Effect of Nonlinear Convection on Stratified Flow of Third Grade Fluid with Revised Fourier-Fick Relations

Here thermal dependence conductivity and nonlinear convection features in third-grade liquid flow bounded by moving surface having varying thickness are formulated. Stagnation point flow is considered. Revised FourierFick relations and double stratification phenomena are utilized for modeling energy and concentration expressions. Mathematical model of considered physical problem is achieved by implementing the idea of boundary layer theory. The acquired partial differential system is transformed into ordinary ones by employing relevant variables. The homotopic scheme yield convergent solutions of governing nonlinear expressions. Graphs are constructed for distinct values of physical constraints to elaborate the heat/mass transportation mechanisms.     

Hall Effects on Unsteady Magnetohydrodynamic Flow of a Third Grade Fluid

The unsteady magnetohydrodynamic flow of an electrically conducting viscous incompressible third grade fluid bounded by an infinite porous plate is studied with the Hall effect. An external uniform magnetic field is applied perpendicular to the plate and the fluid motion is subjected to a uniform suction and injection. Similarity transformations are employed to reduce the non-linear equations governing the flow under discussion to two ordinary differential equations （with and without dispersion terms）. Using the finite difference scheme, numerical solutions represented by graphs with reference to the various involved parameters of interest are discussed and appropriate conclusions are drawn.     

重力水平对热毛细-浮力对流耗散结构的影响

为了了解重力水平对环形液池内热毛细-浮力对流耗散结构的影响,利用有限容积法进行了非稳态三维数值模拟,环形液池外壁被加热,内壁被冷却,流体为0．65cSt硅油,其Pr数为6．7。结果表明,在微重力条件下,流动为三维振荡流动;当重力水平增加到0．1go时,流动结构转化为沿周向运动的一组滚胞,其轴线与温度梯度方向一致;当重力...     

Simulation of the Second Grade Fluid Model for Blood Flow through a Tapered Artery with a Stenosis

We analyze the blood flow through a tapered artery, assuming the blood to be a second order fluid model. The resulting nonlinear implicit system of partial differential equations is solved by the perturbation method. The expressions for shear stress, velocity, flow rate, wall shear stress and longitudinal impedance are obtained. The physical behavior of different parameters is also discussed, as are trapping phenomena.     

三阶非线性效应对三次谐波振荡转换的影响

使用快速傅里叶变换和四阶龙格-库塔法,对KDP晶体内以Ⅰ／Ⅱ类角度失谐设置方式的高强度激光三次谐波振荡转换进行了研究,考虑了谐波转换过程中的三阶非线性x^[3]、衍射、离散等效应,并着重研究了KDP晶体的三阶非线性效应对高强度激光三次谐波转换的影响。研究表明,三阶非线性效应降低了三次谐波振荡转换效率,增大了相位扰动对3ω光束的强度调制,然而通过增加二倍频的失谐角△θ8,可以避免三阶非线性效应对三次谐波振荡转换带来的不利影响。     

Thin Film Flow of a Second Grade Fluid over a Stretching/Shrinking Sheet with Variable Temperature-Dependent Viscosity

Effects of variable viscosity on the flow and heat transfer in a thin film on a horizontal porous stretching sheet are analyzed. The steady boundary layer equations for momentum and thermal energy are simplified by using similarity transformations. The resulted and coupled nonlinear differential equations are solved by Homotopy analysis method. The results are presented graphically to interpret various physical parameters appearing in the problem.     

The Fine Transverse Structure of a Vortex Flow Beyond the Edge of a Disc Rotating in a Stratified Fluid

By the methods of schlieren visualization, the evolution of elements of the fine structure of transverse vortex loops formed in the circular vortex behind the edge of a disk rotating in a continuously stratified fluid is traced for the first time. An inhomogeneous distribution of the density of a table-salt solution in a basin was formed by the continuous-squeezing method. The development of periodic perturbations at the outer boundary of the circular vortex and their transformation at the vortex-loop vertex are traced. A slow change in the angular size of the structural elements in the supercritical-flow mode is noted.     

底部加热长方体腔内自然对流的非线性特性

采用SIMPLE算法,QUICK差分格式,对底部加热三维长方体腔内空气的自然对流进行了数值模拟。根据模拟结果,探讨了方腔内流体流动与换热的静态分岔与振荡等非线性现象。数值结果显示,在固定的几何尺寸和不同Ra的情况下,当初始场不同时,会出现若干不同的解,即存在解的静态分岔;在固定的几何尺寸和相同的初始场情况下,低Ra时流动和换热处于稳态,当Ra超过某一临界值时,流动和换热就会随时间振荡,并通过倍周期分岔过渡到混沌;当方腔的几何尺寸不同时,分岔点的特征值Ra也发生变化。     

Conditional Symmetry Groups of Nonlinear Diffusion Equations with x-Dependent Convection and Absorption

The generalized conditional symmetry and sign-invariant approaches are developed to study the nonlinear diffusion equations with x-dependent convection and source terms. We obtain conditions under which the equations admit the second-order generalized conditional symmetries and the first-order sign-invariants on the solutions. Several types of different generalized conditional symmetries and first-order sign-invariants for the equations with diffusion of power law are obtained. Exact solutions to the resulting equations are constructed.     

Optimal Disturbances of Stably Stratified Turbulent Couette Flow

Doklady Physics - Direct numerical simulation data of a stably stratified turbulent Couette flow contains two types of organized structures: the rolls that arise at neutral and close to neutral...     

滑移边界对二维Rayleigh-Bénard热对流流态和传热特性的影响

采用并行直接数值模拟（PDM-DNS）计算无滑移和滑移边界二维Rayleigh-Bénard热对流.与无滑移边界形成的随机羽流运动的湍流热对流不同,滑移边界热对流最终形成湍流特征消失,且温度仅分布于四壁的一个大尺度环流的流动形态.平均场近底板的温度分布特性,无滑移边界逐渐变化而滑移边界出现过冲现象.宽高比Γ=1时,Nusselt数（Nu）随Rayleigh数（Ra）的变化具有相同标度指数,Nu~Ra^0.3.滑移边界热对流具有传热增强作用.滑移边界热对流Nu随Γ变化明显,并分为两个阶段,在Γ=0.5时出现Nu_max≈250,是无滑移边界热流Nu的5倍.     

The Convection Instability of Bhnard-Rayleigh Fluid Under Varied External Force

A new model of Bknard-Rayleigh convection has been put forward from mantle convection and liquid crystal, where the external force deviates from constant to a lineal function of vertical dimension z. The dimensionless parameter ε is induced to describe the scale of this kind of deviations. Through linear stability analyses, we find that even-odd symmetry broken appears. By numerical calculation under rigid boundary conditions, we find that α_c is almost α constant but R_c decreases nonlinearly as ε increases, so the increase of ε benefits convection. When ε=0, all results reduce to the former works automatically.     

Hall Effect on Falkner-Skan Boundary Layer Flow of FENE-P Fluid over a Stretching Sheet

The Falkner-Skan boundary layer steady flow over a flat stretching sheet is investigated in this paper. The mathematical model consists of continuity and the momentum equations, while a new model is proposed for MHD Finitely Extensible Nonlinear Elastic Peterlin (FENE-P) fluid. The effects of Hall current with the variation of intensity of non-zero pressure gradient are taken into account. The governing partial differential equations are first transformed to ordinary differential equations using appropriate similarity transformation and then solved by Adomian decomposition method (ADM). The obtained results are validated by generalized collocation method (GCM) and found to be in good agreement. Effects of pertinent parameters are discussed through graphs and tables. Comparison with the existing studies is made as a limiting case of the considered problem at the end.     

Simulation of Vortex Convection in a Compressible Viscous Flow with Dynamic Mesh Adaptation

In this work, vortex convection is simulated using a dynamic mesh adaptation procedure. In each adaptation period, the mesh is refined in the regions where the phenomena evolve and is coarsened in the regions where the phenomena deviate since the last adaptation. A simple indicator of mesh adaptation that accounts for the solution progression is defined. The generation of dynamic adaptive meshes is based on multilevel refinement/coarsening. The efficiency and accuracy of the present procedure are validated by simulating vortex convection in a uniform flow. Two unsteady compressible turbulent flows involving blade-vortex interactions are investigated to demonstrate further the applicability of the procedure. Computed results agree well with the published experimental data or numerical results.     

Electroosmosis-Optimized Thermal Model for Peristaltic Transportation of Thermally Radiative Magnetized Liquid with Nonlinear Convection

The present study addresses the heat transfer efficiency and entropy production of electrically conducting kerosene-based liquid led by the combined impact of electroosmosis and peristalsis mechanisms. Effects of nonlinear mixed convection heat transfer, temperature-dependent viscosity, radiative heat flux, electric and magnetic fields, porous medium, heat sink/source, viscous dissipation, and Joule heating are presented. The Debye–Huckel linearization approximation is employed in the electrohydrodynamic problem. Mathematical modeling is conducted within the limitations of δ << 1 and Re → 0. Coupled differential equations after implementing a lubrication approach are numerically solved. The essential characteristics of the production of entropy, the factors influencing it, and the characteristics of heat and fluid in relation to various physical parameters are graphically evaluated by assigning them a growing list of numeric values. This analysis reveals that heat transfer enhances by enhancing nonlinear convection and Joule heating parameters. The irreversibility analysis ensures that the minimization of entropy generation is observed when the parameters of viscosity and radiation are held under control. Fluid velocity can be regulated by adjusting the Helmholtz–Smoluchowski velocity and magnetic field strength.     

An MHD Effect on a Newtonian Fluid Flow Due to a Superlinear Stretching Sheet

The preliminary aim of this article is to investigate the effect of magnetohydrodynamic (MHD) flows of a viscous fluid due to a superlinear stretching sheet. These boundary layer flows arise in the industrial processes such as polymer extrusion processes, metal spinning, glass blowing and heat exchangers. The representing frameworks of highly nonlinear partial differential equations are mapped to nonlinear ordinary differential equations with a constant coefficient via similarity transformation and are solved analytically. The results are analyzed by means of various plots to provide the comparison and found to be in better agreement with the classical results of Crane and Pavlov. The viscous fluid due to a superlinear stretching sheet in the presence ofMHDhas enormous amount of nonlinearity in conducting the solution area with different arrangements.     

Invariant Sets and Exact Solutions to Nonlinear Diffusion Equations with x-Dependent Convection and Absorption

In this paper, we introduce a new invariant set Eo={u：ux=f＇（x）F（u）＋ε[g＇（x）-f＇（x）g（x）]F（u）×exp（-∫^u1/F（z）dz）}where f and g are some smooth functions of x, ε is a constant, and F is a smooth function to be determined. The invariant sets and exact sohltions to nonlinear diffusion equation ut = （ D（u）ux）x ＋ Q（x, u）ux ＋ P（x, u）, are discussed. It is shown that there exist several classes of solutions to the equation that belong to the invariant set Eo.     

Flow Reversal of Fully-Developed Mixed MHD Convection in Vertical Channels

The present analysis is concerned with flow reversal phenomena of the fully-developed laminar combined free and forced MHD convection in a vertical parallel-plate channel. The effect of viscous dissipation is taken into account. Flow reversal adjacent to the cold （or hot） wall is found to exist within the channel as Gr/Re is above （or below） a threshold value. Parameter zones for the occurrence of reversed flow are presented.     

Variable Fluid Property Effect on Heat Transfer and Frictional Flow Characteristics of Water Flowing through Microchannel

The effects of temperature-dependent viscosity and thermal conductivity on heat transfer and frictional flow characteristics of water flowing through a microchannel are numerically investigated in this work. The hydrodynamically and thermally developing flow with no-slip, notemperature jump, and constant wall heat flux boundary condition is numerically studied using 2D continuum-based conservation equations. A significant deviation in Nusselt number from conventional theory is observed due to flattening of axial velocity profile due to temperaturedependent viscosity variation. The Nusselt number shows a significant deviation from conventional theory due to flattening of the radial temperature profile due to temperature-dependent thermal conductivity variation. It is noted that the deviation in Nusselt number from conventional theory is maximum for combined temperature-dependent viscosity and thermal conductivity variations. The effects of temperature-dependent viscosity and thermal conductivity on the Fanning friction factor are also investigated. Additionally, the effects of variable fluid properties on Poiseuille number, Prandtl number, and Peclet number are also investigated.     

MHD Three-Dimensional Flow of Viscoelastic Fluid with Convective Surface Boundary Condition

This article reports the magnetohydrodynamic (MHD) three-dimensional flow of viscoelastic fluid over a stretching surface with heat transfer. Mathematical analysis is formulated using convective boundary conditions. Computations of dimensionless velocity and temperature fields are presented. The tabulated values show excellent agreement between present and previous limiting analysis. Graphical results show the impact of embedded parameters entering into the problem.