On the flow of a viscous incompressible fluid between two coaxial rotating porous cylinders

Exact solution of the Navier-Stokes equations for the laminar flow of a viscous incompressible fluid between two coaxial rotating porous cylinders, kept at constant temperatures, has been studied. The rate of injection at one cylinder is taken to be the same as the rate of suction at the other. Expressions for the velocity and temperature distributions and for the torque required to turn the outer cylinder are obtained. The effects of λ (injection parameter), σ (the ratio of the radii of the cylinders) and Pé (Péclet number = λPr) on them are shown graphically.     

On the plane couette flow of a viscous compressible fluid with transpiration cooling

The exact solution for the plane couette flow of a viscous compressible, heat conducting, perfect gas with the same gas injection at the stationary plate and its corresponding removal at the moving plate has been studied. It is found that the gas injection is very helpful in reducing the temperature recovery factor. Effects of injection on the shearing stress at the lower plate, longitudinal velocity profiles and the enthalpy are shown graphically.     

Three-dimensional Couette flow of a dusty fluid with heat transfer

This work is focused on the mathematical modeling of three-dimensional Couette flow and heat transfer of a dusty fluid between two infinite horizontal parallel porous flat plates. The problem is formulated using a continuum two-phase model and the resulting equations are solved analytically. The lower plate is stationary while the upper plate is undergoing uniform motion in its plane. These plates are, respectively, subjected to transverse exponential injection and its corresponding removal by constant suction. Due to this type of injection velocity, the flow becomes three dimensional. The closed-form expressions for velocity and temperature fields of both the fluid and dust phases are obtained by solving the governing partial differential equations using the perturbation method. A selective set of graphical results is presented and discussed to show interesting features of the problem.     

Free convection flow of a second order fluid past a hot vertical plate

Laminar free convection flow of a second order fluid past a hot vertical plate with varying wall temperature has been studied in this paper. Exact solutions for the velocity and temperature fields have been obtained. The effects of elastic coefficient on the velocity and temperature fields, rate of heat transfer and the skin-friction have been studied.     

Entropy generation under the effect of suction/injection

This work investigates entropy generation in a steady flow of viscous incompressible fluids between two infinite parallel porous plates. The fluid temperature variation is due to asymmetric heating of the porous plates as well as viscous dissipation. Two different physical situations are discussed with their entropy generation profiles: (i) Couette flow with suction/injection and (ii) pressure-driven Poiseuille flow with suction/injection. In each case, closed form expressions for entropy generation number and Bejan number are derived in dimensionless form by using the expressions for velocity and temperature which are derived by solving the resulting momentum and energy equations by the method of undetermined coefficient. The effect of the governing parameters on velocity, temperature, entropy generation and Bejan number are extensively discussed with the help of graphs. It is interesting to remark that entropy generation number increases with suction on one porous plate while it decreases on the other porous plate with injection.     

热幅射对抽吸或喷射三维Couette流温度分布的影响

在固定的底板上有横向正弦射流,而匀速运动的多孔介质顶板以常速率完全抽出的情况下,理论分析了热幅射对三维Couette流动温度分布的影响.在这种射流速度下,流动呈现三维流动.利用图形分析了Prandtl数、幅射参数和射流参数对传热速率的影响.Prandtl数对温度分布的影响比射流参数或幅射参数大得多.     

Stability and instability in adiabatic shearing motions of incompressible fluids

We investigate the effect of temperature dependence of the viscosity on the stability of the adiabatic shearing flows of an incompressible Newtonian viscous fluid between two parallel plates. When the viscosity strongly decreases with temperature, the shearing flow caused by a steady motion of the upper plate (steady shearing) becomes unstable, while the shearing flow caused by a time-dependent body force is found to be stable.     

A Mixed Analytical/Numerical Method for Velocity and Heat Transfer of Laminar Power-Law Fluids

This paper presents a relatively simple numerical method to investigate the flow and heat transfer of laminar power-law fluids over a semi-infinite plate in the presence of viscous dissipation and anisotropy radiation. On one hand, unlike most classical works, the effects of power-law viscosity on velocity and temperature fields are taken into account when both the dynamic viscosity and the thermal diffusivity vary as a power-law function. On the other hand, boundary layer equations are derived by Taylor expansion, and a mixed analytical/numerical method (a pseudo-similarity method) is proposed to effectively solve the boundary layer equations. This method has been justified by comparing its results with those of the original governing equations obtained by a finite element method. These results agree very well especially when the Reynolds number is large. We also observe that the robustness and accuracy of the algorithm are better when thermal boundary layer is thinner than velocity boundary layer.     

Unsteady hydromagnetic Couette flow of dusty fluid with temperature dependent viscosity and thermal conductivity under exponential decaying pressure gradient

In the present paper the unsteady Couette flow and heat transfer of a dusty conducting fluid between two parallel plates with temperature dependent viscosity and thermal conductivity are studied. The fluid is acted upon by an exponential decaying pressure gradient and an external uniform magnetic field is applied. The governing coupled momentum and energy equations are solved numerically using finite differences. The effect of the variable viscosity and thermal conductivity of the fluid and the uniform magnetic field on the velocity and temperature fields for both the fluid and dust particles is discussed.     

Generalized couette flow with suction and injection

PART A: The unsteady viscous incompressible flow between two parallel flat plates with suction and injection in presence of a pressure gradient is studied. PART B: An exact solution for temperature distribution at different constant wall temperatures is obtained. It is assumed that the rate of injection at the lower plate equals the rate of suction at the upper plate.     

Effects of chemical reaction and variable viscosity on hydromagnetic mixed convection heat and mass transfer for Hiemenz flow through porous media with radiation

The effect of chemical reaction and variable viscosity on hydromagnetic mixed convection heat and mass transfer for Hiemenz flow through porous media has been studied in the presence of radiation and magnetic field. The plate surface is embedded in a uniform Darcian porous medium in order to allow for possible fluid wall suction or blowing and has a power-law variation of both the wall temperature and concentration. The similarity solution is used to transform the system of partial differential equations, describing the problem under consideration, into a boundary value problem of coupled ordinary differential equations, and an efficient numerical technique is implemented to solve the reduced system. Numerical calculations are carried out, for various values of the dimensionless parameters of the problem, which include a variable viscosity, chemical reactions, radiation, magnetic field, porous medium and power index of the wall temperature parameters. Comparisons with previously published works are performed and excellent agreement between the results is obtained. The results are presented graphically and the conclusion is drawn that the flow field and other quantities of physical interest are significantly influenced by these parameters.     

Numerical study of the flow in a three-dimensional thermally driven cavity

Solutions for the fully compressible Navier–Stokes equations are presented for the flow and temperature fields in a cubic cavity with large horizontal temperature differences. The ideal-gas approximation for air is assumed and viscosity is computed using Sutherland's law. The three-dimensional case forms an extension of previous studies performed on a two-dimensional square cavity. The influence of imposed boundary conditions in the third dimension is investigated as a numerical experiment. Comparison is made between convergence rates in case of periodic and free-slip boundary conditions. Results with no-slip boundary conditions are presented as well. The effect of the Rayleigh number is studied.     

Anyons and the Bose-Fermi duality in the finite-temperature thirring model

Solutions to the Thirring model are constructed in the framework of algebraic quantum field theory. Fermionic solutions exist for all positive temperatures only if the coupling constants is $\lambda = \sqrt {2 (2n + 1) \pi } $ , n ∈ ?. These fermions are not equivalent and become canonical fields only forn=1. In the general case, the solutions are anyons. Different anyons (uncountably many) exist in orthogonal spaces and satisfy dynamic equations (of the Heisenberg “Urgleichung” type) characterized by corresponding values of the statistical parameter, which, in turn, is related to the coupling constant λ. The whole Hilbert space becomes nonseparable with a different Urgleichung satisfied in each sector. This feature is absent from any power expansion in λ, which, being related to the statistical parameter, definitely fails and never reveals the true structure of the theory. The correlation functions in the temperature state for canonically dressed fermions coincide with the ones for the bare fields. This is in agreement with the uniqueness of the τ-Kubo-Martin-Schwinger state over the canonical anticommutation relation algebra (τ being the shift automorphism). The α-anyon two-point function is computed and reproduces the previously known result for a scalar field.     

Local well-posedness to the cauchy problem of the 3-D compressible navier-stokes equations with density-dependent viscosity

In this article, we prove the local existence and uniqueness of the classical solution to the Cauchy problem of the 3-D compressible Navier-Stokes equations with large initial data and vacuum, if the shear viscosity μ is a positive constant and the bulk viscosity λ(ρ) = ρ^β with β ≥ 0. Note that the initial data can be arbitrarily large to contain vacuum states.     

Exact solution of thermal radiation on MHD flow over a stretching porous sheet

The effect of radiation on MHD steady asymmetric flow of an electrically conducting fluid past a stretching porous sheet in the presence of radiation has been analyzed. Exact solutions for the velocity and temperature fields have been derived and the effects of radiation, magnetic, Prandtl number, wall temperature and suction (or injection) parameters have been studied with the help of graphs.     

Unsteady MHD two-phase Couette flow of fluid–particle suspension

The problem of two-phase unsteady MHD Couette flow between two parallel infinite plates has been studied taking the viscosity effect of the two phases into consideration. Unified closed form expressions are obtained for the velocities and the skin frictions for both cases of the applied magnetic field being fixed to either the fluid or the moving plate. The novelty of this study is that we have obtained the solution of the unsteady flow using the Laplace transform technique, D’Alemberts method and the Riemann-sum approximation method. The solution obtained is validated by assenting comparisons with the closed form solutions obtained for the steady states which have been derived separately and also by the implicit finite difference method. Graphical result for the velocity of both phases based on the semi-analytical solutions are presented and discussed. A parametric study of some of the physical parameters involved in the problem is conducted. The skin friction for both the fluid and the particle phases decreases with time on both plates until a steady state is reached, it is also observed to decrease with increase in the particle viscosity on the moving plate while an opposite behaviour has been noticed on the stationary plate.     

二维横观各向同性厚板在空间变化热源及体力作用下的动力学响应

研究热源和体力作用下的横观各向同性厚板的二维问题,板的上表面无应力作用,但有规定的表面温度作用;板的下表面置于刚性基础之上,并处于绝热状态.采用Green和Naghdi提出的广义热弹性理论,通过Laplace和Fourier双重变换,在Laplace-Fourier变换域中,得到位移和温度场的控制方程.数值求解双重变换的逆变换,采用一个基于Fourier级数展开的方法,数值地求解Laplace变换的逆变换.对材料镁(Mg)进行数值计算,并用图形表示其结果.推演出各向同性材料铜(Cu)的数值结果,并用图形与横观各向同性材料镁进行比较.同时研究了体力的影响.     

Numerical study of forced and free convective boundary layer flow of a magnetic fluid over a flat plate under the action of a localized magnetic field

The two-dimensional, steady, laminar, forced and free convective boundary layer flow of a magnetic fluid over a semi-infinite vertical plate, under the action of a localized magnetic field, is numerically studied. The magnetic fluid is considered to be water-based with temperature dependent viscosity and thermal conductivity. The study of the boundary layer is separated into two cases. In case I the boundary layer is studied near the leading edge, where it is dominated by the large viscous forces, whereas in case II the boundary layer is studied far from the leading edge of the plate where the effects of buoyancy forces increase. The numerical solution, for these two different cases, is obtained by an efficient numerical technique based on the common finite difference method. Numerical calculations are carried out for the value of Prandl number Pr =  49.832 (water-based magnetic fluid) and for different values of the dimensionless parameters entering into the problem and especially for the magnetic parameter Mn, the viscosity/temperature parameter Θ _r and the thermal/conductivity parameter S*. The analysis of the obtained results show that the flow field is influenced by the application of the magnetic field as well as by the variation of the viscosity and the thermal conductivity of the fluid with temperature. It is hoped that they could be interesting for engineering applications.     

Group method analysis of magneto-elastico-viscous flow along a semi-infinite flat plate with heat transfer

The group theoretic method is applied for solving problem of the flow of an elastico-viscous liquid past an infinite flat plate in the presence of a magnetic field normal to the plate. The application of one-parameter transformation group reduces the number of independent variables, by one, and consequently the system of governing partial differential equations with boundary conditions reduces to a system of ordinary differential equations with appropriate corresponding conditions. Numerical solution of the velocity field and heat transfer have been obtained. The effect of the magnetic parameter M on velocity field, shear stress, temperature fields and heat transfer has been discussed.     

Numerical study of forced and free convective boundary layer flow of a magnetic fluid over a flat plate under the action of a localized magnetic field

The two-dimensional, steady, laminar, forced and free convective boundary layer flow of a magnetic fluid over a semi-infinite vertical plate, under the action of a localized magnetic field, is numerically studied. The magnetic fluid is considered to be water-based with temperature dependent viscosity and thermal conductivity. The study of the boundary layer is separated into two cases. In case I the boundary layer is studied near the leading edge, where it is dominated by the large viscous forces, whereas in case II the boundary layer is studied far from the leading edge of the plate where the effects of buoyancy forces increase. The numerical solution, for these two different cases, is obtained by an efficient numerical technique based on the common finite difference method. Numerical calculations are carried out for the value of Prandl number Pr =  49.832 (water-based magnetic fluid) and for different values of the dimensionless parameters entering into the problem and especially for the magnetic parameter Mn, the viscosity/temperature parameter Θ _r and the thermal/conductivity parameter S*. The analysis of the obtained results show that the flow field is influenced by the application of the magnetic field as well as by the variation of the viscosity and the thermal conductivity of the fluid with temperature. It is hoped that they could be interesting for engineering applications.