Flow of viscoelastic fluids through an abrupt contraction

Summary Developing and fully developed velocity profiles were measured for viscoelastic fluids flowing through an abrupt 2 to 1 glass-contraction. An R 16Weissenberg-Rheogoniometer was used to measure the rheological properties of the viscoelastic fluids in the shear rates range of interest in the contraction. The measured entry lengths for the viscoelastic fluids were significantly less than predictions and experimental values for inelastic fluids with the same power-law parameters. Deviations from inelastic entry behaviour ranged from 11.6–100%, were independent ofReynolds number, but were strongly dependent on the ratio of the friction velocity to the shear wave velocity. Increasing the friction velocity relative to the shear wave velocity resulted in an increased deviation from inelastic behaviour. When the friction velocity was of the same order as the shear wave velocity a zero entry length and a fully developed entry velocity profile were observed. Further increase in the friction velocity relative to the shear wave velocity resulted in anomalous entry behaviour accompanied by unusual flow patterns upstream of the contraction.

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Zusammenfassung Es wurden sich bildende sowie voll ausgebildete Geschwindigkeitsprofile viskoelastischer Flüssigkeiten in einer scharfkantigen Rohrverengung von 2 zu 1 gemessen. Ein Weissenbergsches Rheogoniometer R 16 diente zur Charakterisierung der viskoelastischen Flüssigkeiten im betreffenden Deformationsgeschwindigkeitsbereich.Meßergebnisse für die Einlauflänge viskoelastischer Flüssigkeiten weichen bedeutend von den Voraussagen sowie von Meßergebnissen für unelastische Flüssigkeiten ab, die, nach demOstwald- de Waeleschen Modell berechnet, die gleichen Kenngrößen aufzeigen.Die Abweichung vom viskosen Einlaufverhalten beträgt 11,6 bis 100%. Sie ist unabhängig von der Reynoldschen Zahl, hängt aber sehr stark ab von dem Verhältnis zwischen zwei Geschwindigkeiten u^*=Schubspannungsgeschwindigkeit undu=Scherwellengeschwindigkeit.Eine Erhöhung vonu ^* gegenüberu verursacht eine erhöhte Abweichung vom unelastischen Verhalten. Wenn die zwei Geschwindigkeitenu ^* undu von der gleichen Größenordnung sind, verschwindet die Einlaufsentwicklung und ein vollausgebildetes Geschwindigkeitsprofil tritt schon am Eingang auf. Ein weiteres Erhöhen vonu ^* überu verursacht anomales Einlaufverhalten mit ungewöhnlichem Strömungsbild oberhalb der Verengung.

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On Sabbatical Leave: Dept. of Chemical Engineering, University of Toronto, Toronto 181, Ontario, Canada.     

Integral equation formulation for buoyancy-driven convection problems

An integral equation formulation for buoyancy-driven convection problems is developed and illustrated. Buoyancy-driven convection in a bounded cylindrical geometry with a free surface is studied for a range of aspect ratios and Nusselt numbers. The critical Rayleigh number, the nature of the cellular motion, and the heat transfer enhancement are computed using linear theory. Green's functions are used to convert the linear problem into linear Fredholm integral equations. Theorems are proved which establish the properties of the eigenvalues and eigenfunctions of the linear integral operator which appears in these equations.     

Some hydrodynamic aspects of 3-phase inverse fluidized bed

Hydrodynamics of 3-phase inverse fluidized bed is studied experimentally using low density particles for different liquid and gas velocities. The hydrodynamic characteristics studied include pressure drop, minimum liquid and gas fluidization velocities and phase holdups. The minimum liquid fluidization velocity determined using the bed pressure gradient, decreases with increase in gas velocity. The axial profiles of phase holdups shows that the liquid holdup increases along the bed height, whereas the solid holdup decreases down the bed. However, the gas holdup is almost uniform in the bed.     

Dual solutions in mixed convection with variable physical properties

Assisting and opposing flows in a mixed convection boundary layer flow over an isothermal vertical plate are studied for the case of variable physical properties and uniform free stream. Fluid viscosity and thermal conductivity are assumed to be linear functions of temperature. Using local similarity the flow and heat transfer quantities are found to be functions of four parameters, i.e. Richardson number, Prandtl number, a viscosity variation parameter and a thermal conductivity variation parameter. Numerical solutions are obtained by two methods, a shooting technique and Nachtsheim-Swigert technique, for selected values of parameters appropriate for the fluids considered and specific temperatures of the plate and ambient fluid. For assisting flows, there exist solutions for all values of Richardson number while for opposing flows solutions exist only for a finite set of its values and, in addition, there also exist dual solutions. Important flow and heat transfer quantities of practical interest are determined and the influence of different parameters is discussed.     

Effect of viscous dissipation on natural convection heat and mass transfer from vertical cone in a non-Newtonian fluid saturated non-Darcy porous medium

In this paper we investigate the influence of viscous dissipation and Soret effect on natural convection heat and mass transfer from vertical cone in a non-Darcy porous media saturated with non-Newtonian fluid. The surface of the cone and the ambient medium are maintained at constant but different levels of temperature and concentration. The Ostwald-de Waele power law model is used to characterize the non-Newtonian fluid behavior. The governing equations are non-dimensionalized into non-similar form and then solved numerically by local non-similarity method. The effect of non-Darcy parameter, viscous dissipation parameter, Soret parameter, buoyancy ratio, Lewis number and the power-law index parameter on the temperature and concentration field as well as on the heat and mass transfer coefficients is analyzed.     

Synthesis and characterization of Eu doped SrY2O4 phosphor

The present paper reports that TL glow curve and kinetic parameter of Eu³⁺ doped SrY₂O₄ phosphor irradiated by beta source. Sample was prepared by solid state preparation method. Sample was characterized by XRD analysis and particle size was calculated by Debye–Scherrer formula. The sample was irradiated with Sr-90 beta source giving a dose of 10 Gy and the heating rate used for TL measurements are 6.7 °C/s. The samples display good TL peaks at 106 °C, 225 °C and 382 °C. The corresponding kinetic parameters are calculated. The photoluminescence excitation spectrum at 247 and 364 nm monitored with 400 nm excitation and the corresponding emission peaks at 590, 612 and 624 nm are reported.     

Diffusion tensor magnetic resonance imaging of the normal breast

Purpose

The objective of this study was to evaluate diffusion anisotropy of the breast parenchyma and assess the range and repeatability of diffusion tensor imaging (DTI) parameters in normal breast tissue.

Materials and Methods

The study was approved by our institutional review board and included 12 healthy females (median age, 36 years). Diffusion tensor imaging was performed at 1.5 T using a diffusion-weighted echo planar imaging sequence. Diffusion tensor imaging parameters including tensor eigenvalues (λ₁, λ₂, λ₃), fractional anisotropy (FA) and apparent diffusion coefficient (ADC) were measured for anterior, central and posterior breast regions.

Results

Mean normal breast DTI measures were λ₁=2.51×10⁻³ mm²/s, λ₂=1.89×10⁻³ mm²/s, λ₃=1.39×10⁻³ mm²/s, ADC=1.95±0.24×10⁻³ mm²/s and FA=0.29±0.05 for b=600 s/mm². Significant regional differences were observed for both FA and ADC (P<.05), with higher ADC in the central breast and higher FA in the posterior breast. Comparison of DTI values calculated using b=0, 600 s/mm² vs. b=0, 1000 s/mm², showed significant differences in ADC (P<.001), but not FA. Repeatability assessment produced within-subject coefficient of variations of 4.5% for ADC and 11.4% for FA measures.

Conclusion

This study demonstrates anisotropy of water diffusion in normal breast tissue and establishes a normative range of breast FA values. Attention to the influence of breast region and b value on breast DTI measurements may be important for clinical interpretation and standardization of techniques.     

Thermal dispersion effects on non-Darcy natural convection over horizontal plate with surface mass flux

Summary The effect of surface mass flux on the non-Darcy natural convection over a horizontal flat plate in a saturated porous medium is studied using similarity solution technique. Forchheimer extension is considered in the flow equations. The suction/injection velocity distribution has been assumed to have power function form Bx ^l , similar to that of the wall temperature distribution Ax ⁿ , where x is the distance from the leading edge. The thermal diffusivity coefficient has been assumed to be the sum of the molecular diffusivity and the dynamic diffusivity due to mechanical dispersion. The dynamic diffusivity is assumed to vary linearly with the velocity component in the x direction, i.e. along the hot wall. For the problem of constant heat flux from the surface (n=1/2), similarity solution is possible when the exponent l takes the value −1/2. Results indicate that the boundary layer thickness decreases whereas the heat transfer rate increases as the mass flux parameter passes from the injection domain to the suction domain. The increase in the thermal dispersion parameter is observed to favor the heat transfer by reducing the boundary layer thickness. The combined effect of thermal dispersion and fluid suction/injection on the heat transfer rate is discussed. Received 7 December 1995; accepted for publication 7 January 1997