COMBINED FORCED AND FREE CONVECTION IN BOUNDARY LAYER FLOW OF NON-NEWTONIAN FLUID ON A HORIZONTAL PLATE

An analysis is presented to study the effects of buoyancy-induced streamwise pressure gradients on laminar forced convection heat transfer to non-Newtonian fluids from a horizontal plate. Numerical solution of the transformed boundary layer equations has been carried out for different values of the flow behavior index and the buoyancy parameter by means of the local nonsimilarity method. A discussion is provided for the effect of the buoyancy force on the friction factor, the dimensionless heat transfer rate and the details of the velocity as well as temperature fields.     

NON-NEWTONIAN POWER-LAW FLUID FLOW PAST A SHRINKING SHEET WITH SUCTION

The steady boundary-layer flow of a non-Newtonian fluid, represented by a power-law model, over a shrinking sheet is investigated. The transformed boundary-layer equation is solved numerically for some values of the power-law index n and suction parameter s. The effects of these parameters on the skin friction coefficient are analyzed and discussed. Different from those of a stretching sheet, the solutions are not unique and exist only if adequate suction on the boundary is imposed.     

FURTHER RESULTS ON HYDROMAGNETIC BOUNDARY-LAYER FLOW OF A NON-NEWTONIAN POWER-LAW FLUID OVER A CONTINUOUSLY MOVING SURFACE WITH SUCTION

The flow of a non-Newtonian, power-law conducting fluid under the effect of a constant transverse magnetic field is considered. The flow is produced by a plate moving with constant velocity in a calm fluid. The plate is porous and fluid can either be sucked or injected through it. The boundary layer equations are transformed into a nondimensional form and are solved with a finite difference method. Part of this problem has been investigated in the past but only for suction and pseudo-plastic fluids. However, all flows of the present work reach an asymptotic state and exact analytical solutions exist for Newtonian fluids. In the present work we extend the investigation to both pseudo-plastic Newtonian and dilatant fluids in both suction and injection cases.     

FLOW OF A NON-NEWTONIAN FLUID WITH HEAT TRANSFER ABOVE A ROTATING DISK CONSIDERING THE ION SLIP

The steady flow and heat transfer of a conducting non-Newtonian fluid due to the rotation of an infinite nonconducting disk in the presence of an axial uniform steady magnetic field are studied considering the ion slip. The governing nonlinear equations are solved numerically using finite differences, and the solution shows that the ion slip and the non-Newtonian fluid characteristics give some interesting results.     

FLOW OF A NON-NEWTONIAN FLUID WITH HEAT TRANSFER ABOVE A ROTATING DISK CONSIDERING THE ION SLIP

The steady flow and heat transfer of a conducting non-Newtonian fluid due to the rotation of an infinite nonconducting disk in the presence of an axial uniform steady magnetic field are studied considering the ion slip. The governing nonlinear equations are solved numerically using finite differences, and the solution shows that the ion slip and the non-Newtonian fluid characteristics give some interesting results.     

MASS TRANSFER AND HYDRODYNAMICS IN AN AIRLIFT REACTOR WITH VISCOUS NON-NEWTONIAN FLUID

In an internal loop airlift reactor of 55L working volume,the gas-liquid volumetric oxygenmass transfer coefficient k_Lα,gas holdup ε_G and liquid circulation time t_c were measured with the sol-ution of carboxymethyl cellulose(CMC)to simulate the performance of a reactor with highly viscousbroth.Electric conductivity and oxygen probes were used to measure the local gas holdup,liquidcirculation time and oxygen mass transfer coefficient in the individual sections of the reactor(riser,downcomer and the gas-liquid separating section at the top of the reactor)and the total reactor,respectively.The values of k_Lα for the riser,downcomer and separation sections of the reactor were alsoestimated and compared with that for the total reactor.The results show that,both k_Lα and ε_G in-crease but t_c decreases with increasing gas velocity.Correlations and comparisons with works reportedin the literature are also presented.Data show that the methods developed for k_Lα measurements inthe individual section and     

圆管内含颗粒幂律流体的密相两相湍流

阐述了幂律流体控制方程的特点,研究了幂律流体的稠度系数和流动指数的变化对两相流动的影响.随着流动指数的增加,幂律流体在圆管中心附近的主流速度减小,同时颗粒相速度在圆管中心附近增大,而在管壁附近减小.随着稠度系数的增加,幂律流体和颗粒相的主流速度分布出现了与流动指数带来的影响相似的趋势.对带颗粒的幂律流体的两相流流动与液固两相流流动做了比较,幂律流体两相流的流体速度在管道中心附近的大部分区域比液固两相流的流体速度流动的速度大,而颗粒相的速度分布比较平坦.     

MIXED CONVECTION BOUNDARY LAYER FLOW OF A MICROPOLAR FLUID ON A HORIZONTAL PLATE

An analysis is performed to study the heat transfer characteristics of laminar mixed convection boundary layer flow of a micropolar fluid past a semi-infinite horizontal fiat plate with variable surface heat flux. A nonsimilar mixed convection parameter £ and a pseudosimilarity variable v are introduced to cast the governing boundary layer equations into a system of dimensionless equations, which are solved numerically using the finite difference method. A single mixed convection parameter is used to cover the entire regime of mixed convection from the pure forced convection limit to the pure free convection limit. The effect of material parameters, the power-law variation of surface heat flux, nonsimilar mixed convection parameter and Prandtl number are considered. The micropolar fluids are observed to display drag reduction and reduced surface heat transfer rate when compared to Newtonian fluids. The effect of the buoyancy force results in the enhancements of friction factor, heat transfer rate and wall couple stress.     

A STUDY OF NON-NEWTONIAN FLOW AND HEAT TRANSFER OVER A NON-ISOTHERMAL WEDGE USING THE HOMOTOPY ANALYSIS METHOD

The thermoconvective boundary layer flow of a generalized third-grade viscoelastic power-law non-Newtonian fluid over a porous wedge is studied theoretically. The free stream velocity, the surface temperature variations, and the injection velocity at the surface are assumed variables. A similarity transformation is applied to reduce the governing partial differential equations for mass, momentum, and energy conservation to dimensionless, nonlinear, coupled, ordinary differential equations. The homotopy analysis method (HAM) is employed to generate approximate analytical solutions for the transformed nonlinear equations under the prescribed boundary conditions. The HAM solutions, in comparison with numerical solutions (fourth-order Runge-Kutta shooting quadrature), admit excellent accuracy. The residual errors for dimensionless velocity and dimensionless temperature are also computed. The influence of the “power-law” index on flow characteristics is also studied. The mathematical model finds important applications in polymeric processing and biotechnological manufacture. HAM holds significant promise as an analytical tool for chemical engineering fluid dynamics researchers, providing a robust benchmark for conventional numerical methods.     

A MATHEMATICAL MODEL FOR LAMINAR DISPLACEMENT OF ONE NON-NEWTONIAN FLUID BY ANOTHER IN HORIZONTAL CONCENTRIC ANNULI

This paper develops a mathematical model and a computational algorithm, which enable the prediction of laminar displacement efficiency in concentric horizontal annuli. Power-law model is used to characterize rheological properties of both displaced and displacing fluids. This model allows a careful investigation of individual effects of various parameters such as fluid rheology, flow geometry and displacement rate on the displacement efficiency. Simulated results demonstrate the dominant influence of rheological properties of displaced and displacing fluids on the laminar displacement efficiency. The model can be used to optimize fluid flow parameters in chemical process designs.     

A MATHEMATICAL MODEL FOR LAMINAR DISPLACEMENT OF ONE NON-NEWTONIAN FLUID BY ANOTHER IN HORIZONTAL CONCENTRIC ANNULI

This paper develops a mathematical model and a computational algorithm, which enable the prediction of laminar displacement efficiency in concentric horizontal annuli. Power-law model is used to characterize rheological properties of both displaced and displacing fluids. This model allows a careful investigation of individual effects of various parameters such as fluid rheology, flow geometry and displacement rate on the displacement efficiency. Simulated results demonstrate the dominant influence of rheological properties of displaced and displacing fluids on the laminar displacement efficiency. The model can be used to optimize fluid flow parameters in chemical process designs.     

UNSTEADY MIXED CONVECTION WITH SORET AND DUFOUR EFFECTS PAST A POROUS PLATE MOVING THROUGH A BINARY MIXTURE OF CHEMICALLY REACTING FLUID

This study investigates the unsteady mixed convection flow past a vertical porous flat plate moving through a binary mixture in the presence of radiative heat transfer and nth-order Arrhenius type of irreversible chemical reaction by taking into account the diffusion-thermal (Dufour) and thermo-diffusion (Soret) effects. Assuming an optically thin radiating fluid and using a local similarity variable, the governing nonlinear partial differential equations have been transformed into a set of coupled nonlinear ordinary differential equations, which are solved numerically by applying shooting iteration technique together with fourth-order Runge-Kutta integration scheme. Graphical results for the dimensionless velocity, temperature, and concentration distributions are shown for various values of the thermophysical parameters controlling the flow regime. Finally, numerical values of physical quantities, such as the local skin-friction coefficient, the local Nusselt number, and the local Sherwood number are presented in tabular form.     

OSCILLATORY FLOW OF FOURTH-ORDER FLUID IN A POROUS HALF SPACE

This work describes the incompressible flow of fourth-order fluid in a porous half space. The flow in the porous space is caused by the porous plate oscillations in its own plane. Modified Darcy's law has been taken into account to discuss the flow characteristics in a porous space. Numerical solution of the governing nonlinear problem is obtained and the effects of various pertinent parameters are discussed.     

UNSTEADY FLUID AND HEAT FLOW INDUCED BY A STRETCHING SHEET WITH MASS TRANSFER AND CHEMICAL REACTION

The effect of chemical reaction on the flow, heat, and mass transfer within a viscous fluid on an unsteady stretching sheet is examined. The stretching rate, temperature and concentration of the sheet, and the chemical reaction rate are assumed to vary with time. The time-dependent boundary layer equations governing the flow are reduced through a convenient similarity transformation to a set of ordinary differential equations, which are numerically solved by applying the fourth-order Runge-Kutta-Fehlberg scheme with the shooting technique. Results for the velocity, temperature, and concentration distributions as well as the wall temperature and concentration gradients are presented graphically for various values of the unsteadiness parameter A, Prandtl number Pr, Schmidt number Sc, and chemical reaction parameter γ.     

UNSTEADY MAGNETOHYDRODYNAMIC NON-NEWTONIAN FLOW DUE TO NON-COAXIAL ROTATIONS OF DISK AND A FLUID AT INFINITY

An analysis is carried out to study the flow generated in a semi-infinite expanse of an incompressible second-grade fluid bounded by a porous oscillating disk. The flow is due to non-coaxial rotations of a disk and a fluid at infinity. The fluid is electrically conducting in the presence of a uniform transverse magnetic field. The solutions of the developed flow are obtained for the cases when the angular velocity is greater than, smaller than, or equal to the frequency of oscillation. The velocity field is found analytically by a Laplace transform technique. It is found that for uniform suction and blowing at the disk, shear oscillations are confined to the Ekman-Hartmann layer near the disk for all values of the frequencies.     

含油轴承非牛顿流体动力润滑理论的推导

选用幂指式流变模型τ=mγn作为非牛顿流体的本构方程。推导了描述多孔介质内渗流规律的变形达西公式及多孔质滑动轴承的变形雷诺方程。结果分析表明我们所得到的变形雷诺方程数学表达式具有普遍意义 ,从而为分析非牛顿流体润滑的含油轴承的润滑性能提供了理论分析基础。     

DYNAMIC BEHAVIOR OF FLUID FLOW THROUGH A VERTICAL TUBE INTO A SEALED TANK FILLED WITH GAS

This paper describes a model of the unsteady filling process that occurs when liquid entraps air in sealed lank vented by a vertical round tube. A mathematical model is developed to predict the pressure fluctuation of the closed tank and the rate of transfer of liquid into the tank. A drift-flux model is used to describe the two-phase effects in the tube with particular attention being focused on the boundary condition at the bottom of the tube. The experimental setup consists of flow of water from a constant head reservoir into a sealed tank through a single vertical tube. The pressure in the sealed tank is measured using a pressure transducer. Experiments are run with tubes of varying diameter and lengths. The agreement of the theoretical model with the experimentally measured pressure fluctuation is quite good.     

卧式双轴T型搅拌器在非牛顿流体中的搅拌功率特性

考察了卧式双轴Ｔ型搅拌在非牛顿流体中的搅拌功率与表观雷诺数（Ｒｅ＾＊）、弗劳德数（Ｆｒ）以及加料量的变化关系,实验结果表明：Ｍｅｔｚｎｅｒ常数Ｋｓ随加料量的减少而急剧增加;在层流区域,Ｎｐ．Ｒｅ＝Ｋｐ关系仍然成立且非牛顿流体功率曲线与牛顿流体重合。对实验数据进行关联得到了非牛顿流体搅拌功率准数关联式。     

DYNAMIC BEHAVIOR OF FLUID FLOW THROUGH A VERTICAL TUBE INTO A SEALED TANK FILLED WITH GAS

This paper describes a model of the unsteady filling process that occurs when liquid entraps air in sealed lank vented by a vertical round tube. A mathematical model is developed to predict the pressure fluctuation of the closed tank and the rate of transfer of liquid into the tank. A drift-flux model is used to describe the two-phase effects in the tube with particular attention being focused on the boundary condition at the bottom of the tube. The experimental setup consists of flow of water from a constant head reservoir into a sealed tank through a single vertical tube. The pressure in the sealed tank is measured using a pressure transducer. Experiments are run with tubes of varying diameter and lengths. The agreement of the theoretical model with the experimentally measured pressure fluctuation is quite good.     

倾斜压差移动床中的气固流动

应用散体力学及多相流理论,分析倾斜压差移动床中的气固流动,推导出倾斜压差移动床的力平衡方程和空隙率方程,从而使计算固定床压降及气体流率的Ergun方程、Lewis方程及Kwank方程,可以普遍地适用于垂直和倾斜的移动床压降及气体流率的计算。 选用三种颗料状物料,在四种不同倾斜度的斜管中测定了不同负压差和固体流率条件下的气体流率。计算结果与大量实验数据吻合。