ON THE MOMENT COEFFICIENT CALCULATION OF A ROTATING DISK IN A TURBULENT FLUID FLOW

Mixing in co-rotating sinusoidal cavity flows is studied with period, T, and phase shift, a, as parameters. Notice that the main obstacle to uniform mixing is the existence of stable :ower periodic orbits, mixing windows, where uniform mixing takes place, are found in the T— a space u:iing bifurcation analysis. The main advantage of this method is a great saving of the computation time.     

EFFECTS OF HALL CURRENT ON UNSTEADY FLOW OF A SECOND GRADE FLUID IN A ROTATING SYSTEM

Rotating flow of a second grade conducting fluid on an infinite oscillating plate is investigated when the fluid is permeated by a transverse magnetic field and the Hall effects are taken into account. It is once again found that an asymptotic solution exists in the presence of both suction and blowing at the plate. For fixed magnetic field parameter the boundary layer thickness increases with the increase in Hall parameter. The present analysis is more general than any previous investigations.     

EFFECTS OF HALL CURRENT ON UNSTEADY FLOW OF A SECOND GRADE FLUID IN A ROTATING SYSTEM

Rotating flow of a second grade conducting fluid on an infinite oscillating plate is investigated when the fluid is permeated by a transverse magnetic field and the Hall effects are taken into account. It is once again found that an asymptotic solution exists in the presence of both suction and blowing at the plate. For fixed magnetic field parameter the boundary layer thickness increases with the increase in Hall parameter. The present analysis is more general than any previous investigations.     

二级不可逆反应半分批操作的渐近解

对半分批反应器中等温进行的二级不可逆反应Ａ＋Ｂ→Ｐ进行了分析，在限制性反应物Ａ一次投料，反应物Ｂ连续恒速流加情况下，导出了非线性物料衡算微分方程的渐近解，即ＭＡ＝（Ｖｏ／ｋ）（１＋βｔ）＾ｓ／（Ｖ０／ｋＭＡ０＋Ｎ／Σｎ＝０ｆ＾（ｎ）（０）／（ｋｃｂ０）＾（ｎ＋１）ｅｘｐ（ＫＣｂｏ＾ｔ）－ＮΣｎ－０ｆ＾（ｎ）（ｔ）／（ＫＣｂ０）＾（ｎ＋１）本文将渐近解的结果与数值解的结果进行了比较，二者极为吻合。渐     

BINARY INTERACTION FORCE ON SPHERES II: INVISCID FLUID

A first order correction to the force over an isolated spherical particle in inviscid flow is presented, considering binary sphere-sphere interactions. The two-particle distribution function derived by Drew and Mandyam (1998) is used to calculate the effect of the presence of other particles surrounding a test particle. The calculations are performed for a monodisperse distribution. The introduction of first neighbor particle-particle interactions results in the prediction of forces that depend on particle concentration and concentration gradients. For the case of non-accelerated sphere we obtain forces that oppose particle concentration. When the particles are accelerated we obtain an increase of the virtual-mass coefficient with particle concentration.     

BINARY INTERACTION FORCE ON SPHERES II: INVISCID FLUID

A first order correction to the force over an isolated spherical particle in inviscid flow is presented, considering binary sphere-sphere interactions. The two-particle distribution function derived by Drew and Mandyam (1998) is used to calculate the effect of the presence of other particles surrounding a test particle. The calculations are performed for a monodisperse distribution. The introduction of first neighbor particle-particle interactions results in the prediction of forces that depend on particle concentration and concentration gradients. For the case of non-accelerated sphere we obtain forces that oppose particle concentration. When the particles are accelerated we obtain an increase of the virtual-mass coefficient with particle concentration.     

A NOTE ON WAVE MOTIONS WITH A CYLINDRICAL FLUID INTERFACE STABILIZED BY ROTATION

The Rayleigh's capillary instability of a cylindrical fluid interface can be suppressed by the centrifugal force due to coaxial rotation when the outer fluid is heavier than the inner one. Thus, wave motions on the rotationally stabilized cylindrical interfaces can occur in natural and technological processes, notwithstanding the lack of coherent treatment in the literature. This work provides a supplementary linear analysis of various wave motions in a three-dimensional framework for two-phase inviscid fluid systems with cylindrical interfaces stabilized by rotation. Many previous results found in the literature are recast in a general from. With gravity acting perpendicularly to the rotation axis, the interface disturbance is considered as an externally forced wave motion. The condition for the stability of the gravity-induced interface displacement in a two-phase rotating system is found to be exactly the same as that for the one-phase case such as an air column in a rotating liquid.     

THE EFFECT OF VARIABLE THERMAL CONDUCTIVITY ON MICRO-POLAR FLUID FLOW BY CHEBYSHEV COLLOCATION METHOD

In this article, the authors analyzed the effect of thermal conductivity on unsteady magnetohydrodynamic (MHD) free convection in a micro-polar fluid past a semi-infinite vertical porous plate. The fluid thermal conductivity is assumed to vary as a linear function of temperature. By using the Chebyshev collocation method in the spatial direction and the Crank-Nicolson method in the time direction, the boundary layer equations are transformed into a linear algebraic system. There are several material parameters whose affect on the flow have been studied, for instance, thermal conductivity, radiation, magnetic, micro-polar, suction (or injection) parameters, and Prandtl number. Boundary layer and Boussineq approximations have been introduced together to describe the flow field. The domain of the problem is discretized according to the Chebyshev collocation scheme. The numerical results show that, the values of velocity, angular velocity and temperature profiles approach to the steady state when the time reach to infinity. However, the friction factor has been found to increase as micro-polar and thermal conductivity parameters increase. But it decreases as magnetic parameter increases. Meanwhile, Nusselt number increases as thermal conductivity parameter increases, and vice versa with the micro-polar parameter. Moreover, the local couple stress has been found to decrease as micro-polar and thermal conductivity parameters increase. On the other hand, it increases as magnetic parameter increases.     

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.     

DRAG AND TORQUE ON A SLOWLY TRANSLATING DISK IN A ROTATING FLUID; EFFECTS OF A PLANE WALL, ANOTHER DISK OR A SIDE WALL

A previously presented analytical method for determining the Stokes drag on a disk sedimenting in the presence of fixed boundaries (Davis, 1990) is adapted to the case of a disk translating broadside in a rotating fluid, possibly with relative rotation. By carefully simplifying the potentially lengthy algebra, concise formulations are again developed for the cases of two disks translating together with opposite relative rotations, a disk translating towards a rigid plane that rotates with the fluid and a disk translating within a similarly rotating concentric circular container. Flows that are asymmetric allow the possibility of adjusting the relative rotation so that the disk is torque free. Values of the Taylor number, based on the disk radius, up to 50 are considered.     

MASS TRANSFER WITH HETEROGENEOUS CHEMICAL REACTION OF THE FIRST ORDER IN FALKNER-SKAN FLOW OF A POWER-LAW FLUID

ABSTRACT

Mass transfer with a heterogeneous chemical reaction of the first order in a Falkner-Skan flow of non-Newtonian power-law fluid is investigated. This problem is solved by the method of Laplace transform following the approach suggested by Apelblat (1980 Apelblat , A. ( 1980 ). Chem. Eng. J. , 19 , 19 – 37 . [CSA] [CROSSREF]  [Google Scholar]). The solution is obtained in a closed analytical form.     

MASS TRANSFER WITH HETEROGENEOUS CHEMICAL REACTION OF THE FIRST ORDER IN FALKNER-SKAN FLOW OF A POWER-LAW FLUID

Mass transfer with a heterogeneous chemical reaction of the first order in a Falkner-Skan flow of non-Newtonian power-law fluid is investigated. This problem is solved by the method of Laplace transform following the approach suggested by Apelblat (1980). The solution is obtained in a closed analytical form.     

EXACT SOLUTIONS FOR THE UNSTEADY FLOW OF A BURGERS' FLUID BETWEEN TWO SIDEWALLS PERPENDICULAR TO THE PLATE

This article presents the exact solutions for the unsteady flow of an incompressible Burgers' fluid induced by the impulsive motion of a plate between two sidewalls perpendicular to the plate. Employing the Fourier sine transforms, the expressions for the velocity field, the tangential stresses, and the volume flux are obtained. The obtained solutions satisfy all imposed initial and boundary conditions and in the absence of the sidewalls reduce to the solutions corresponding to the flow over an infinite flat plate. The effect of the material parameters on the velocity field and the tangential stress at the bottom wall is spotlighted by means of the graphical illustrations.     

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.     

FLUID1ZED BED SPRAY GRANULATION AND FILM COATING A NEW METHOD FOR THE INVESTIGATION OF THE COATING PROCESS ON A SINGLE SPHERE

ABSTRACT

The coating and granulation of solid particles in a fluidized bed is a process which converts pumpable and atomizable liquids (solutions, slurries, melts) into granular solids in one step through drying. Although this process has been applied in industry for several years, there is still a lack of understanding the physical fundamentals and the mechanisms by which spherical granules are formed. Hence a new method was developed which allows the direct observation of the subsequent particle-forming mechanisms such as droplet deposition, spreading, wetting and drying. The authors will present a laboratory scale apparatus in which a single freely suspended particle can be coated under well defined and constant coating and drying conditions. With this device, particle-growth-rate and the development of particle morphology were measured and investigated under various experimental conditions.     

FLUID1ZED BED SPRAY GRANULATION AND FILM COATING A NEW METHOD FOR THE INVESTIGATION OF THE COATING PROCESS ON A SINGLE SPHERE

The coating and granulation of solid particles in a fluidized bed is a process which converts pumpable and atomizable liquids (solutions, slurries, melts) into granular solids in one step through drying. Although this process has been applied in industry for several years, there is still a lack of understanding the physical fundamentals and the mechanisms by which spherical granules are formed. Hence a new method was developed which allows the direct observation of the subsequent particle-forming mechanisms such as droplet deposition, spreading, wetting and drying. The authors will present a laboratory scale apparatus in which a single freely suspended particle can be coated under well defined and constant coating and drying conditions. With this device, particle-growth-rate and the development of particle morphology were measured and investigated under various experimental conditions.     

APPLICATION OF THE HOMOTOPY ANALYSIS METHOD (HAM) TO THIN FILM FLOW OF A GENERALIZED SECOND-GRADE FLUID ON A VERTICALLY MOVING BELT

We formulate and apply the homotopy analysis method (HAM) to determine the solution of the nonlinear differential equation governing thin film flow of a generalized second-grade fluid on a vertically moving belt. This problem is also known as the Landau–Levich or drag-out problem, which is the problem of withdrawal of a plate or fiber from a liquid bath. We make use of a modified model that has shear-dependent viscosity and that can predict normal stress differences. The results obtained exhibit the effectiveness and reliability of HAM.     

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.