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.

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.

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.

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.

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.

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.

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.

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.

Some exact solutions of the oscillatory motion of a generalized second grade fluid in an annular region of two cylinders

The velocity field and the associated shear stress corresponding to the longitudinal oscillatory flow of a generalized second grade fluid, between two infinite coaxial circular cylinders, are determined by means of the Laplace and Hankel transforms. Initially, the fluid and cylinders are at rest and at t = 0＋ both cylinders suddenly begin to oscillate along their common axis with simple harmonic motions having angular frequencies Ω1 and Ω2. The solutions that have been obtained are presented under integral and series forms in terms of the generalized G and R functions and satisfy the governing differential equation and all imposed initial and boundary conditions. The respective 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 the similar flow of ordinary second grade fluid and Newtonian fluid are also obtained as limiting cases of our general solutions. At the end, the effect of different parameters on the flow of ordinary second grade and generalized second grade fluid are investigated graphically by plotting velocity profiles.

MHD Fluctuating Flow of Non-Newtonian Fluid through a Porous Medium Bounded by an Infinite Porous Plate

In present paper, an investigation has been made on the fluctuating flow of a non-Newtonian second grade fluid through a porous medium over a semi-infinite porous plate in presence of a transverse magnetic field B0. The governing equations have been solved analytically and the expressions for the velocity and stress fields are obtained. The free stream velocity U(t) fluctuates in time about a non-zero constant mean. The effects of the permeability parameter K and magnetic field parameter M on velocity field have been analyzed quantitatively with the help of figures. It is noticed that the velocity field asymptotically approaches free stream velocity as it goes far away from the plate.

INVESTIGATION OF RELATIONSHIPS BETWEEN KI－67SCORE，DNA INDEX，AND HISTOLOGIC GRADEIN SOFT TISSUE SARCOMAS

Proliferative activity of soft tissue sarcomas(STS)in 31 cases was estimated by histologic grading, mitotic count, DNA analysis by flow cytometry, and immunohistochemical procedures with monoclonal antibody Ki-67.Aneuploid was found in 12 of 16 cases(75.0%) with Grade 3, and in 4 of 15 cases(26.7%) with Grade 1, 2(P=0.0121).Tumors with more than 100 Ki-67 positive tumor cells per 10 high power fields(HPF) had a higher rate of aneuploid(81.3%) than those with less than 100 Ki-67 per 10 HPF (26.7%)(P=0.0038). There were significant correlations between Grade and DI (r=0.4901, P=0.0051), Grade and Ki-67(r=0.4636, P=0.0086), Ki-67 and DI(r=0-6368, P=0.0001). The results indicate that DI and reactivity of tumor cells to Ki-67 may reflect Proliferative activity and be helpful for clinicians to judge the biological behaviour of tumors more accurately and objectively. Supplementary to the grading of STS, DI and Ki-67 score could be useful as Prognostic parameters for clinical investigation of multimodality therapy for individual Patients.

Application of He’s Variational Iterative Method for Solving Thin Film Flow Problem Arising in Non-Newtonian Fluid Mechanics

In this paper, He’s variational iteration method is successfully employed to solve a nonlinear boundary value problem arising in the study of thin film flow of a third grade fluid down an inclined plane. For comparison, the same problem is solved by the Adomian decomposition method. The results show that the difference between the two solutions is negligible. The conclusion is that this technique may be considered an alternative and efficient method for finding approximate solutions of both linear and nonlinear boundary value problems. Furthermore, the variational iteration method has an advantage over the decomposition method in that it solves the nonlinear problems without using the Adomian polynomials.

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。

Beneficiation of low-grade diasporic bauxite with hydrocyclone

Low-grade diasporic bauxite was treated with hydrocyclone of small cone-angle.The effects of apex diameter,feed pressure and feed concentration on separation indexes were tested,and then the separation process was discussed by hydrokinetics tentatively.The results show that the increase of apex diameter changes the spacial locality of the envelope of zero vertical velocity, resulting in decrease of the ratio of Al2O3/SiO2 in overflow and increase of the recovery of Al2O3 in underflow,while feed pressure and feed concentration have no remarkable effect on the spacial locality of the envelope of zero vertical velocity,however,the separation indexes are improved by the increase of feed pressure,but are worsened by the increase of feed concentration.

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。

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。