Similarity solutions for non-Newtonian power-law fluid flow

The problem of the boundary layer flow of power law non-Newtonian fluids with a novel boundary condition is studied.The existence and uniqueness of the solutions are examined,which are found to depend on the curvature of the solutions for different values of the power law index n.It is established with the aid of the Picard-Lindel¨of theorem that the nonlinear boundary value problem has a unique solution in the global domain for all values of the power law index n but with certain conditions on the curvature of the solutions.This is done after a suitable transformation of the dependent and independent variables.For 0 n 1,the solution has a positive curvature,while for n 1,the solution has a negative or zero curvature on some part of the global domain.Some solutions are presented graphically to illustrate the results and the behaviors of the solutions.     

Unsteady rotative flow of non-Newtonian fluid in an annular pipe

ＵＮＳＴＥＡＤＹＲＯＴＡＴＩＶＥＦＬＯＷＯＦＮＯＮ－ＮＥＷＴＯＮＩＡＮＦＬＵＩＤＩＮＡＮＡＮＮＵＬＡＲＰＩＰＥＨｕａｎｇＪｕｎ－ｑｉ（黄军旗）（Ｄｅｐｔｏｆ＇Ｒｅｓｏｕｒ＆Ｅｎｖｉ．Ｓｃｉ．Ｂｅｉｊｉｎｇ．ＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙＢｅｉｊｉｎ...     

非稳态分数阶Oldroyd-B流体绕楔形体流动研究

研究了非稳态分数阶Oldroyd-B流体在多孔介质中通过楔形拉伸板的驻点流动问题。基于分数阶Oldroyd-B流体的本构模型建立了动量方程,并在其中引入了浮升力和驻点流动特征。此外,考虑了具有热松弛延迟时间的修正的分数阶Fourier定律,并将其应用于能量方程和对流换热边界条件。接着,采用与L1算法相结合的有限差分法求解控制偏微分方程。最后,分析了相关物理参数对流动的影响。结果表明,随着楔角参数的增加,流体受到的浮升力增大,导致速度加快;达西数越大,介质的孔隙度变大,流体的流动越快;此外,温度分布先略有上升后明显下降,这表明Oldroyd-B流体具有热延迟特性。     

A study on non-steady flow of upper-convected maxwell fluid in tube

The transient response of an upper-convected Maxwell fluid flow in a circular tube is analysed by variational approach of Kantorovich and the method of finite difference. The solution of the variational method is in agreement with the numerical results by the difference schemes. The results show that the method of Kantorovich is suitable for the study of non-steady flow of non-Newtonian fluids and the effect of elasticity of the fluid has an influence on the non-steady flow. project supported by National Natural Science Foundation of China     

Evolution of the diffusion-induced flow over a sphere submerged in a continuously stratified fluid

The problem of the stabilization of the diffusion-induced flow over a sphere submerged in a continuously stratified fluid is solved using both asymptotic and numerical methods. The analytical solution describes the structure of the main convective cells, including thin meridional jets flowing along the surface and plumes spreading from the flow convergence regions above the upper and lower poles of the sphere which gradually return the fluid particles to the neutral buoyancy horizon. The total width of the flows adjacent to the surface exceeds the thickness of the salinity deficit layer or the density boundary layer. The numerical solution of the complete problem in the nonlinear formulation describes the main convective cells and two systems of unsteady integral waves formed in the vicinity of the sphere poles. At large times, out of the entire system of internal waves only those nearest to the neighborhood of their horizon of formation remain clearly defined. The calculated flow patterns are in agreement with each other and the data of shadow visualization of the stratified fluid structure near a submerged obstacle at rest.     

Numerical simulation of vortical ideal fluid flow through curved channel

A numerical algorithm to study the boundary‐value problem in which the governing equations are the steady Euler equations and the vorticity is given on the inflow parts of the domain boundary is developed. The Euler equations are implemented in terms of the stream function and vorticity. An irregular physical domain is transformed into a rectangle in the computational domain and the Euler equations are rewritten with respect to a curvilinear co‐ordinate system. The convergence of the finite‐difference equations to the exact solution is shown experimentally for the test problems by comparing the computational results with the exact solutions on the sequence of grids. To find the pressure from the known vorticity and stream function, the Euler equations are utilized in the Gromeka–Lamb form. The numerical algorithm is illustrated with several examples of steady flow through a two‐dimensional channel with curved walls. The analysis of calculations shows strong dependence of the pressure field on the vorticity given at the inflow parts of the boundary. Plots of the flow structure and isobars, for different geometries of channel and for different values of vorticity on entrance, are also presented. Copyright © 2003 John Wiley & Sons, Ltd.     

Linear stability of homogeneous elongational flow of the upper convected Maxwell fluid

We prove that planar elongational flow of the upper convected Maxwell fluid is linearly stable and analyze the associated spectral problem.     

Exact solutions of a dipolar fluid flow

Exact solutions for three canonical flow problems of a dipolar fluid are obtained: (i) The flow of a dipolar fluid due to a suddenly accelerated plate, (ii) The flow generated by periodic oscillation of a plate, (iii) The flow due to plate oscillation in the presence of a transverse magnetic field. The solutions of some interesting flows caused by an arbitrary velocity of the plate and of certain special oscillations are also obtained.     

MHD boundary-layer flow of an upper-convected Maxwell fluid in a porous channel

Two-dimensional magnetohydrodynamic (MHD) boundary layer flow of an upper-convected Maxwell fluid is investigated in a channel. The walls of the channel are taken as porous. Using the similarity transformations and boundary layer approximations, the nonlinear partial differential equations are reduced to an ordinary differential equation. The developed nonlinear equation is solved analytically using the homotopy analysis method. An expression for the analytic solution is derived in the form of a series. The convergence of the obtained series is shown. The effects of the Reynolds number Re, Deborah number De and Hartman number M are shown through graphs and discussed for both the suction and injection cases.     

Nitrogen/non-Newtonian fluid two-phase upward flow in non-circular microchannels

This paper presents experimental investigations on nitrogen/non-Newtonian fluid two-phase flow in vertical noncircular microchannels, which have square or triangular cross-section with the hydraulic diameters being D_h = 2.5, 2.886 and 0.866 mm, respectively, by visualization method. Three non-Newtonian aqueous solutions with typical rheological properties, i.e., 0.4% carboxymethyl cellulose (CMC), 0.2% polyacrylamide (PAM) and 0.2% xanthan gum (XG) are chosen as the working fluids. The common flow patterns are identified as slug flow, churn flow and annular flow. The dispersed bubble flow is only found in the case with nitrogen/CMC solution two-phase flow in the largest channel. A new flow pattern of nitrogen/PAM solution two-phase flow, named chained bubble/slug flow, is observed in all the test channels. The flow regime maps are also developed and the results show that the rheological properties of the non-Newtonian fluid have remarkable influence on the flow pattern transitions. The geometrical factors of the microchannel such as the cross-section shape and hydraulic diameter of the channel can also affect the flow regime map. Finally, the results obtained in this work are compared with the available flow pattern transitions.     

Sakiadis flow of an upper-convected Maxwell fluid

The flow of an upper-convected Maxwell (UCM) fluid is studied theoretically above a rigid plate moving steadily in an otherwise quiescent fluid. It is assumed that the Reynolds number of the flow is high enough for boundary layer approximation to be valid. Assuming a laminar, two-dimensional flow above the plate, the concept of stream function coupled with the concept of similarity solution is utilized to reduce the governing equations into a single third-order ODE. It is concluded that the fluid's elasticity destroys similarity between velocity profiles; thus an attempt was made to find local similarity solutions. Three different methods will be used to solve the governing equation: (i) the perturbation method, (ii) the fourth-order Runge-Kutta method, and (iii) the finite-difference method. The velocity profiles obtained using the latter two methods are shown to be virtually the same at corresponding Deborah number. The velocity profiles obtained using perturbation method, in addition to being different from those of the other two methods, are dubious in that they imply some degree of reverse flow. The wall skin friction coefficient is predicted to decrease with an increase in the Deborah number for Sakiadis flow of a UCM fluid. This prediction is in direct contradiction with that reported in the literature for a second-grade fluid.     

On the dispersion of soluble matter in a channel flow of non-Newtonian fluid

Summary An analysis of the dispersion of a solute in Rivlin-Ericksen third-order fluid in a parallel plate channel is carried out. It is seen that the solute which is dispersed relative to a plane moving with the mean speed of the flow has its effective Taylor diffusion coefficient which decreases with increasing the non-Newtonian parameter With 1 table     

Solution of the Rayleigh problem for a powerlaw non-Newtonian conducting fluid via group method

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Analytical solutions of the helical flow of non newtonian fluid in eccentric annular space

ＡＮＡＬＹＴＩＣＡＬＳＯＬＵＴＩＯＮＳＯＦＴＨＥＨＥＬＩＣＡＬＦＬＯＷＯＦＮＯＮＮＥＷＴＯＮＩＡＮＦＬＵＩＤＩＮＥＣＣＥＮＴＲＩＣＡＮＮＵＬＡＲＳＰＡＣＥＺｈａｎｇＨａｉ－ｑｉａｏ（张海桥）ＷｕＪｉ－ｚｈｏｕ（吴继周）（ＴｈｅＤｅｐａｒｔｍｅｎｔｏｆ...     

Effect of thermal conductivity on heat transfer for a power-law non-Newtonian fluid over a continuous stretched surface with various injection parameters

The two-dimensional non-Newtonian steady flow on a power-law stretched surface with suction or injection is studied. Thermal conductivity is assumed to vary as a linear function of temperature. The transformed governing equations in the present study are solved numerically using the Runge-Kutta method. Through a comparison, results for a special case of the problem show excellent agreement with those in a previous work. Two cases are considered, one corresponding to a cooled surface temperature and the other to a uniform surface temperature. Numerical results show that the thermal conductivity variation parameter, the injection parameter, and the power-law index have significant influences on the temperature profiles and the Nusselt number.     

Thermal radiation effect on flow and heat transfer of unsteady MHD micropolar fluid over vertical heated nonisothermal stretching surface using group analysis

The aim of this paper is to study the thermal radiation effects on the flow and heat transfer of an unsteady magnetohydrodynamic (MHD) micropolar fluid over a vertical heated nonisothermal stretching surface in the presence of a strong nonuniform magnetic field. The symmetries of the governing partial differential equations are de- termined by the two-parameter group method. One of the resulting systems of reduced nonlinear ordinary differential equations are solved numerically by the Chebyshev spec- tral method. The effects of various parameters on the velocity, the angular velocity, and the temperature profiles as well as the skin-friction coefficient, the wall couple stress co- efficient, and the Nusselt number are studied.     

Effect of spatial discretization schemes on numerical solutions of viscoelastic fluid flows

This study examines the effect of discretization schemes for the convection term in the constitutive equation on numerical solutions of viscoelastic fluid flows. For this purpose, a temporally evolving mixing layer, a two-dimensional vortex pair interacting with a wall, and a fully developed turbulent channel flow are selected as test cases, and eight different discretization schemes are considered. Among them, the first-order upwind difference scheme (UD) and artificial diffusion scheme (AD), which are commonly used in the literature, show most stable and smooth solutions even for highly extensional flows. However, the stress fields are smeared too much by these schemes and the corresponding flow fields are quite different from those obtained by higher-order upwind difference schemes. Among higher-order upwind difference schemes investigated in this study, a third-order compact upwind difference scheme (CUD3) with locally added AD shows stable and most accurate solutions for highly extensional flows even at relatively high Weissenberg numbers.     

Computational intellectual analytical theory of computational analytical approach to rotating flow of non-Newtonian fluid

Ａｎｅｗｆｉｅｌｄｏｆｍｏｄｅｒｎｃｏｍｐｕｔｅｒｓｃｉｅｎｃｅ—ａｒｔｉｆｉｃｉａｌｉｎｔｅｌｌｉｇｅｎｃｅｉｓｄｅｖｅｌｏｐｅｄｒａｐｉｄｌｙ．Ｔｈｅｓｙｍｂｏｌｉｃｍａｎｉｐｕｌａｔｉｏｎｉｓｔｈｅｆｒｏｎｔｄｉｒｅｃｔｉｏｎｉｎｔｈｅａｒｔｉｆｉｃｉａｌｉｎｔｅｌｌｉｇｅｎｃｅ．Ａｓｅｒｉｅｓｏｆｔｈｅｃｏｍｐｕｔｅｒｓｏｆｔｗａｒｅｉｓｄｅｖｅｌｏｐｅｄｆｏｒｔｈｅｃｏｍｐｕｔａｔｉｏｎａｌｍａｎｉｐｕｌａｔｉｏｎ,ｓｕｃｈａｓＭａｃｓｙｍａ,Ｍａｐｌｅ,Ｍａｔｈｅｍａｔｉｃａ,ｔｏｃ…     

Unsteady flow of viscoelastic fluid with fractional Maxwell model in a channel

The unsteady flow of viscoelastic fluid with the fractional derivative Maxwell model (FDMM) in a channel is studied in this note. The exact solutions are obtained for an arbitrary pressure gradient by means of the finite Fourier cosine transform and the Laplace transform. Two special cases of pressure gradient are discussed. Some results given by the classical models with integer-order are included in this note.     

Three-dimensional stretched flow of Jeffrey fluid with variable thermal conductivity and thermal radiation

This article addresses the three-dimensional stretched flow of the Jeffrey fluid with thermal radiation. The thermal conductivity of the fluid varies linearly with respect to temperature. Computations are performed for the velocity and temperature fields. Graphs for the velocity and temperature are plotted to examine the behaviors with different parameters. Numerical values of the local Nusselt number are presented and discussed. The present results are compared with the existing limiting solutions, showing good agreement with each other.