多孔介质中卡森流体的分形分析

研究了非牛顿流体中的卡森流体在多孔介质中的流动特性.基于服从分形分布的弯曲毛细管束模型,运用分形几何理论推导出了该流体在多孔介质中流动的流量、流速、启动压力梯度和有效渗透率的分形解析解.模型中的每一个参数都有明确的物理意义,它将卡森流体在多孔介质中的流动特性与多孔介质的微结构参数有机联系起来.文中给出了卡森流体的流速、启动压力梯度和有效渗透率随着各影响因素的变化趋势,并进行了讨论.所得分形模型可以更深刻地理解卡森流体在多孔介质中流动的内在物理机理. 关键词： 多孔介质 卡森流体 分形     

Casson fluid flow and heat transfer over a nonlinearly stretching surface

A boundary layer analysis is presented for non-Newtonian fluid flow and heat transfer over a nonlinearly stretching surface. The Casson fluid model is used to characterize the non-Newtonian fluid behavior. By using suitable transformations, the governing partial differential equations corresponding to the momentum and energy equations are converted into non-linear ordinary differential equations. Numerical solutions of these equations are obtained with the shooting method. The effect of increasing Casson parameter is to suppress the velocity field. However the temperature is enhanced with the increasing Casson parameter.     

Effects of thermal radiation on Casson fluid flow and heat transfer over an unsteady stretching surface subjected to suction/blowing

The unsteady flow of a Casson fluid and heat transfer over a stretching surface in presence of suction/blowing are investigated.The transformed equations are solved numerically by using the shooting method.The exact solution corresponding to the momentum equation for the steady case is obtained.Fluid velocity initially decreases with the increase of unsteadiness parameter.Due to an increasing Casson parameter the velocity field is suppressed.Thermal radiation enhances the effective thermal diffusivity and the temperature rises.     

Exact solutions for the flow of Casson fluid over a stretching surface with transpiration and heat transfer effects

The effects of transpiration on forced convection boundary layer non-Newtonian fluid flow and heat transfer toward a linearly stretching surface are reported.The flow is caused solely by the stretching of the sheet in its own plane with a velocity varying linearly with the distance from a fixed point.The constitutive relationship for the Casson fluid is used.The governing partial differential equations corresponding to the momentum and energy equations are converted into non-linear ordinary differential equations by using similarity transformations.Exact solutions of the resulting ordinary differential equations are obtained.The effect of increasing Casson parameter,i.e.,with decreasing yield stress(the fluid behaves as a Newtonian fluid as the Casson parameter becomes large),is to suppress the velocity field.However,the temperature is enhanced as the Casson parameter increases.It is observed that the effect of transpiration is to decrease the fluid velocity as well as the temperature.The skin-friction coefficient is found to increase as the transpiration parameter increases.     

Boundary layer flow and heat transfer of a Casson fluid past a symmetric porous wedge with surface heat flux

The aim of this paper is to investigate numerically the boundary layer forced convection flow of a Casson fluid past a symmetric porous wedge. Similarity transformations are used to convert the governing partial differential equations into ordinary ones. With the help of the shooting method, the reduced equations are then solved numerically. Comparisons are made with the previously published results in some special cases and they are found to be in excellent agreement with each other. The results obtained in this study are illustrated graphically and discussed in detail. The velocity is found to increase with an increasing Falkner-Skan exponent whereas the temperature decreases. With the rise of the Casson fluid parameter, the fluid velocity increases but the temperature is found to decrease in this case. Fluid velocity is suppressed with the increase of suction. The skin friction decreases with the increasing value of Casson fluid parameter. It is found that the temperature decreases as the Prandtl number increases and thermal boundary layer thickness decreases with the increasing value of Prandtl number. A significant finding of this investigation is that flow separation can be controlled by increasing the value of the Casson fluid parameter as well as by increasing the amount of suction.     

Peristaltic Flow of Couple Stress Fluid in a Non-Uniform Rectangular Duct Having Compliant Walls

The present study investigates the peristaltic flow of couple stress fluid in a non-uniform rectangular duct with compliant walls.Mathematical modeling is based upon the laws of mass and linear momentum.Analytic solutions are carried out by the eigen function expansion method under long-wavelength and low-Reynolds number approximations.The features of the flow characteristics are analyzed by plotting the graphs of various values of physical parameters of interest.Trapping bolus scheme is also presented through streamlines.     

Analytic solution for magnetohydrodynamic boundary layer flow of Casson fluid over a stretching/shrinking sheet with wall mass transfer

In this analysis,the magnetohydrodynamic boundary layer flow of Casson fluid over a permeable stretching/shrinking sheet in the presence of wall mass transfer is studied.Using similarity transformations,the governing equations are converted to an ordinary differential equation and then solved analytically.The introduction of a magnetic field changes the behavior of the entire flow dynamics in the shrinking sheet case and also has a major impact in the stretching sheet case.The similarity solution is always unique in the stretching case,and in the shrinking case the solution shows dual nature for certain values of the parameters.For stronger magnetic field,the similarity solution for the shrinking sheet case becomes unique.     

Unique Outcomes of Internal Heat Generation and Thermal Deposition on Viscous Dissipative Transport of Viscoplastic Fluid over a Riga-Plate

Boundary layer stagnation point flow of Casson fluid over a Riga plate of variable thickness is investigated in present article. Riga plate is an electromagnetic actuator consists of enduring magnets and gyrated aligned array of alternating electrodes mounted on a plane surface. Physical problem is modeled and simplified under appropriate transformations. Effects of thermal radiation and viscous dissipation are incorporated. These differential equations are solved by Keller Box Scheme using MATLAB. Comparison is given with shooting techniques along with RangeKutta Fehlberg method of order 5. Graphical and tabulated analysis is drawn. The results reveal that Eckert number,radiation and fluid parameters enhance temperature whereas they contribute in lowering rate of heat transfer. The numerical outcomes of present analysis depicts that Keller Box Method is capable and consistent to solve proposed nonlinear problem with high accuracy.     

Depinning Dynamics of Fluid Monolayer on a Quenched Substrate

Langevin simulations are preformed on the depinning dynamics of fluid monolayer on a quenched substrate. With increase in the strength of the substrate, we find for the first time a crossover from elastic crystal to smectic flows as well as a crossover from smectic to plastic flows above the depinning. A power-law scaling relationship can be derived between the drift velocity and the driving force for both the elastic crystal and smectic flows, but fails to be obtained for the plastic flow. The power-law exponents are found to be no larger than 1 for the elastic crystal flow and larger than 1 for the smeetic flow. The critical driving force and the averaged intensity of Bragg peaks remain invariant basically in the regime of smectic flow. A sudden increase in the critical driving force is observed within the crossover from the smeetic to plastic flows, and the averaged intensity of Bragg peaks shows sudden decreases within the crossovers both from the elastic crystal to smectic flows and from the smectic to plastic flows. The results are helpful for understanding the slip dynamics of fluids on a molecular level.     

Influence of radiative heat flux in nonlinear convection of quartic order in Casson fluid past a vertical permeable plate with variable suction and Hall current

The current study centralizes on unsteady free convection slip flow of Casson fluid past a vertical permeable plate with Hall current, radiative heat flux, and variable suction. The nonlinear convection is subjected to quartic order. Perturbation method is used to convert the non-linear coupled partial differential equation of the momentum and energy to a system of ordinary differential equations. The dimensionless governing equations are solved analytically for velocity and temperature profiles. The graphs are plotted for sundry parameters for variations in the distinct flow fields w.r.t distance from the plate. Variation in the skin friction for the axial and transverse cases are presented in the form of graphs for various parameters. It is observed that with the increase in the order of non-linear convection and value of radiation parameter, the velocity field increases in Casson fluid. The increase in heat absorption parameter and Prandtl number decreases the temperature profile and increase in radiative heat flux parameter increases the temperature profile.     

Depinning Dynamics of Fluid Monolayer on a Quenched Substrate

Langevin simulations are preformed on the depinning dynamics of fluidmonolayer on a quenched substrate. With increase in the strength of thesubstrate, we find for the first time a crossover from elastic crystal tosmectic flows as well as a crossover from smectic to plastic flows above thedepinning. A power-law scaling relationship can be derived between the driftvelocity and the driving force for both the elastic crystal and smecticflows, but fails to be obtained for the plastic flow. The power-lawexponents are found to be no larger than 1 for the elastic crystal flow andlarger than 1 for the smectic flow. The critical driving force and theaveraged intensity of Bragg peaks remain invariant basically in the regimeof smectic flow. A sudden increase in the critical driving force is observedwithin the crossover from the smectic to plastic flows, and the averagedintensity of Bragg peaks shows sudden decreases within the crossovers bothfrom the elastic crystal to smectic flows and from the smectic to plastic flows.The results are helpful for understanding the slip dynamics of fluids on a molecular level.     

Peristaltic Flow of Shear Thinning Fluid via Temperature-Dependent Viscosity and Thermal Conductivity

In this paper Williamson fluid is taken into account to study its peristaltic flow with heat effects. The study is carried out in a wave frame of reference for symmetric channel. Analysis of heat transfer is accomplished by accounting the effects of non-constant thermal conductivity and viscosity and viscous dissipation. Modeling of fundamental equations is followed by the construction of closed form solutions for pressure gradient, stream function and temperature while assuming Reynold's number to be very low and wavelength to be very long. Double perturbation technique is employed, considering Weissenberg number and variable fluid property parameter to be very small. The effects of emerging parameters on pumping, trapping, axial pressure gradient, heat transfer coefficient, pressure rise, velocity profile and temperature are analyzed through the graphical representation. A direct relation is observed between temperature and thermal conductivity whereas the indirect proportionality with viscosity. The heat transfer coefficient is lower for a fluid with variable thermal conductivity and variable viscosity as compared to the fluid with constant thermal conductivity and constant viscosity.     

Dual solutions and stability analysis of flow and heat transfer of Casson fluid over a stretching sheet

The aim of the current study is to find out the dual solutions of the two-dimensional magnetohydrodynamic (MHD) flow of Casson fluid and heat transfer over the stretching sheet. The focus of the study is to examine the linear thermal radiation effects on dual solutions for both the steady and unsteady flow of Casson fluid over the stretching sheet under the influence of uniform magnetic field. The governing equations are formed as system of partial differential equations (PDEs). Using suitable transformations, the system of PDEs are converted into favorable nonlinear system of ordinary differential equations (ODEs). Simulations are performed in Maple 2015 to form the dual solutions in order to achieve the velocity, temperature, skin friction and heat transfer profiles of the Casson fluid over the stretching sheet. It is concluded that the dual solutions for the corresponding model are numerically stable. Furthermore, the upper branch solutions of the Casson fluid profiles are numerically stable as compared to the lower branch solutions. Results indicate that positive Eigen values of the MHD flow of Casson fluid provide stable profiles as compared to the negative Eigen values. It is believed that the current study would provide a base for the dual solution of the other types of the non-Newtonian fluid flows over various categories of surfaces.     

非牛顿流体二维溃坝问题的数值模拟

移动粒子半隐式法(Moving Particle Semi-implicit,MPS)是一种广泛应用于不可压缩自由表面流动的粒子方法。本文通过把非牛顿流体转化为变黏度牛顿流体的处理方法将MPS方法拓展至非牛顿自由表面流动,以Casson流体和Cross流体为例计算了非牛顿流体的二维溃坝问题。将计算结果与前人数据进行了对比,结果吻合较好。同时对比了非牛顿流体与牛顿流体的计算结果,发现非牛顿流体的溃坝前端发展速度较慢。     

Free Convective Nonaligned Non-Newtonian Flow with Non-linear Thermal Radiation

The present study explores the free convective oblique Casson fluid over a stretching surface with non-linear thermal radiation effects. The governing physical problem is modelled and transformed into a set of coupled non-linear ordinary differential equations by suitable similarity transformation, which are solved numerically with the help of shooting method keeping the convergence control of 10^-5 in computations. Influence of pertinent physical parameters on normal, tangential velocity profiles and temperature are expressed through graphs. Physical quantities of interest such as skin friction coefficients and local heat flux are investigated numerically.     

The Mathematical Analysis for Peristaltic Flow of Hyperbolic Tangent Fluid in a Curved Channel

In the present paper, we have investigated the peristaltic flow of hyperbolic tangent fluid in a curved channel. The governing equations of hyperbolic tangent fluid model for curved channel are derived including the effects of curvature. The highly nonlinear partial differential equations are simplified by using the wave frame transformation,long wave length and low Reynolds number assumptions. The reduced nonlinear partial differential equation is solved analytically with the help of homotopy perturbation method (HPM). The physical features of pertinent parameters have been discussed by plotting the graphs of pressure rise and stream functions.     

Numerical Investigation of Micropolar Casson Fluid over a Stretching Sheet with Internal Heating

This theoretical study investigates the microrotation effects on mixed convection flow induced by a stretching sheet. Casson fluid model along with microrotation is considered to model the governing flow problem. The system is assumed to undergo internal heating phenomenon. The governing physical problem is transformed into system of nonlinear ordinary differential equations using scaling group of transformations. These equations are solved numerically using Runge Kutta Fehlberg scheme coupled with shooting technique. Influence of sundry parameters for the case of strong and weak concentration of microelements on velocity, temperature, skin friction and local heat flux at the surface are computed and discussed. Lower skin friction and heat flux is observed for the case of weak concentration(n = 0.5)compared to strong concentration of microelements(n = 0.0) near the wall.     

微管换热器流动与传热的实验研究

本文对自制微管换热器的流动与传热性能进行了实验研究。提出了微细圆管换热器管内单相强制对流换热努摩尔数准则式,并与已有相关文献提出的关联式做了对比,结果表明:微管管内换热系数比常规尺度计算公式预测值要高,同时本文分析了微细管内的压力降、摩擦阻力系数f随雷诺数的关系。研究表明微管管内压降、摩擦系数都比常规尺度预测值要高。     

A New Numerical Solution of Fluid Flow in Stratigraphic Porous Media

A new numerical technique based on a lattice-Boltzmann method is presented for analyzing the fluid flow in stratigraphic porous media near the earth's surface. The results obtained for the relations between porosity, pressure, and velocity satisfy well the requirements of stratigraphic statistics and hence are helpful for a further study of the evolution of fluid flow in stratigraphic media.