Passive Boundary Layer Flow Control Using Porous Lamination

The flow over a porous laminated flat plate is investigated from a flow control perspective through experiments and computations. A square array of circular cylinders is used to model the porous lamination. We determine the velocities at the fluid–porous interface by solving the two-dimensional Navier–Stokes and the continuity equations using a staggered flow solver and using LDV in experiments. The control parameters for the porous region are porosity, \(\phi \) and Reynolds number, Re, based on the diameter of the circular cylinders used to model the porous lamination. Computations are conducted for \(0.4< \phi < 0.9\) and \(25< Re < 1000\), and the experiments are conducted for \(\phi = 0.65\) and 0.8 at \(Re \approx 391,\ 497\) and 803. The permeability of the porous lamination is observed to induce a slip velocity at the interface, effectively making it a slip wall. The slip velocity is seen to be increasing functions of \(\phi \) and Re. For higher porosities at higher Re, the slip velocity shows non-uniform and unsteady behavior and a breakdown Reynolds number is defined based on this characteristic. A map demarcating the two regimes of flow is drawn from the computational and experimental data. We observe that the boundary layer over the porous lamination is thinner than the Blasius boundary layer and the shear stress is higher at locations over the porous lamination. We note that the porous lamination helps maintain a favorable pressure gradient at the interface which delays separation. The suitable range of porosities for effective passive separation control is deduced from the results.     

Electro-kinetic transport of acetone,water and their binary mixtures

Summary Electroosmosis of acetone, water and their binary mixtures through thorium oxide (ThO₂) plug membrane has been studied and the data analysed using non-equilibrium thermodynamics. The phenomenological coefficients,L ₁₁ andL ₁₂ have been found to vary nonlinearly with composition. Excess phenomenological coefficients have therefore been evaluated and the results explained in terms of the membrane permeant and permeant-permeant interactions. The results on the measurement of electrophoretic velocity of ThO₂ particles dispersed in acetone-water mixtures also lead to the conclusion that the components of the mixture interact appreciably.

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Zusammenfassung Die Elektroosmose von Aceton, Wasser and deren binären Gemische durch eine ThO₂-Pflock-Membran wurde untersucht; die Daten wurden mit Hilfe der Nichtgleich-gewichts-Thermodynamik analysiert. Die phänomenologischen KoeffizientenL ₁₁ undL ₁₂ ändern sich hiernach nichtlinear mit der Zusammensetzung. Es wurden daher Exzess-L ₁₁-und -L ₁₂-Werte berechnet; die Ergebnisse wurden auf Grund der Membran-Permeant- und Permeant-Permeant-Wechselwirkungen diskutiert. Aus der Messung der elektrophoretischen Geschwindigkeit von ThO₂-Teilchen, die in Aceton-Wasser-Gemischen dispergiert sind, folgt, daß eine merkliche Wechselwirkung zwischen den Komponenten der Mischung vorliegt.

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With 8 figures and 1 table     

An ?-uniform hybrid scheme for singularly perturbed delay differential equations

In this paper, a singularly perturbed delay differential equation of first order has been considered. The problem is solved by using a hybrid scheme on a Shishkin mesh. The difference scheme is shown to converge to the continuous solution uniformly with respect to the perturbation parameter. Truncation errors are obtained. Finally, numerical experiments are carried out on a test problem, confirming the effectiveness of the proposed technique.     

Chiral ionic liquid-catalyzed Biginelli reaction: stereoselective synthesis of polyfunctionalized perhydropyrimidines

A chiral ionic liquid-catalyzed, efficient and unprecedented version of the Biginelli reaction using new variants of its active methylene component, viz. 2-phenyl-1,3-oxazol-5-one/2-methyl-2-phenyl-1,3-oxathiolan-5-one, with aromatic aldehydes and urea/thiourea enantio- and diastereoselectively, yields 5-amino-/mercaptoperhydropyrimidines. This three-component domino cyclocondensation reaction is effected via ring transformation of an isolable intermediate in a one-pot procedure.     

Synthesis and characterization of coordination compounds of organotin(IV) with nitrogen and sulfur donor ligands

The reactions of dimethyltin dichloride with nitrogen and sulfur donor ligands derived by condensation of S‐benzyldithiocarbazate with indol‐3‐carboxylaldehyde, thiophene‐2‐aldehyde and furfuraldehyde have been investigated in 1:1 and 1:2 molar ratios in anhydrous alcohol. These ligands act as mononegatively charged bidentate species and coordinate to the central tin(IV) atom through the thiosulfur by proton exchange with the azomethine nitrogen. The newly synthesized complexes have been characterized by elemental analysis, conductance measurements and molecular weight determinations. The mode of bonding and the geometry of the complexes have been suggested on the basis of infrared, electronic and ¹H, ¹³C and ¹¹⁹Sn NMR spectroscopy, and probable structures have been assigned to these complexes. A few representative ligands and their tin(IV) complexes have also been screened for their antifungal and antibacterial activities and found to be quite active in this respect. Copyright © 2001 John Wiley & Sons, Ltd.     

Axially symmetric thermal-stress distribution in an infinite elastic solid containing an annular crack under torsion

Summary In the present work the axially symmetric thermal-stress distribution in an infinite elastic solid containing an annular crack under torsion has been studied. The problem is reduced to triple integral equations which in their turn are reduced to simultaneous algebraic equations by using Hankel transform technique. The quantities of physical interest have also been computed and illustrated graphically for different values of the inner and outer radius of the crack.

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Riassunto In questo lavoro si studia la distribuzione a simmetria assiale dello stress termico in un solido elastico infinito che contiene un crack annulare sotto torsione. Il problema è ridotto alle equazioni integrali triple che per contro sono ridotte ad equazioni algebriche simul tanee usando la tecnica di trasformazione di Hankel. Sono state calcolate ed illustrate graficamente per valori differenti del raggio interno ed esterno del crack anche le quantità di interesse fisico.

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Резюме В работе исследуется аксиально симметричное распределение термических напряжений в бесконечном упрутом твердом теле, содержащем кольцевые трещины при кручении. Рассматриваемая проблема сводится к интегральным уравнениям с тройными интегралами, которые, в свою очередь, сводятся к совместным алгебраическим уравнениям, испрльзуя технику преобразований Ганкеля. Вычисляются величины, представляющие физический интерес. Полученные величины иллюстрируются графически для различных значений внутреннего и внешнего радиусов трещин.

     

THE ESTIMATION OF PRIOR FROM FISHER INFORMATION

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Kink instability of a highly deformable elastic cylinder

When a soft elastic cylinder is bent beyond a critical radius of curvature, a sharp fold in the form of a kink appears catastrophically at its compressed side while the tensile side remains smooth. The critical radius increases linearly with the diameter of the cylinder but remains independent of its material properties such as modulus; the maximum deflection at the location of the kink depends on both the material and geometric properties of the cylinder. The catastrophic dynamics of evolution of the kink depicts propagation of a shear wave from the location of the kink towards the edges signifying that kinking is an elastic response of the material which results in extreme localization of curvature. We have rationalized this phenomenon in the light of the classical Euler's buckling instability in slender elastic rods.