化联系更密切;初始杨氏模量与刚度比呈负相关,其他参数对其影响不大;与泊松比相关的变化关系中,刚度比与切向黏结强度较其他参数对其影响更大。研究成果可为颗粒流模拟级配碎石的细观参数标定提供参考,也为级配碎石作为道路基层填料的力学性能研究提供了基础。

Hall Effects on Unsteady Magnetohydrodynamic Flow of a Third Grade Fluid

The unsteady magnetohydrodynamic flow of an electrically conducting viscous incompressible third grade fluid bounded by an infinite porous plate is studied with the Hall effect. An external uniform magnetic field is applied perpendicular to the plate and the fluid motion is subjected to a uniform suction and injection. Similarity transformations are employed to reduce the non-linear equations governing the flow under discussion to two ordinary differential equations （with and without dispersion terms）. Using the finite difference scheme, numerical solutions represented by graphs with reference to the various involved parameters of interest are discussed and appropriate conclusions are drawn.

阿利西尤单抗联用海博麦布对急性ST段抬高型心肌梗死的疗效

目的探究阿利西尤单抗联用海博麦布在急性ST段抬高型心肌梗死(STEMI)中的临床疗效。方法将112例STEMI患者随机分为对照组和研究组,各56例。所有患者入院后行PCI治疗。对照组术后口服海博麦布治疗,研究组联合阿利西尤单抗治疗。维持治疗6个月后,比较两组的低密度脂蛋白胆固醇(LDL-C)、高密度脂蛋白胆固醇(HDL-C)、甘油三酯、总胆固醇、左心室射血分数(LVEF)、二尖瓣口舒张早期与晚期峰值血流速度比(E/A)、左心室收缩末期内径(LVESD)、脑利钠肽前体(NT-proBNP)、心肌肌钙蛋白(cTnI)、脂蛋白相关磷脂酶A2(Lp-PLA2)、基质金属蛋白酶-9(MMP-9)、白细胞介素-6(IL-6)、血流灌注分级(TIMI)、药物毒性及术后心血管不良事件。结果治疗后,两组LDL-C、甘油三酯、总胆固醇较治疗前均降低,研究组低于对照组(P<0.05)。两组治疗前后HDL-C比较,差异无统计学意义(P>0.05)。治疗后,两组LVEF、E/A较治疗前均升高,研究组高于对照组(P<0.05);两组LVESD、NT-proBNP、c TnI、Lp-PLA2、MMP-9、IL-6较治疗前均降低,研究组低于对照组(P<0.05)。术后6个月,研究组TIMIⅢ级占比高于对照组(P<0.05)。药物不良反应及术后心血管不良事件发生率比较,差异无统计学意义(P>0.05)。结论阿利西尤单抗联用海博麦布应用于STEMI PCI术后的治疗中,更有助于降低患者的血脂水平,促进血流灌注,改善心肌功能,安全性良好。

优先提锂湿法工艺回收废旧磷酸铁锂电池

文章详细介绍了一种优先提锂湿法回收碳酸锂的工艺流程,先用碱除铝,再酸浸分离磷酸铁,除杂后沉锂,工艺流程简化、试剂消耗量小、锂浸出选择性较高,工艺经济效益相对更好,可以为磷酸铁锂电池回收企业提供一种工艺流程简化、试剂消耗量小、锂浸出选择性较高、工艺经济效益相对更好的工艺技术路线。

高海拔地区宽级配泥石流冲击拦砂坝试验研究

在高海拔地区,由于山高谷深,坡表物质受物理风化严重,物源级配宽度范围大,泥石流的发育频率高,冲击力大,导致拦砂坝损毁严重。为研究高海拔地区宽级配泥石流对拦砂坝的冲击规律,以西藏地区发育的泥石流为原型,建立宽级配泥石流冲击拦砂坝的物理试验模型,选取泥石流容重、水槽坡度与泥石流固相最大粒径为变量,进行27组水槽试验,研究冲击力特征。结果表明:(1)宽级配泥石流在冲击拦砂坝过程中经历“冲击爬高、旋滚回流、堆积回淤”3个接触演化阶段,泥石流容重越小,爬高越大,冲淤过程的阶段性表现越明显;(2)拦砂坝的坝前冲击力随宽级配泥石流容重的增大而减小,在相同坡度和级配的条件下,容重越大,水流携带固体物源运动越困难,泥石流流速降低,泥石流的冲击力减小;(3)拦砂坝的坝前冲击力随沟槽坡度增大而增大,沟槽坡度越大,宽级配泥石流的流速和流深越大,泥石流冲击力就越大,并且泥石流固相粒径越大,坡度对冲击力的影响效果越明显;(4)拦砂坝的坝前冲击力随宽级配泥石流固相最大粒径增大而增大,且变化趋势较泥石流容重及沟槽坡度条件改变时更加显著,最大粒径与泥石流流速、流深没有明显规律关系。研究成果将为宽级配泥石流防治和研究提供一定的数据参考。

内蒙古白云鄂博某低品位含铁岩矿磁悬浮联合分级流程工业试验研究

白云鄂博铁矿石储量巨大,缓解了国家铁矿石对外依存度过高的问题,同时也助力了包钢集团生产发展。但是在采矿过程中,产生了大量TFe品位低于20%的低品位含铁岩矿。对该类矿石,采用传统连续磨矿-磁选流程,在细磨至-0.074 mm粒级含量95%情况下,铁精矿品位最高只有60.8%,无法达到合格铁精矿质量要求;如果采用浮选流程,选矿经济性能不佳,故该部分矿石一直进行堆放未得到应用。本文通过对原矿性质进行分析,引入新型磁悬浮精选机作为磁选精选设备,同时设计三条全磁工艺流程进行工业试验,均可得到TFe品位64.5%以上的合格铁精矿,同时铁精矿中杂质元素K、Na、Si含量远低于浮选工艺流程。其中,自主开发的阶段磨选-磁悬浮联合分级分选流程,在细磨至-0.074 mm粒级含量95%情况下,最终可得到铁精矿TFe品位64.5%、磁性铁回收率95.07%的优良技术指标,分选效率高,效果好。现场应用后可实现白云鄂博低品位含铁矿经济性绿色利用,经济效益显著,同时极大地延长了白云鄂博铁资源的供给年限,对国家自有铁矿石产能接续、矿山自身可持续发展及资源绿色利用具有深远意义。