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.

Carreau-Extended非牛顿流体圆管层流流动的摄动解

非牛顿流体在工业生产中应用广泛。文中基于同时包含屈服应力、时间常数和幂律指数的Carreau-Extended(简称Carreau-E)复杂流变方程及剪切应力与压降平衡关系,建立了圆管内充分发展的稳定Carreau-E流体层流管流的运动方程,并采用摄动方法推导出相应运动方程的一阶渐近解,获得了不同类型流体管流的速度分布以及压力梯度、流核宽度、屈服应力和时间常数对Carreau-E流体管流流场分布的影响规律,该研究对Carreau-E流体及其他复杂非牛顿流体管流特性研究具有参考价值。

Series solution of a natural convection flow for a Carreau fluid in a vertical channel with peristalsis

An analysis has been achieved to study the natural convection of a non-Newtonian fluid （namely a Carreau fluid） in a vertical channel with rhythmically contracting walls. The Navier-Stokes and the energy equations are reduced to a system of non- linear PDE by using the long wavelength approximation. The optimal homotopy analysis method （OHAM） is introduced to obtain the exact solutions for velocity and temperature fields. The convergence of the obtained OHAM solution is discussed explicitly. Numerical calculations are carried out for the pressure rise and the features of the flow and temperature characteristics are analyzed by plotting graphs and discussed in detail.

Series solution of unsteady peristaltic flow of a Carreau fluid in small intestines

The study of peristaltic flow of a Carreau fluid in a non-uniform tube under the con- sideration of long wavelength is presented. The flow is investigated in a wave frame of reference moving with velocity of the wave e. Numerical integration has been used to obtain the graphical results for pressure rise and frictional forces. The effects of various emerging parameters are investigated through graphs.

Blood flow of Carreau fluid in a tapered artery with mixed convection

This research is concerned with the mathematical modeling and analysis of blood flow in a tapered artery with stenosis. The analysis has been carried out in the presence of heat and mass transfer. Constitutive equation of Carreau fluid has been invoked in the mathematical formulation. The representation of blood flow is considered through an axially non-symmetrical but radially symmetric stenosis. Symmetry of the distribution of the wall, shearing stress and resistive impectartce and their growth with the developirtg stenosis is given due attention. Solutions have been obtained for the velocity, temperature, concentration, resistance impedance, wall shear stress and shearing stress at the stenosis throat. Graphical illustrations associated with the tapered arteries namely converging, diverging and non-tapered arteries are examined for different parameters of interest. Streamlines have been plotted and discussed.

A HYDROMAGNETIC MATHEMATICAL MODEL FOR BLOOD FLOW OF CARREAU FLUID

This paper constructs a mathematical model for blood flow through an artery with mild stenosis. Constitutive equations for Carreau fluid are employed in the mathematical modeling. Analysis has been carried out in the presence of constant magnetic field. Symmetric and asymmetric shapes of stenosis are taken. Governing flow model is computed for the series solution. Whe flow quantities of interest, for instance, axial velocity, pressure gradient, pressure drop, impedance and shear stress at the walls of stenotic artery are described for various pertinent parameters entering into the problem.

Magnetically propelled Carreau fluid flow over penetrable sensor surface influenced by thermal radiation,Joule heating and heat generation

This examination emphasizes the analysis of thermal transmission of Carreau fluid flow on a permeable sensor surface equipped with radiation,Joule heating,an internal heat source,and a magnetic field.With the above effects and assumptions,the equations that administer the flow are formulated.A configured system of equations is productively reduced to a system of ordinary differential equations.The reduced system is then dealt with using the Runge–Kutta-Fehlberg fourth–fifth order tool equipped by the shooting technique.Derived numerical solutions are utilized to plot graphs and tables.The conclusion of the study outlines some important findings such as the power law index,the thermal radiation parameter and the heat source parameter enhance the thermal panel whereas the Weissenberg number deescalates the same.The power law index and permeable velocity decrease the velocity panel significantly.Diagrammatic representation of streamlines of the flow has been given to strengthen the study.A detailed description has been produced about the results obtained in the study.

Peristaltic transport of a MHD Carreau fluid in a tapered asymmetric channel with permeable walls

The effect of permeable walls and magnetic field on the peristaltic flow of a Carreau fluid in a tapered asymmetric channel is studied. The tapered asymmetric channel is normally created due to the intra-uterine fluid flow induced by myometrial contractions and it was simulated by asymmetric peristaltic fluid flow in a two-dimensional infinite non-uniform channel. The analysis has been performed under long wavelength and low- Reynolds number assumptions to linearize the governing flow equations. A series solution in respect of a small Weissenberg number is obtained for the stream function, axial pressure gradient and shear stress. Time average of pressure rise and frictional force on the upper wall has also been computed using numerical integration. The results have been presented graphically for the various interested physical parameters. It is observed that for Carreau fluids the peristalsis works as a pump against a greater pressure rise compared with a Newtonian fluid, while there exists no significant difference in free pumping flux for Newtonian and Carreau fluids in the tapered asymmetric channel.

Numerical analysis for peristaltic transport of Carreau-Yasuda fluid with variable thermal conductivity and convective conditions

Peristalsis of Carreau-Yasuda fluid is investigated. Analysis is carried out in the presence of velocity slip and convective boundary conditions. Thermal conductivity of the fluid is taken to be temperature dependent. Lubrication analysis is used in the formulation of the problem. Resulting nonlinear system of equations is solved numerically. Impact of embedded parameters on the quantities of interest is examined through graphs and tables. Comparison of the behavior of the Carreau-Yasuda, Carreau and Newtonian fluid models is presented. Results show that the heat transfer rate at the wall for the Carreau fluid model is large when compared with the Newtonian or the Carreau-Yasuda fluid model. Also the heat transfer rate at the wall decreases with increase in the velocity slip and variable thermal conductivity parameters. Further, an increase in the Biot number reduces the fluid temperature by a considerable amount.

基于Carreau流变模型的圆柱滚子轴承热混合润滑分析

为了研究圆柱滚子轴承接触区的混合润滑性能,建立基于Carreau非牛顿流体的热混合润滑模型,求解非牛顿流体线接触热混合润滑数值解。研究滑滚比、卷吸速度及载荷对线接触混合润滑特性的影响,并与相同工况下牛顿流体热混合润滑的结果进行对比。结果表明:随着滑滚比、卷吸速度及载荷的增大,油膜温度都会升高,Carreau非牛顿流体的温度要低于牛顿流体的温度;油膜厚度随着滑滚比、载荷的增大而减小,随着卷吸速度的增大而增大,Carreau非牛顿流体与牛顿流体膜厚相差不大;随着滑滚比的增大,2种流体的平均摩擦因数均增大,随着卷吸速度和载荷的增大,2种流体的载荷比均减小。

Bird-Carreau型黏性van der Waals流体周期解的渐近稳定性

讨论了一维可压缩黏性van der Waals流体系统的渐近稳定性,其中黏性系数为满足Bird-Carreau模型的非线性函数,压力为非凸函数。通过构造能量函数并运用能量估计方法及单调算子理论,证明得出:大黏性条件下初值位于稳定区域时,以及大黏性、小扰动条件下初值位于亚稳定区域时,该类van der Waals流体的解是渐近稳定的。

Dissipative flow features of Carreau nanofluid with thermal radiation inside plane wall channel:Jeffery-Hamel analysis

The current article communicates a numerical investigation on laminar flow of dissipative generalized Newtonian Carreau nanofluid flowing through vertical conduit with converging and diverging plane walls.Thermal and concentration characteristics due to enthalpy change,activation energy,and non-linear thermal radiation have been examined in the presence of buoyancy forces.The channel walls for both temperature and volumetric fraction are assumed to be isothermal.The instability mechanism of nanofluids is reported using a two-phase nanofluid model,which works reasonably well for nanoparticle concentrations below a certain threshold.A Jeffery-Hamel(J-H)flow model is developed by assuming an incompressible purely radial flow of Carreau nanofluids with heat and mass transportation.Using the suitable non-dimensional variables,the resulting nonlinear partial differential equations are turned into a system of ordinary differential equations.The modified governing equations are then numerically solved using the built-in boundary value problem solver bvp4c,on the template form of commercial software MATLAB.The impacts of material,geometrical and thermophysical parameters governing the J-H problem are discussed and illustrated.Results indicate that higher buoyance forces incline the velocity profiles in converging enclosure,while a slight reduction is perceived in opposing forces.A significant decrease of wall heat transmission is reflected for larger values of activation energy and radiation parameter.For endorsing this communication,a comparison analysis is established with existing research and noticed a remarkable agreement.Practically,the flow inside converging and diverging channels are deployed in nuclear reactors that use plate-type nuclear energies,high heat-flux condensed heat exchangers,high-performance micro-electronic cooling systems,jets,rockets nozzles,and jet propulsion inlet.

聚合物熔体的非等温平板收缩流动的数值模拟

用有限元法模拟了 Carreau流体在 4∶ 1平板收缩口模中的非等温挤出流动。采用 3节点的三角形单元对速度、压力和温度进行等阶插值 ,运用特殊的罚函数处理流体的不可压缩条件 ,解决了压力场的数值振荡问题 ,并用改进的 Newton迭代法对非线性方程进行求解 ,成功地计算了 Carreau流体在平板收缩流动中的速度、压力、粘度以及应力的分布 ,同时得到温度场的分布。计算的应力分布与实验的结果及

基于FLUENT的SK型静态混合器的数值模拟

为提高混合器的优化设计水平和工程应用的速度,应用商业CFD软件—FLUENT,分析了聚酯在SK型静态混合器的混合流动。采用FLUENT中的Carreau模型描述了非牛顿流体聚酯的黏-温特性,得出了混合器的压力降及出口混合温度。

钢塑共挤模具分流段成形过程数值模拟

以聚合物挤出过程模拟的罚有限元模型为基础,采用VC++语言自主开发了模拟软件,对Carreau流体在钢塑共挤模具分流段的流动过程进行模拟,获得模具内聚合物熔体的三维速度场分布,采用SUPG方法求解能量方程,在对流项占优的情况下获得温度场的分布,分析不同体积流量对速度的影响。结果表明实例分析给出钢塑共挤模具内流场的一般规律对模具设计具有一定的指导意义。

飞机除冰液流变特性研究

冬季飞行时,寒冷的天气常会导致机翼、测压测速传感头等关键表面结冰,影响飞机的空气动力学性能,严重时甚至会造成安全事故。据此,美国联邦航空管理局(FAA)要求寒冷天气飞机起飞时必须进行除防冰操作。目前,最常用的方法是喷洒二醇基除冰液,如Ⅱ型、Ⅳ型除冰液。由于Ⅱ、Ⅳ型除冰液粘度较Ⅰ型除冰液更高,FAA要求对其空气动力学性能进行测试,而除冰液的流变性能直接影响空气动力学性能,因此,采用Brookfield粘度计对防冰液在不同温度、不同转速下的流变性能进行研究,讨论了不同模型对防冰液流变性能的拟合程度。结果表明,在一定范围,Brookfield粘度计测量除冰液粘度具有较高的精度和重现性,幂律模型和Carreau模型均能较好的拟合剪切速率与粘度的关系,相对而言,Carreau方程拟合精度较高,但是其方程更为复杂,参数较多。

HEAT AND MASS TRANSFER EFFECTS ON CARREAU FLUID MODEL FOR BLOOD FLOW THROUGH A TAPERED ARTERY WITH A STENOSIS

In the current critique, we deliberate the blood flow through narrowing vein with a steno- sis in the manifestation of heat and mass transmission. The non-Newtonian flora of blood in small veins are examined mathematically by demonstrating the blood as Carreau fluid. The illustration for the blood flow is debated through an axially irregular but outward regular stenosis. Regularity in the dissemination of the fortification clipping stress and resistive impedance and their evolution with the emerging stenosis is a new significant feature of our investigation. Analytical solutions have been appraised for ＂velocity, tem- perature, concentration, resistance impedance, wall shear stress and shearing stress at the stenosis throat＂. The graphical consequences of different types of tapering arteries （i.e. ＂converging tapering, diverging tapering, non-tapered artery＂） have been studied for dissimilar constraints of attention. Rivulet shapes have been strategized for different parameters at the culmination of the article.

流变模型对剪切稀化流体弹流油膜厚度影响的研究

基于Carreau流变模型和Ree-Eyring流变模型,对剪切稀化流体线接触弹流润滑进行了完全数值分析,得到了同一种润滑油在不同流变模型下的弹流油膜厚度。将理论分析得到的油膜厚度、经典弹流膜厚公式计算的油膜厚度以及实测的油膜厚度进行了对比,结果表明:基于Carreau流变模型的理论分析结果更能反映剪切稀化流体的实际弹流油膜厚度;在相同工况下,基于Ree-Eyring流变模型的理论分析结果低估了剪切稀化流体的油膜厚度,经典弹流膜厚公式过高地估计了剪切稀化流体的油膜厚度。研究结果表明:幂函数形式的流变模型更能反映剪切稀化流体的流变特性。

Perturbation analysis for pulsatile flow of Carreau fluid through tapered stenotic arteries

The pulsatile flow of blood in a tapered narrow artery with overlapping time-dependent stenosis is mathematically analyzed, modeling blood as Caxreau fluid. Perturbation method is employed for solving the resulting nonlinear system of equations along with the appropriate boundary conditions. The analytic solutions to the pressure gradient, velocity distribution, flow rate, wall shear stress and longitudinal impedance to flow axe obtained in the asymptotic form. The variation of the aforesaid flow quantities with respect to various physical parameters such as maximum depth of the stenosis, angle of tapering of the artery, power law index, Reynolds number, pulsatile amplitude of the flow and Weissenberg number is investigated. It is found that the wall shear stress and longitudinal impedance to flow increase with the increase of the angle of tapering of the artery, the maximum depth of the stenosis and pulsatile Reynolds number and these decrease with the increase of the amplitude of the flow, power law index and Weis- senberg number. The mean velocity of blood decreases significantly with the increase of the artery radius, maximum depth of the stenosis, angle of tapering of the artery.

非牛顿流体经波纹管流动的阻力特性

本文对Carreau流体经波纹管的蠕动流的阻力特性用差分方法作了数值求解。先施行坐标变换,提出一种保证周期性条件的混合迭代法,能较快得到问题的收敛解。流体的物质参数以及流动区域的几何参数对流动阻力特性的影响作了讨论,同时指出了直径均匀的毛管模型作为渗流模型的不足之处。