Steady flow of a micropolar fluid due to a rotating disc

Summary Three-dimensional, axially-symmetric, steady flow of a micropolar fluid, due to a rotating disc, is considered. The resulting equations of motion are solved numerically, for four different combinations of the six parameters involved, using the Gauss-Seidel iterative procedure and Simpson's rule. Results are presented both in tabular and graphical form.     

Surface acoustic waves propagating over a rotating piezoelectric half-space

Surface acoustic waves (SAW) propagating over a piezoelectric half-space rotating at a constant angular rate about a fixed axis are analyzed using the linear theory of piezoelectricity, including Coriolis and centrifugal forces. Rotation sensitivity, the rotation induced change of wave speed, is studied. The dependence of the rotation sensitivity on the orientation of the rotation axis and the orientation of the material is examined. Numerical results for polarized ceramics PZT-5H are presented to show the detailed characteristics of the rotation sensitivity. The implications of the numerical results are discussed for different applications     

An unsteady flow due to eccentrically rotating porous disk and a fluid at infinity

An exact solution of the unsteady Navier-Stokes equations is obtained for the flow due to non-coaxial rotations of a porous disk, executing non-torsional oscillations in its own plane, and a fluid at infinity. It is shown that the infinite number of solutions existing for a flow confined between two disks reduce to a single unique solution in the case of a single disk. The adjustment of the unsteady flow near the rotating disk to the flow at infinity rotating about a different axis is explained.     

Nonlinear waves on a rotating viscous fluid with a cylindrical free surface

Summary An asymptotic theory is developed for the study of nonlinear wave motion of a rotating viscous fluid with a cylindrical free surface. The method used here is based upon a multiple-parameter singular perturbation scheme within the framework of long-wave approximation. Wave speed and a set of asymptotic evolution equations are derived, and a criterion for the instability of the wave motion is defined.     

Splitting of the resonance frequencies of acoustic waves in a rotating compressible fluid

In a rotating compressible fluid bounded by cylindrical walls, the resonance frequencies of acoustic waves propagating along and against the direction of rotation exhibit splitting into two components. The magnitude of such splitting in a model case that can be realized in experiment has been calculated. The results can be of interest for the acoustics of rotating technical devices and for the measurement of velocities of rotating fluids.     

On the slow steady motion of a viscous fluid due to two rotating tori

Summary An approximate solution, correct to order three in a small parameter, is established for the velocity field induced in a viscous fluid by the slow rotation of two tori. The tori possess a common axis and have concentric circular sections. The small parameter is the ratio of the radius of the outer circular section to the distance of the section centre from the axis of rotation. The torque acting on each toroidal surface is also obtained.With 3 Figures     

Penetrative convection in fluid layers with internal heat sources

Summary The stability problem for penetrative convection in a fluid layer that is heated internally is analyzed using the methods of linear instability theory and unconditional nonlinear energy theory. Critical Rayleigh numbers in the case of a constant heat source are determined numerically from both theories. Although it is not known whether exchange of stabilities holds for this problem, a comparison between the linear and nonlinear results suggests that for top temperatures close to 4°C stationary convection is predominant when the heat source is not too large. The nonlinear results delimit a band of Rayleigh numbers where possible subcritical instabilities could arise.     

Thermoelastic plane waves in a rotating solid

Summary Plane waves in a homogeneous and isotropic unbounded thermoelastic solid rotating with a uniform angular velocity are discussed in the context of the generalised thermoelasticity theory of Green and Lindsay. The effects of rotation of the body on the phase velocity, energy loss and decay coefficient are discussed in some detail for waves of small and large frequencies, and for small coupling between the thermal and mechanical fields. Results of earlier works are deduced as particular cases of the more general results obtained here.     

Laminar film condensation due to a rotating disk

Summary Regular perturbation methods are employed to investigate the problem of laminar film condensation on a rotating disk in a large volume of quiescent vapour for small and large rates of cooling at the disk surface. The flow and thermal fields are represented by the Von Karman similar solution. Exact numerical solutions of the similar equations are obtained for the case of steam-water condensation and compared with those derived analytically.     

Thermoconvective waves in a layer with free boundaries

We show that in a thin layer of a liquid, for which the influence of its boundaries is substantial, the propagation of weakly attenuating thermoconvective waves is possible close to and beyond the stability threshold. We obtain the characteristics of weakly attenuating harmonics.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 26, No. 1, pp. 104–111, January, 1974.     

Effects of uniform radial electric field on the MHD heat and fluid flow due to a rotating disk

The flow and heat transfer of an incompressible electrically conducting fluid over a rotating infinite disk are studied in the present paper. The disk finds itself subjected to a uniform normal magnetic field. The particular interest lies in searching for the effects of an imposed radial electric field on the behavior of the physical flow. The gradient of an electric potential generated on the disk penetrates through the fluid and greatly influences the boundary layer formation. The presented model representing the fluid motion is a general case since it reduces to the traditional Karman’s viscous pump when the electric potential is ignored. The governing Navier–Stokes and Maxwell equations of the constructed model together with the energy equation are converted into self-similar forms using suitable similarity transformations. The flow and thermal boundary layers are shown to be much affected by the presence of a uniform radial electric parameter. Some parameters of fundamental physical significance such as the surface shear stresses in the radial and tangential directions and the heat transfer rate are numerically evaluated. The effects of electric conductivity of the disk on the flow and forced convection heat transfer are further discussed.     

Flexural- and capillary-gravity waves due to fundamental singularities in an inviscid fluid of finite depth

Wave motion due to line, point and ring sources submerged in an inviscid fluid are analytically investigated. The initially quiescent fluid of finite depth, covered by a thin elastic plate or by an inertial surface with the capillary effect, is assumed to be incompressible and homogenous. The strengths of the sources are time-dependent. The linearized initial-boundary-value problem is formulated within the framework of potential flow. The perturbed flow is decomposed into the regular and the singular components. An image system is introduced for the singular part to meet the boundary condition at the flat bottom. The solutions in integral form for the velocity potentials and the surface deflexions due to various singularities are obtained by means of a joint Laplace-Fourier transform. To analyze the dynamic characteristics of the flexural- and capillary-gravity waves due to unsteady disturbances, the asymptotic representations of the wave motion are explicitly derived for large time with a fixed distance-to-time ratio by virtue of the Stokes and Scorer methods of stationary phase. It is found that the generated waves consist of three wave systems, namely the steady-state gravity waves, the transient gravity waves and the transient flexural/capillary waves. The transient wave system observed depends on the moving speed of the observer in relation to the minimal and maximal group velocities. There exists a minimal depth of fluid for the possibility of the propagation of capillary-gravity waves on an inertial surface. Furthermore, the results for the pure gravity and capillary-gravity waves in a clean surface can also be recovered as the flexural and inertial parameters tend to zero.     

Surface waves on viscoelastic magnetic fluid film flow down a vertical column

Long-wave perturbation method is employed to solve the nonlinear hydromagnetic stability of a thin electrically conductive viscoelastic fluid film flowing down on the outside surface of a vertical cylinder. As the viscoelastic effect and the magnetic force are introduced into governing equation, the results are more compatible with the practice situation. The modeling results display that the degree of instability in the film flow is further intensified by the lateral curvature of cylinder. It is also observed that by increasing the effect of the magnetic field and by decreasing the viscoelastic effect tends to enhance the stability as traveling down along the vertical cylinder. Moreover, the instability state could be neutralized by controlling the applied magnetic field. The optimum conditions can be found through the use of a system to alter stability of the film flow by controlling the applied magnetic field.     

Thermoelastic plane waves in a rotating isotropic medium

Summary We discuss the theory of thermoelastic wave propagation in a rotating isotropic material. In any given direction there are four waves. In general, all of these waves are attenuated, and none of them is purely dilatational or transverse. Some earlier published results are found to be false.