Influence of the magnetic field on merging flow of the Powell-Eyring fluids: an exact solution

In this article, the merging flow of the stagnation point and the stretching (or shrinking) flows for the Powell-Eyring fluid (one of the non-Newtonian fluids) in the presence of magnetic field is formulated and analyzed mathematically. An analytical solution was developed on the basis of the homotopy analysis method. The effect of the Hartmann number on fluid-velocity and skin-friction is examined. It is observed that the intensive magnetic field reduces the growth of the reverse/secondary flow which is generated after the mixing of the stagnation-point and shrinking-sheet flows. The magnetic force dominates on the viscous force for stretching as well as for shrinking flows. Furthermore, the magnetic force intensifies the axial velocity of the fluids (the Newtonian as well as the Powell-Eyring fluids) but it decays the transverse-velocity of the fluids. Present results are validated with the existing results for the Newtonian fluids and found comparable with negligible errors.     

Coaxial-disk flow of an Oldroyd-B fluid: exact solution and stability

This paper reports an exact solution for the coaxial disk flow of an Oldroyd-B fluid. The flow is approximately generated by the parallel-plate viscometer. Asymptotic and numerical solutions are reported showing that there is a critical Weissenberg number based on the angular velocity and the Maxwellian relaxation time, above which the flow is unstable. A linearized stability analysis for the basic inertialess flow confirms this numerical instability and yields the critical Weissenberg number.     

The exact solution for thick laminated cantilever cylindrical shell

Discarding any assumption regarding displacement or stress models, the state equation for orthotropy is established in a cylindrical system. The exact solution is presented for the statics of thick closed laminated cantilever cylindrical shells. Every equation of elasticity can be satisfied and all the elastic constants are taken into account. Arbitrary precision of a desired order can be obtained. Project supported by the National Natural Science Foundation of China     

弱粘结的斜交铺设层合圆柱壳的柱形弯曲

导出了两端简文的具有弱粘结界面的任意斜交铺设层合圆柱壳柱形弯曲问题的一个精确弹性理论解。分析中采用线性弹簧模型来表征界面的弱粘结特性。引进新的物理量改写了基本方程,导出了对应的状态空间列式,并利用变量替换技术将该状态方程转换成常系数状态方程,从而方便求解。最后给出了数值算例,并讨论了弱界面的影响。     

An exact axisymmetric solution for a simply supported piezoelectric cylindrical shell

Summary Three-dimensional axisymmetric solution is presented for a simply supported piezoelectric cylindrical shell. The variables are expanded in Fourier series to satisfy the boundary conditions at the ends. The solution of the governing differential equations with variable coefficients is constructed as a product of an exponential function and a power series. The coefficients of terms of all degrees in the governing equations are set to zero, yielding a characteristic equation for the exponent and recursive relations for the coefficients of the power series. Results are presented illustrating the effect of thickness parameter of the shell. An inverse problem of inferring the applied temperature from the measured potential difference has been solved. Accepted for publication 26 July 1996     

An exact solution for the flow of a non-newtonian fluid past an infinite porous plate

Summary The flow of an incompressible fluid of second grade past an infinite porous plate subject to either suction or blowing at the plate is studied. It is found that existence of solutions is tied in with the sign of material moduli and in marked contrast to the Classical Newtonian, fluid solutions can be exhibited for the blowing problem.

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Sommario Si studia la corrente di un fluido incomprimibile di secondo grado che lambisce una lastra porosa da cui è succhiato o soffiato. Si trova che l'esistenza delle soluzioni è legata al segno dei moduli del materiale e, in netto contrasto col fluido newtoniano classico, si possono trovare soluzioni per il problema del soffiamento.

     

A new exact solution for the flow of a Maxwell fluid past an infinite plate

A new exact solution corresponding to the flow of a Maxwell fluid over a suddenly moved flat plate is determined. This solution is in all accordance with a previous one and for λ→0 it goes to the well-known solution for Navier-Stokes fluids.     

An exact solution for the steady-state thermoelastic response of functionally graded orthotropic cylindrical shells

We analyze the steady-state response of a functionally graded thick cylindrical shell subjected to thermal and mechanical loads. The functionally graded shell is simply supported at the edges and it is assumed to have an arbitrary variation of material properties in the radial direction. The three-dimensional steady-state heat conduction and thermoelasticity equations, simplified to the case of generalized plane strain deformations in the axial direction, are solved analytically. Suitable temperature and displacement functions that identically satisfy the boundary conditions at the simply supported edges are used to reduce the thermoelastic equilibrium equations to a set of coupled ordinary differential equations with variable coefficients, which are then solved by the power series method. In the present formulation, the cylindrical shell is assumed to be made of an orthotropic material, although the analytical solution is also valid for isotropic materials. Results are presented for two-constituent isotropic and fiber-reinforced functionally graded shells that have a smooth variation of material volume fractions, and/or in-plane fiber orientations, through the radial direction. The cylindrical shells are also analyzed using the Flügge and the Donnell shell theories. Displacements and stresses from the shell theories are compared with the three-dimensional exact solution to delineate the effects of transverse shear deformation, shell thickness and angular span.     

New exact solution of the problem of rotationally symmetric Couette-Poiseuille flow

An exact solution is obtained for the problem of steady-state viscous incompressible flow under a pressure difference in the gap between coaxial cylinders for the case where the inner cylinder rotates at a constant angular velocity. The solution differs from the classical Couette-Poiseuille result by the presence of radial mass transfer, which provides for interaction between the poloidal and azimuthal circulations. The flow rate is found to depend linearly on the angular velocity of rotation of the inner cylinder. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 5, pp. 71–77, September–October, 2007.     

An exact solution for one-dimensional unsteady nonlinear groundwater flow

After a brief review of the validity of Darcy's law, a nonlinear flow law is adopted for the analytical solution of a groundwater flow problem. A one-dimensional unsteady flow in plane geometry, with prescribed head at the boundaries, is studies. The solution of the analogous linear case is reviewed through the use of Boltzmann's transformation. A solution for nonlinear flow is obtained through a generalization of this transformation. Detailed expressions for specific discharge and drawdown are derived for two significant values of the exponent of the flow law. All results are presented in dimensionless form for a comparative analysis. Some significant cases are plotted. Finally, some implications of the adoption of a nonlinear flow law are discussed.

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Sommario Dopo un breve riepilogo sui limiti di validità della legge di Darcy, si adotta una formulazione non lineare della legge del moto per la risoluzione analitica di un problema di filtrazione. Si studia un moto non stazionario monodimensionale in geometria piana, con carico assegnato al contorno. Viene richiamata la soluzione dell'analogo caso lineare, tramite l'applicazione della trasformata di Boltzmann. Una soluzione per il moto non lineare è ottenuta mediante la generalizzazione di tale trasformazione. Si ricavano le espressioni della velocità apparente di filtrazione e del drawdown per due valori significativi dell'esponente della legge del moto. Tutti i risultati sono presentati in forma adimensionale per una analisi comparativa. Alcuni casi significativi sono diagrammati. In conclusione, sono discusse alcune implicazioni dell'adozione di una legge del moto non lineare.

     

Mass transfer effects on flow past an impulsively started infinite vertical plate with constant mass flux — an exact solution

An exact solution to the problem of flow past an impulsively started infinite vertical plate in the presence of a foreign mass and constant mass flux at the plate is presented by the Laplace-transform technique. The velocity, the temperature and the concentration profiles are shown on graphs. The skin-friction and the Sherwood number are also shown on graphs. The effects of different parameters likeG (the Grashof number),Gc (the modified Grashof number),Pr (the Prandtl number) andSc (the Schmidt number) are discussed.     

基于流固耦合理论的长寿命陀螺仪浮子内部流场及温度场分析

为精确计算出陀螺仪内部温度场,有效改善影响陀螺仪精度的温度梯度分布状况,采用了精度更高的流固耦合计算方法,结合FLUENT软件,对卫星等上使用的某型长寿命陀螺仪浮子组件进行了内部流场及温度场计算。结果表明,浮子内部结构形式对高速旋转的电机产生的介质流场有较大影响,合理的结构设计有利于降低电机功耗;陀螺仪浮子表面存在最大温差为0.52℃的温度梯度,其所产生的液流力矩会对陀螺仪精度产生一定影响;浮子表面温度分布表现出一定的对称性和规律性。计算结果为下一步旨在减小温度梯度、提高陀螺仪精度的精密分区温控提供了数据基础。     

Experimental investigations of the unsteady rotating flow field in a cylindrical vessel

The rotating flow field in a cylindrical vessel — the so-called whirlpool — is widely used in food engineering as a method for separating particles out of a suspension (Cup-of-tea-method). However many of these whirlpools do not operate adequately or fail entirely. In order to solve this problem, the first step was to investigate the flow field and its time dependency which has not been sufficiently understood until now.The rotating flow in a cylindrical vessel — induced by a fluid jet during the filling period of this vessel — is slowed down by fluid friction after the closing of the inlet valve. The velocity fields to be found mainly near, and pressure distributions at the bottom of the vessel, are measured during this unsteady flow. The results, especially those which describe vortex systems, are used to improve the separation system. This paper is restricted to the hydrodynamic aspect. Therefore success in industrial applications can only be indicated.     

An exact solution for flow past an accelerated horizontal plate in a rotating fluid with the generalized Oldroyd-B model

In this paper, the generalized Oldroyd-B with fractional calculus approach is used. An exact solution in terms of Fox-H function for flow past an accelerated horizontal plate in a rotating fluid is obtained by using discrete Laplace transform method. A comparison among the influence of various parameters in the Oldroyd-B model and the angular velocity of the fluid on the velocity profiles is made through numerical method in graphic form.     

Statistics of the surface temperature field of an air/water interface under air flow

Experimental results are presented that reveal the relationship between the root mean square of the surface temperature field of an air/water interface (σ) and the heat flux (q′′) emanating from that interface, over a range of wind speeds. Experiments were conducted for wind speeds ranging from 1.0 to 4.0 m/s to determine if and how the σ versus q′′ relationship was affected by wind speed. Consistent surfactant coverage conditions were maintained for wind speeds ranging from 1.0 to 2.6 m/s, and these are the focus of the results presented herein. For wind speeds above 2.6 m/s the surfactant was consistently pushed downstream, resulting in an inhomogeneous surface condition for the air/water interface. For wind speeds less than 2.6 m/s the relationship between σ and q′′ is approximately linear and is weakly dependent on wind speed. The surface temperature field was obtained by infrared (IR) imaging. Sample IR images are presented in addition to the σ versus q′′ data. IR images are presented for surfaces covered with insoluble surfactants (liquid phase and solid phase), a soluble surfactant, and a clean water surface.

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Scattering far field solution of SH-wave by movable rigid cylindrical interface inclusion

The Green's function is used to solve the scattering far field solution of SH-wave by a movable rigid cylindrical interface inclusion in a linear elastic body. First, a suitable Green's function is developed, which is the fundamental displacement solution of an elastic half space with a movable rigid half-cylindrical inclusion impacted by out-of-plane harmonic line source loaded at any point of its horizontal surface. By using the Green's function, a series of Fredholm integral equations of the first kind which determine the scattering far field can be set up. Then the paper gives the expressions on the far field including the displacement mode of scattering wave and the solution of scattering cross-section. Finally, some examples and numerical results are discussed to analyze the influence of the combination of different media parameters on the answer of far field.