The analysis of the flow of a micropolar fluid between two orthogonally moving porous disks with counter rotating directions

The present work investigates the unsteady, imcompressible flow of a micropolar fluid between two orthogonally moving porous coaxial disks. The lower and upper disks are rotating with the same angular speed in counter directions. The flows are driven by the contraction and the rotation of the disks. An extension of the Von Kármán type similarity transformation is proposed and is applied to reduce the governing partial differential equations (PDEs) to a set of non-linear coupled ordinary differential equations (ODEs) in dimensionless form. These differential equations with appropriate boundary conditions are responsible for the flow behavior between large but finite coaxial rotating disks. The analytical solutions are obtained by employing the homotopy analysis method. The effects of some various physical parameters like the expansion ratio, the rotational Reynolds number, the permeability Reynolds number, and micropolar parameters on the velocity fields are observed in graphs and discussed in detail.     

Rotation effect on near-wall turbulence statistics and flow structures

Turbulent flow in an axially rotating pipe, involving complicated physical mecha- nism of turbulence, is a typical problem for the study of rotating turbulent flow. The pipe rotation induces two effects on the flow. One is the stabilizing effect due to the centrifu- gal and Coriolis forces, which accounts for the relaminarization of the turbulence[1—3] and the reduction of the friction coefficient at the pipe wall. The behavior is also related to the wall streaks inclining to the azimuthal di…     

Entropy generation minimization and statistical declaration with probable error for skin friction coefficient and Nusselt number

Main emphasis of present work is to analyze the novel feature of entropy generation in MHD nanomaterial flow between two rotating disks. Heat transfer process is explored in the presence of Joule heating and thermal radiation. Tiwari–Das nanofluid model is employed in mathematical modeling. Aluminum oxide and copper water nanoparticles are accounted. Statistical declaration and probable error for problem accuracy are computed. Total entropy generation subject to Bejan number is scrutinized. Suitable variables are utilized to transform nonlinear PDEs to ordinary ones. Convergent series solutions are computed. Zeroth and mth order problems are discussed for stability analysis. The impact of physical flow variables like Reynolds number, magnetic parameter, porosity parameter, stretching parameter, rotational parameter, radiation parameter, Eckert number, suction injection parameter, Brinkman number and temperature ratio parameter on velocities, temperature, total entropy generation and Bejan number are examined and discussed through graphs. Velocity and thermal gradients at the surface of disks are computed.     

A steadily rotating plasma disk

A homogeneously rotating plasma disk can be formed in a radially directed Ar-arc discharge at reduced pressure with an externally applied axial magnetic field. The radial pressure distribution is measured, as well as the emitted continuum radiation and the arc voltage. With these experimental values profiles of temperature, radial and azimuthal current density, and flow velocity in the disk are evaluated. Viscosity determines the flow pattern essentially. The effects of magnetic field and rotational motion on the discharge are investigated. The disk exhibits at nonrigid rotation a strong centrifugal force and a minor Coriolis force. A weak double vortex is found to develop in the meridional plane. The electric field in the discharge is altered by the azimuthal plasma flow.     

Unstable Process Identification in a Pure Thermal Plume under Forced Rotating Conditions

A pure thermal plume development arising from a finite-size rotating heat source was analyzed experimentally. Qualitative investigation through extensive visualization has brought into focus the existence of a threshold rotation frequency (i.e., a swirl number) above which stretching effects are strengthened, thereby forcing the ascending plume motion to spiral around the geometrical axis heat source. Nevertheless, above the threshold frequency (i.e., above the swirl number), unstable processes appear through flow field pulsation in close proximity to the heat source; the pulsations literally beat and drive the flow field vicinity. From a strictly quantitative point of view, the data underscore the fact that heat source rotation presents two opposed trends. Below the threshold frequency, the higher the frequency, the more the temperature level is concentrated on the plume axis. In contrast, at the strongest rotation frequencies studied, the opposite is observed. Above the threshold rotating frequency, the characteristic rotating time scale appears to be too short to interact with the characteristic plume time scale. As a consequence, rotation of the heat source enhances transition from laminar to turbulence.     

Variable fluid properties and variable heat flux effects on the flow and heat transfer in a non-Newtonian Maxwell fluid over an unsteady stretching sheet with slip velocity

The effects of variable fluid properties and variable heat flux on the flow and heat transfer of a non-Newtonian Maxwell fluid over an unsteady stretching sheet in the presence of slip velocity have been studied. The governing differential equations are transformed into a set of coupled non-linear ordinary differential equations and then solved with a numerical technique using appropriate boundary conditions for various physical parameters. The numerical solution for the governing non-linear boundary value problem is based on applying the fourth-order Runge-Kutta method coupled with the shooting technique over the entire range of physical parameters. The effects of various parameters like the viscosity parameter, thermal conductivity parameter, unsteadiness parameter, slip velocity parameter, the Deborah number, and the Prandtl number on the flow and temperature profiles as well as on the local skin-friction coefficient and the local Nusselt number are presented and discussed. Comparison of numerical results is made with the earlier published results under limiting cases.     

Heat transfer due to the flow between two moderately rotating porous disks

The problem of the heat transfer due to a viscous incompressible flow between two infinite parallel porous disks is considered. It is assumed that the disks are rotating with moderate angular velocity. The governing equations are solved by a perturbation procedure. The results obtained reveal that the temperature distribution is more or less parabolic, approaching to a linear from as the cross flow decreases.     

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.     

直拉法晶体生长过程非稳态流体热流耦合

为了改善复杂对流形态下的晶体生长品质, 提出了一种改进的格子Boltzmann方法研究非稳态熔体流动和传热的耦合性质. 该方法基于不可压缩轴对称D2Q9模型, 构建了包含旋转惯性力和热浮力等外力项的演化关系, 实现了对轴对称旋转流体的速度、温度和旋转角速度的计算与分析. 结果表明, 非稳态熔体中的流、热耦合性质与格拉斯霍夫数和雷诺数的相互作用有关; 通过调节高雷诺数, 可有效抑制熔体中的自然对流, 改善温度分布, 有助于提高单晶的品质. 数值计算结果与实际硅单晶生长试验均证明了所提方法的正确性及有效性.     

Heat Transfer Study in a Discoidal System: The Influence of an Impinging Jet and Rotation

Abstract

This article presents an experimental study of the local heat transfer on the rotor surface in a discoidal rotor-stator system air-gap in which an air jet comes through the stator and impinges the rotor. To determine the surface temperatures, measurements were taken on the rotor, using an experimental technique based on infrared thermography. A thermal balance was used to identify the local convective heat transfer coefficient. The influence of the axial Reynolds number Re _j and the rotational Reynolds number Re was measured and compared with the data available in the literature. Local convective heat transfer coefficients were obtained for a dimensionless space between the two disks G = 0.01, for Re _j between 0 and 41,666, and for Re between 20,000 and 516,000. The flow data found in the literature can be used to explain the heat transfers in this small space configuration. In fact, the rotating disk can be divided into two influence zones: one dominated by the air jet near the center of the rotor and one affected by both the air jet and rotation. Heat transfers with non zero impinging jets appear to be continuously improved compared to those with no jets, even if the two influence zones mentioned previously are situated differently.     

中等半径比反向旋转圆Couette系统流动稳定性的实验和数值研究

圆Couette系统已成为研究从层流转捩为湍流以及有限几何尺寸对图案选择影响的范例.本文以实验和计算机模拟方法研究中等半径比圆Couette系统的稳定性.考察同轴独立旋转圆筒之间的粘性不可压缩流体运动，推广了经典的Rayleigh离心不稳定性理论，导出稳定性判据，用来定量地确定稳定界限.实验采用了流动显示和激光散射技术.仪器有半径比η=0.699，形状比Γ=18.流动状态相图中的显著特征是新的首次失稳态：当外筒静止或反向旋转时，首次失稳出现具有非零方位角波数的螺旋涡流，在轴向和方位角方向为行进波，而并非与时间无关的Taylor涡.初步实验所得的转捩Reynolds数与数值计算结果一致.实验室和数值实验显示出半径比对图案形成和转捩序列的影响. 关键词：     

Effects of variable properties on MHD heat and mass transfer flow near a stagnation point towards a stretching sheet in a porous medium with thermal radiation

The effect of variable viscosity and thermal conductivity on steady magnetohydrodynamic(MHD) heat and mass transfer flow of viscous and incompressible fluid near a stagnation point towards a permeable stretching sheet embedded in a porous medium are presented,taking into account thermal radiation and internal heat genberation/absorbtion.The stretching velocity and the ambient fluid velocity are assumed to vary linearly with the distance from the stagnation point.The Rosseland approximation is used to describe the radiative heat flux in the energy equation.The governing fundamental equations are first transformed into a system of ordinary differential equations using a scaling group of transformations and are solved numerically by using the fourth-order Rung-Kutta method with the shooting technique.A comparison with previously published work has been carried out and the results are found to be in good agreement.The results are analyzed for the effect of different physical parameters,such as the variable viscosity and thermal conductivity,the ratio of free stream velocity to stretching velocity,the magnetic field,the porosity,the radiation and suction/injection on the flow,and the heat and mass transfer characteristics.The results indicate that the inclusion of variable viscosity and thermal conductivity into the fluids of light and medium molecular weight is able to change the boundary-layer behavior for all values of the velocity ratio parameter λ except for λ = 1.In addition,the imposition of fluid suction increases both the rate of heat and mass transfer,whereas fluid injection shows the opposite effect.     

New type of magnetorotational instability in cylindrical taylor-couette flow

We study the stability of cylindrical Taylor-Couette flow in the presence of combined axial and azimuthal magnetic fields, and show that adding an azimuthal field profoundly alters the previous results for purely axial fields. For small magnetic Prandtl numbers Pm, the critical Reynolds number Re(c) for the onset of the magnetorotational instability becomes independent of Pm, whereas for purely axial fields it scales as Pm-1. For typical liquid metals, Re(c) is then reduced by several orders of magnitude, enough that this new design should succeed in realizing this instability in the laboratory.     

Hall effect on Hartmann flow and heat transfer of a Burgers' fluid

The effect of Hall current on the steady magnetohydrodynamics (MHD) flow of an electrically conducting, incompressible Burgers' fluid between two parallel electrically insulating infinite planes is studied. The MHD flow is generated by applying constant pressure gradient. An external uniform magnetic field normal to the disks is applied. The disks are kept at two different constant temperatures. Exact solutions are obtained for the governing momentum and energy equations. The effects of Hartmann number M, Reynolds number Re, Prandtl number Pr, Eckert number Ec, pressure gradient dp/dx and Hall parameter η are examined.     

Observation of a free-Shercliff-layer instability in cylindrical geometry

We report on observations of a free-Shercliff-layer instability in a Taylor-Couette experiment using a liquid metal over a wide range of Reynolds numbers, Re～10(3)-10(6). The free Shercliff layer is formed by imposing a sufficiently strong axial magnetic field across a pair of differentially rotating axial end cap rings. This layer is destabilized by a hydrodynamic Kelvin-Helmholtz-type instability, characterized by velocity fluctuations in the r-θ plane. The instability appears with an Elsasser number above unity, and saturates with an azimuthal mode number m which increases with the Elsasser number. Measurements of the structure agree well with 2D global linear mode analyses and 3D global nonlinear simulations. These observations have implications for a range of rotating MHD systems in which similar shear layers may be produced.     

内嵌微流道低温共烧陶瓷基板传热性能（英）

随着系统级封装（SIP）所容纳的电子元器件和集成密度迅速增加,传统的散热方法（热通孔、风冷散热等）越来越难以满足系统级封装的热管理需求。低温共烧陶瓷（LTCC）作为常见的封装基板材料之一,设计并研制了三种内嵌于LTCC基板的微流道,其中包括直排型、蛇型和螺旋型微流道（高度为0.3 mm,宽度分别为0.4, 0.5和0.8 mm）。通过数值仿真和红外热像仪测试相结合的方式分析了微流道网络结构、流体质量流量、雷诺数、材料热导率对内嵌微流道LTCC基板换热性能的影响,实验结果表明:当去离子水的流量为10 mL/min,热源等效功率为2 W/cm2时,直排型微流道的LTCC基板最高温度在3.1 kPa输入泵压差下能降低75.4 ℃,蛇型微流道的LTCC基板最高温度在85.8 kPa输入泵压差下能降低80.2 ℃,螺旋型微流道的LTCC基板最高温度在103.1 kPa输入泵压差下能降低86.7 ℃。在三种微流道中,直排型微流道具有最小的雷诺数,在相同的输入泵压差下有最好的散热性能。窄的直排型微流道（0.4 mm）在相同的流道排布密度和流体流量时比宽的微流道（0.8 mm）能多降低基板温度10 ℃。此外,提高封装材料的热导率有助于提高微流道的换热性能。     

Cooling performance of a nanofluid flow in a heat sink microchannel with axial conduction effect

In this work, the forced convection of a nanofluid flow in a microscale duct has been investigated numerically. The governing equations have been solved utilizing the finite volume method. Two different conjugated domains for both flow field and substrate have been considered in order to solve the hydrodynamic and thermal fields. The results of the present study are compared to those of analytical and experimental ones, and a good agreement has been observed. The effects of Reynolds number, thermal conductivity and thickness of substrate on the thermal and hydrodynamic indexes have been studied. In general, considering the wall affected the thermal parameter while it had no impact on the hydrodynamics behavior. The results show that the effect of nanoparticle volume fraction on the increasing of normalized local heat transfer coefficient is more efficient in thick walls. For higher Reynolds number, the effect of nanoparticle inclusion on axial distribution of heat flux at solid–fluid interface declines. Also, less end losses and further uniformity of axial heat flux lead to an increase in the local normalized heat transfer coefficient.     

Convection heat transfer in a Maxwell fluid at a non-isothermal surface

Analysis is carried out to study the convection heat transfer in an upper convected Maxwell fluid at a non-isothermal stretching surface. This is a generalization of the paper by Sadeghy et al. [21] to study the effects of free convection currents, variable thermal conductivity and the variable temperature at the stretching surface. Unlike in Sadeghy et al., here the governing nonlinear partial differential equations are coupled. These coupled equations are transformed in to a system of nonlinear ordinary differential equations and are solved numerically by a finite difference scheme (known as the Keller-Box method) and the numerical results are presented through graphs and tables for a wide range of governing parameters. The results obtained for the flow and heat transfer characteristics reveal many interesting behaviors that warrant further study of nonlinear convection heat transfer.