An exact solution for flow past an accelerated horizontal plate in a rotating fluid with the generalized Oldroyd-B model

In this paper, the generalized Oldroyd-B with fractional calculus approach is used. An exact solution in terms of Fox-H function for flow past an accelerated horizontal plate in a rotating fluid is obtained by using discrete Laplace transform method. A comparison among the influence of various parameters in the Oldroyd-B model and the angular velocity of the fluid on the velocity profiles is made through numerical method in graphic form.

EXACT SOLUTIONS FOR MAGNETOHYDRODYNAMIC FLOW IN A ROTATING FLUID

An analytical solution is obtained for the flow due to solid-body rotations an oscillating porous disk and of a fluid at infinity. Neglecting the induced magnetic field, the effects of the transversely applied magnetic field on the flow are studied. Further, the flow confined between two disks is also discussed. It is found that an infinite number of solutions exist for the flow confined between two disks.

DISTURBANCES TO A ROTATING FLUID WITH A SPHEREMOVING ALONG THE AXIS OF ROTATION

In this paper, the disturbances to a uniformly rotating ideal fluid with a sphere moving steadily along the axis of rotation are analysed by using linearization theory, the equations of disturbance pressure and disturbance stream function governing the stability of motion are derived based on the assumption that the flow is rotational symmetric. The equation of disturbance stream function is analysed with the method of normal modes, and the constraints on wave number and wave velocity of the nontrivial neutral disturbances are established and the exact expression of the neutral disturbances are obtained. The conclusion is drawn that there are three kinds of possible forms of neutral disturbances.

Dedicated to Professor Dr.-Ing. Prof.E.h.Dr.techn.E.h.Dr.h.c. Jurgen Zierep for his 80^(th) birthday Pattern Formation in Rotating Fluids

Flows in nature and technology are often associated with specific structures and pattern. This paper deals with thedevelopment and behaviour of such flow pattern. Flow structures are important for the mass, momentum and energytransport. The behaviour of different flow pattern is used by engineers to obtain an efficient mass and energyconsumption. Mechanical power is transmitted via the momentum of rotating machine parts. Therefore thephysical and mathematical knowledge of these basic concepts is important. Theoretical and experimental investigationsof principle experiments are described in the following. We start with the classical problem of the flowbetween two concentric cylinders where the inner cylinder rotates. Periodic instabilities occur which are calledTaylor vortices. The analogy between the cylindrical gap flow, the heat transfer in a horizontal fluid layer exposedto the gravity field and the boundary layer flow along concave boundaries concerning their stability behaviour isaddressed. The vortex breakdown phenomenon in a cylinder with rotating cover is also described. A generalizationto spherical sectors leads then to investigations with different boundary conditions. The spherical gap flowexhibits interesting phenomena concerning the nonlinear character of the Navier-Stokes equations. Multiple solutionsin the nonlinear regime give rise to different routes during the laminar-turbulent transition. The interactionof two rotating spheres results in flow structures with separation and stagnation lines. Experimental results areconfirmed by numerical simulations.

Numerical and analytical investigations of thermosolutal instability in rotating Rivlin-Ericksen fluid in porous medium with Hall current

Numerical and analytical investigations of the thermosolutal instability in a viscoelastic Rivlin-Ericksen fluid are carried out in the presence of a uniform vertical magnetic field to include the Hall current with a uniform angular velocity in a porous medium. For stationary convection, the stable solute gradient parameter and the rota- tion have stabilizing effects on the system, whereas the magnetic field and the medium permeability have stabilizing or destabilizing effects on the system under certain condi- tions. The Hall current in the presence of rotation has stabilizing effects for sufficiently large Taylor numbers, whereas in the absence of rotation, the Hall current always has destabilizing effects. These effects have also been shown graphically. The viscoelastic effects disappear for stationary convection. The stable solute parameter, the rotation, the medium permeability, the magnetic field parameter, the Hall current, and the vis- coelasticity introduce oscillatory modes into the system, which are non-existent in their absence. The sufficient conditions for the non-existence of overstability are also obtained.

Pattern Formation Around Interacting Bodies in Rotating Fluids

The interaction of bodies like spheres and disks in rotating fluids leads to novel flow structures. The primary swirling flow in circumferential direction is superimposed by a secondary motion in the meridional plane. The flow is visualized by introducing ink through a hole in the center of the axes and distributed radially in the central plane between the interacting bodies. The flow structure depends on the shape of the bodies, their geometrical arrangement and the Reynolds number given by the rotational speed. The observed flow structures gave rise to further investigations with PIV-measurcments and numerical simulations.

The Effects of Wettability on Primary Vortex and Secondary Flow in Three-Dimensional Rotating Fluid

The secondary flow driven by the primary vortex in a cylinder,generating the so called"tea leaf paradox",is fundamental for understanding many natural phenomena,industrial applications and scientific researches.In this work,the effect of wettability on the primary vortex and secondary flow is investigated by the three-dimensional multiphase lattice Boltzmann method based on a chemical potential.We find that the surface wettability strongly affects the shape of the primary vortex.With the increase of the contact angle of the cylinder,the sectional plane of the primary vortex gradually changes from a steep valley into a saddle with two raised parts.Because the surface friction is reduced correspondingly,the core of the secondary vortex moves to the centerline of the cylinder and the vortex intensity also increases.The stirring force has stronger effects to enhance the secondary flow and push the vortex up than the surface wettability.Interestingly,a small secondary vortex is discovered near the three-phase contact line when the surface has a moderate wettability,owing to the interaction between the secondary flow and the curved gas/liquid interface.

Stretching surface in rotating viscoelastic fluid

The boundary layer flow over a stretching surface in a rotating viscoelastic fluid is considered. By applying a similarity transformation, the governing partial differ- ential equations are converted into a system of nonlinear ordinary differential equations before being solved numerically by the Keller-box method. The effects of the viscoelastic and rotation parameters on the skin friction coefficients and the velocity profiles are thor- oughly examined. The analysis reveals that the skin friction coefficients and the velocity in the x-direction increase as the viscoelastic parameter and the rotation parameter in- crease. Moreover, the velocity in the y-direction decreases as the viscoelastic parameter and the rotation parameter increase.

Energy Optimization of Savonius Vertical Axis Wind Turbine

This paper reports a wind-powered water pumping system implemented in rural side of Pakistan. The design methodology presented in this paper shah enhance the efficiency of the existing Savonius turbine＇s performance by modifying it aerodynamically. Blades with different twist angles are designed in Solid Edge and analyzed using computational fluid dynamics （CFD） with ANSYS FLUENT software. Static and rotational analyses are performed to get optimized twist angle and results are highlighted. The performances of the turbine in both static and rotational analyses are compared.

AN EXPERIMENTAL STUDY ON THREE DIMENSIONAL STRUCTURE OF BAROCLINIC WAVY JET STREAM IN A ROTATING ANNULUS SUBJECT TO RADIAL TEMPERATURE GRADIENT

Three dimensional structure of baroclinic wavy jet was experimentally studied in rotating annulus subject to a negative radial temperature gradient. General features of wavy surface jet in the system were obtained. Based on the precise measurements of velocity distribution of the jet with LDV and the three dimensional temperature field in the convective system, three dimensional thermodynamic structures of jet were gained, and by using a correlation of three dimensional disturbed temperature, the unstable mechanism of disturbed temperature of baroclinic fluid in a rotating system was further discussed.

The meridional circulation of the Sun: Observations, theory and connections with the solar dynamo

The meridional circulation of the Sun, which is observed to be poleward at the surface, should have a return flow at some depth. Since large-scale flows like the differential rotation and the meridional circulation are driven by turbulent stresses in the convection zone, these flows are expected to remain confined within this zone. Current observational(based on helioseismology)and theoretical(based on dynamo theory) evidences point towards an equatorward return flow of the meridional circulation at the bottom of the convection zone. Assuming the mean values of various quantities averaged over turbulence to be axisymmetric,we study the large-scale flows in solar-like stars on the basis of a 2D mean field theory. Turbulent stresses in a rotating star can transport angular momentum, setting up a differential rotation. The meridional circulation arises from a slight imbalance between two terms which try to drive it in opposite directions: a thermal wind term(arising out of the higher efficiency of convective heat transport in the polar regions) and a centrifugal term(arising out of the differential rotation). To make these terms comparable,the poles of the Sun should be slightly hotter than the equator. We discuss the important role played by the meridional circulation in the flux transport dynamo model. The poloidal field generated by the Babcock-Leighton process at the surface is advected poleward, whereas the toroidal field produced at the bottom of the convection zone is advected equatorward. The fluctuations in the meridional circulation(with coherence time of about 30-40 yr) help in explaining many aspects of the irregularities in the solar cycle. Finally, we discuss how the Lorentz force of the dynamo-generated magnetic field can cause periodic variations in the large-scale flows with the solar cycle.