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A one-dimensional model is proposed for transportation of a two-phase fluid (sand-containing fluid and pure fluid) in the Hele-Shaw cell with permeable walls through which the pure fluid can escape as the sand concentration increases. The model describes the process of pure fluid displacement with the emergence of the Saffman — Taylor instability and extends the Koval' model to the case of sand concentration variation owing to pure fluid outflow through the cell walls. The Riemann problem is analyzed. New flow configurations, which are not predicted by the Koval' model, are discovered.

In this numerical study, the effects of variable thermal conductivity models on the combined convection heat transfer in a two-dimensional lid-driven square enclosure are investigated. The fluid in the square enclosure is a water-based nanofluid containing alumina nanoparticles. The top and bottom horizontal walls are insulated, while the vertical walls are kept at different constant temperatures. Five different thermal conductivity models are used to evaluate the effects of various parameters, such as the nanofluid bulk temperature, nanoparticle size, nanoparticle volume fraction, Brownian motion, interfacial layer thickness, etc. The governing stream-vorticity equations are solved by using a second-order central finite difference scheme coupled with the conservation of mass and energy. It is found that higher heat transfer is predicted when the effects of the nanoparticle size and bulk temperature of the nanofluid are taken into account.

An analysis is performed to study the effects of the chemical reaction and heat generation or absorption on a steady mixed convection boundary layer flow over a vertical stretching sheet with nonuniform slot mass transfer. The governing boundary layer equations with boundary conditions are transformed into the dimensionless form by a group of nonsimilar transformations. Nonsimilar solutions are obtained numerically by solving the coupled nonlinear partial differential equations using the quasi-linearization technique combined with an implicit finite difference scheme. The numerical computations are carried out for different values of dimensionless parameters to display the distributions of the velocity, temperature, concentration, local skin friction coefficient, local Nusselt number, and local Sherwood number. The results obtained indicate that the local Nusselt and Sherwood numbers increase with nonuniform slot suction, but nonuniform slot injection produces the opposite effect. The local Nusselt number decreases with heat generation and increases with heat absorption.

This paper re-examines the creep life methodology based on the continuum damage mechanics (CDM) of the Kachanov and Rabotnov theory. Uniaxial creep and multiaxial creep rupture formulations are presented taking into account the primary creep effect. The scalar damage parameter is computed up to time-to-rupture as a function of time and stress. The methodology implemented is based on the uniaxial time-to-rupture obtained experimentally. The times-to-rupture for bars with different notches are calculated. It is demonstrated that the use of the damage parameter is vital to indicate the critical damage location where failure occurs. Results are compared to those obtained experimentally. It is shown that the primary creep inclusion has a significant effect on the damage distribution zone.

A kinetic model of creep-rupture strength is constructed using the physicomathematical theory of irreversible strains of metals. An algorithm for the mathematical modeling of the processes occurring during tension of specimens. Results of experimental verification of a uniaxial model of creep-rupture strength are given. It is shown that the proposed model differs from available models fact in that it contains physical structural parameters (scalar densities of dislocations and microcracks) and kinetic equations for them.

The hypotheses of the Reissner theory are used to formulate the problem of equally stressed reinforcement (ESR) of transversely bent elastic plates by fibers with a constant cross section. The corresponding system of governing equations and boundary conditions is performed. The model problem of ESR of rectangular elongated plates subjected to cylindrical bending with various types of loading of one of the longitudinal edges and rigid clamping of the other one. It is shown that there could exist two solutions of the problem of ESR, one of which is regular and the other one singular. The edge effects occurring in the presence of the torque applied to the edge, which significantly affects both the stress-strain state of the binder material and the reinforcement structure.

A model for predicting the strength of a cement ring adjacent to a production well bore without consideration of internal and temperature stresses is proposed based on solutions of the Lame problems for one- and two-layer tubes and the Huber-Mises yield criterion using the model of a perfectly plastic isotropic body.

The KHe molecular system is extensively studied by multi-reference configuration interaction calculations. Potential energy curves are constructed for 20 lowest electronic states, and molecular parameters are extracted. A comparison of our results with previous works shows remarkable agreement. A further calculation of the dipole moment functions through a wide range of the internuclear separation is performed and their corresponding curves are presented. Charge transfer is detected from the change in the sign of these functions particularly for R < R_e. Negative dipole moment values near R_e are predicted for 3 excited states, (1)²Π, (3)²∑⁺ and (1)⁴Π, which are of a relatively short-range strong-binding nature. On the other hand, weakly binding long-range excited states predict positive values of the dipole moment near R_e reflecting the K^-He⁺ polarity.

In this work, the interaction of C₂₀ and the N₂H₂ fragment is investigated at the M062X/6-311G(d,p) level of theory in both gas and solution phases. The interaction energies obtained by the standard method are corrected by the basis set superposition error (BSSE) during the geometry optimization for all molecules at the same levels of theory. The results obtained from these calculations reveal that the interaction between C₂₀ and N₂H₂ increases in the presence of more polar solvents. Values of the electrophilic charge transfer show the charge flow from C₂₀ to N₂H₂. The influence of the solvent on the hyperpolarizability indicates that b_tot values decrease on passing from vacuum to the solution phase.

Vibrational spectra of 1,2-bis(2-aminophenoxy)-ethane, 1,5-bis(2-aminophenoxy)-3-oxapentane, and 1,8-bis(2-aminophenoxy)-3,6-dioxaoctane - podands, different in the length of oxyethylene fragments, are measured and their single crystal X-ray diffraction analysis is performed. It is demonstrated that the strength of intermolecular hydrogen bonds (IMHB) with the participation of NH groups increases with the elongation of the oxyethylene spacer. According to the XRD data for 1,2-bis(2-aminophenoxy)-ethane, the weakest hydrogen bonds are characteristic. From the IR spectra, important intermolecular hydrogen bonds are typical of 1,8-bis(2-aminophenoxy)-3,6-dioxaoctane having the longest oxyethylene fragment.