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Heat transfer characteristics for turbulent flow of heat generating liquid metals between parallel plates with wall heat transfer
Melt-flow instability of extruded polymers - failure criterion and equations of state, and linearized stability analysis in Newtonian fluid, power-law fluid, and elastic fluids
Analysis predicts decrease in fluid viscosity by comparing pressure profile of fluid/gas mixture with that of power-law fluid. Fluid is taken to be viscous, non-Newtonian, and incompressible; the gas to be ideal; the flow to be inertia-free, isothermal, and one dimensional. Analysis assists in design of flow systems for petroleum, coal, polymers, and other materials.
The effective elongational viscosity for an oriented fiber assembly of discontinuous fibers suspended in a viscous matrix fluid is developed for a fiber array with variable overlap length of both symmetric and asymmetric geometries. Further, the relation is developed for a power-law matrix fluid with finite yield stress. The developed relations for a Newtonian fluid reveal that the influence of overlap length upon elongational viscosity may be expressed as a polynomial of second order. The results for symmetric and asymmetric geometries are shown to be equivalent. Finally, for the power-law fluid the influence of fiber aspect ratio on elongational viscosity was shown to be of order m + 1, where m is greater than 0 and less than 1, as compared to 2 for the Newtonian fluid, while the effective yield stress was found to be proportional to the fiber aspect ratio and volume fraction.
The surface of Ganymede, as seen in Voyager images, was greatly modified by tectonic activity. Geologic evidence is consistent with the formation of younger bright terrain by the emplacement of icy material into rift zones formed in the older dark terrain. To better understand the formation of both terrestrial rift zones and bright terrain bands on Ganymede, the mechanics of rift initiation by the growth of necking instabilities in an extending lithosphere are studied. In particular, how an initial, small perturbation in lithosphere thickness at the lithosphere/asthenosphere boundary is amplified by uniform horizontal extension is studied. The lithosphere is treated as a layer of power-law viscous fluid of thickness H overlying a weaker, viscous mantle substrate. In order to assess the relative importance of buoyant upwelling and mechanical instability in rift formation, both density and strength stratification were incorporated into the model.
A solution for the two-dimensional and axisymmetric laminar boundary-layer momentum equation of power-law non-Newtonian fluid is presented. The analysis makes use of the Merk-Chao series solution method originally devised for the flow of Newtonian fluid. The universal functions for the leading term in the series are tabulated for n from 0.2 to 2. Equations governing the universal functions associated with the second and the third terms are provided. The solution together with either Lighthill's formula or Chao's formula constitutes a simple yet general procedure for the calculation of wall shear and surface heat transfer rate. The theory was applied to flows over a circular cylinder and a sphere and the results compared with published data.
Stress is placed on the temperature dependence of both a linear Newtonian rheology and a nonlinear olivine rheology in accounting for narrow mantle flow structures. The boundary-layer theory developed incorporates an arbitrary temperature-dependent power-law rheology for the medium, in order to facilitate the study of mantle plume dynamics under real conditions. Thermal, kinematic, and dynamic structures of mantle plumes are modelled by a two-dimensional natural-convection boundary layer rising in a fluid with a temperature-dependent power-law relationship between shear stress and strain rate. An analytic similarity solution is arrived at for upwelling adjacent to a vertical isothermal stress-free plane. Newtonian creep as a deformation mechanism, thermal anomalies resulting from chemical heterogeneity, the behavior of plumes in non-Newtonian (olivine) mantles, and differences in the dynamics of wet and dry olivine are discussed.
This paper reports the application of a flux-spline scheme to three-dimensional fluid flow problems. The performance of this scheme is contrasted with that of the power-law differencing scheme. The numerical results are compared with reference solutions available in the literature. For the problems considered in this study, the flux-spline scheme is significantly more accurate than the power-law scheme.
The application of a flux-spline scheme to three-dimensional fluid flow is reported. A comparison is made of the performance of this scheme with that of the Power-law differencing scheme. The numerical results are compared with experimental data. For the problem considered in this study, the flux-spline scheme is more accurate than the Power-law. For a prescribed accuracy, the flux-spline scheme requires a far fewer number of grid points. Thus, it has the potential of providing a numerical error-free solution, especially for three-dimensional flows, without requiring an excessively fine grid.
A numerical study is conducted to determine the effect of power-law body forces on a thermally-driven axisymmetric flow field confined between concentric co-rotating spheres. This study is motivated by Spacelab geophysical fluid-flow experiments, which use an electrostatic force on a dielectric fluid to simulate gravity; this force exhibits a (1/r)sup 5 distribution. Meridional velocity is found to increase when the electrostatic body force is imposed, relative to when the body force is uniform. Correlation among flow fields with uniform, inverse-square, and inverse-quintic force fields is obtained using a modified Grashof number.
A numerical study is conducted to determine the effect of power-law body forces on a thermally-driven axisymmetric flow field confined between concentric co-rotating spheres. This study is motivated by Spacelab geophysical fluid-flow experiments, which use an electrostatic force on a dielectric fluid to simulate gravity; this force exhibits a (1/r)sup 5 distribution. Meridional velocity is found to increase when the electrostatic body force is imposed, relative to when the body force is uniform. Correlation among flow fields with uniform, inverse-square, and inverse-quintic force fields is obtained using a modified Grashof number.
A mathematical representation is developed for the behavior of moderately concentrated magnesium-boron carbide suspensions when subjected to electromagnetic stirring or mechanical agitation. A power-law relationship is employed for the apparent non-Newtonian viscosity of the suspension.
Magnetospheric electric-field power spectral densities measured from high-altitude balloons and the Hawkeye 1 satellite are combined in wavenumber space and exhibit a power-law spectrum with index -1.6 + or -0.3 below a wavenumber of 0.05 reciprocal km and index -2.8 + or -0.3 above 2 reciprocal km. This spectrum agrees with that predicted for the inertial subrange of an isotropic homogeneous two-dimensional fluid and for a two-dimensional plasma when energy enters the system at the spectral knee and there exists a viscous dissipation mechanism at large wavenumbers. The wavelength of the spectral knee corresponds to that of folds and curls in the aurora and may be due to an instability of the auroral particle beams.
Choked flow rate and pressure profile data were taken on sequential axially alined inlets of the orifice type, with an orifice length-to-diameter ratio of 0.5. The configuration consisted of two to four inlets spaced at 0.66 and 32 orifice diameters apart. At a spacing of 32 diameters the reduced flow rate appeared to follow the simple power-law relation G(sub r)/G(sub r,1) = N (sup-b), where G(sub r,1) is the reduced flow rate for a single inlet, N is the number of inlets, and b, although temperature dependent, is approximately 0.4. At this spacing the instrumented orifices and spacers gave pressure profiles that dropped sharply at the entrance and partially recovered within each inlet, somewhat independent of N. At low inlet temperature jetting through the last orifice was common. At a spacing of 0.66 diameter fluid jetting through all N inlets was prevalent at low temperatures for each configuration studied, as indicated by the flat pressure profiles and flow rates that were nearlly identical to those for a single orifice inlet. A simplifying relation was developed between the friction loss parameters for flow through N sequential tubes and N sequential inlets. The predicted flow rates for N tubes were in reasonable agreement with the N inlet analysis and followed the simple power-law relation.
Generalized, or power-law, inflation is shown to necessarily exist for a simple, anisotropic, (Bianchi Type-1) cosmology in the Einstein-Cartan gravitational theory with the Ray-Smalley improved energy momentum tensor with spin. Formal solution of the EC field equations with the fluid equations of motion explicitly shows inflation caused by the RS spin angular kinetic energy density. Shear is not effective in preventing inflation in the ECRS model. The relation between fluid vorticity, torsion, reference axis rotation, and shear ellipsoid precession shows through clearly.
Generalized, or power-law, inflation is shown to necessarily exist for a simple, anisotropic (Bianchi Type I) cosmology in the Einstein-Cartan gravitational theory with the Ray-Smalley (RS) improved energy-momentum tensor with spin. Formal solution of the EC field equations with the fluid equations of motion explicitly shows inflation caused by the RS spin angular kinetic energy density.
A new type of self-similar solution of ideal magnetohydrodynamics (MHD) in the nonlinear stage of the undular model (k parallel to B) of the magnetic buoyancy instability (the ballooning instability in fusion plasma physics or the Parker instability in astrophysics) is found through MHD simulation and theory. The linear theory developed agrees well with the simulation in the early (linear) stage. The nonlinear stages of the instability in the simulation show the self-similar evolution. One of the solutions obtained from the nonlinear analysis has the characteristics of nonlinear instability in Lagrangian coordinates; the fluid velocity and the Alfven speed on each magnetic loop increase exponentially with time, because the loop is evacuated by the field-aligned motion of matter resulting from gravitational acceleration. In the later stage of the nonlinear evolution, the solution property changes from exponential to power-law time dependence. The latter corresponds to a force-free expansion solution. The later saturation of the velocity increment is also discussed.
Newtonian flow theory for unsteady flow past oscillating bodies of revolution at very high Mach numbers is completed by adding a centrifugal force correction to the impact pressures. Exact formulas for the unsteady pressure and the stability derivatives are obtained in closed form and are applicable to bodies of revolution that have arbitrary shapes, arbitrary thicknesses, and either sharp or blunt noses. The centrifugal force correction arising from the curved trajectories followed by the fluid particles in unsteady flow cannot be neglected even for the case of a circular cone. With this correction, the present theory is in excellent agreement with experimental results for sharp cones and for cones with small nose bluntness; gives poor agreement with the results of experiments in air for bodies with moderate or large nose bluntness. The pitching motions of slender power-law bodies of revulution are shown to be always dynamically stable according to Newton-Busemann theory.