Band 78, Heft 3

The relevance of the stated subject is conditioned upon the presence of a real possibility to simulate vibrations of elastic membranes in space according to the Hamilton principle using degenerate three-dimensional hyperbolic equations, which is of particular practical importance from the standpoint of the prospects for mathematical modelling of the heat propagation process in oscillating elastic membranes. The purpose of this paper is to study the sequence of the procedure for mathematical modelling of heat propagation in oscillating elastic membranes which is leading to degenerate three-dimensional hyperbolic equations. The methodological approach of this study is based on a combination of theoretical study of the possibilities of constructing mathematical models of heat propagation in oscillating elastic membranes with the practical application of methods for constructing three-dimensional hyperbolic equations with type and order degeneracy to find a single solution to a mixed problem. In the course of this study, the results were presented in the form of a mathematical proof of the possibility of obtaining a single solution to a mixed problem for three-dimensional hyperbolic equations with type and order degeneracy. The results obtained in this study and the conclusions formulated on their basis are of significant practical importance for developers of methods of mathematical modelling of heat propagation processes in oscillating artificial membranes, which is of key importance from the standpoint of prospects for improving methods of mathematical modelling of processes occurring in technical devices used in various fields of modern industries.

In this paper, we study the properties of the general three-dimensional equilibrium solutions for steady-state equations of inviscid fluids. Incompressible, homogeneous, inhomogeneous and compressible flows motion in a gravitational potential are considered. General three-dimensional formulas for the gas pressure and the gravitational potential are obtained. For incompressible flows, the vector and scalar potentials of the velocity field are used to derive general formulas for general three-dimensional solutions. To verify our results, some examples are presented. For compressible flows, a class of three-dimensional solutions is constructed.

Double fractional Jeffreys fluids are widely used in production and life. In this paper, the effects of stretching velocity on the flow and heat transfer of double fractional Jeffreys fluid are studied. Three types of stretching velocity are considered, i.e., (i) uniform velocity; (ii) acceleration; and (iii) deceleration. The rheological synergistic thermal conductivity model introduced to the energy equation is formulated based on experiments. The governing equations are solved by using a combination of the finite difference technique and the L1 algorithm. Results show that there is an inflection point on each velocity profile which divides the velocity field into two sections, convex (the elasticity plays a primary effect) and concave (the viscosity plays a primary effect). As the stretching velocity parameter increases, the thickness of the region where the elasticity plays a major role does not change in case (i), however, it reduces in case (ii) and grows in case (iii). We also found that, compared with uniform stretching, accelerated stretching can lead to higher heat transfer, while decelerated stretching causes less heat transfer. And for uniform velocity stretching, the stretching velocity parameter has little effect on the temperature field. In the case of accelerated stretching, increasing the stretching velocity parameter enhances heat transfer, however, for decelerated stretching, it weakens heat transfer. These results are instructive for industrial design.

The present study intends to solve the problem of low-temperature sensitivity of most conventional period materials. A solid/solid one-dimensional phononic crystal design is proposed as a pragmatic thermal sensor. Here, each unit cell of the proposed phononic crystal sensor is designed from epoxy and concrete. In this structure, irregularity in layers’ arrangement results in the generation of resonant peaks at the transmission spectrum. The irregularity is introduced to the system by stacking two mirror phononic crystals to form a whole symmetric phononic crystal design. Thermal variations lead to significant changes in Young’s modulus of concrete and epoxy; consequently, transmission spectra and local resonant peaks are shifted as well. Firstly, the band gap changes, and sensor performance were investigated under different conditions such as the incident angle and the number of unit cells to get the optimum parameters. Meanwhile, promising results have been obtained, with increasing the incident angle, the sensitivity increases exponentially till it reaches 1.5 × 10 3 Hz/°C at an incident angle = 18°. Also, with increasing the temperature from 25 to 100 °C, the sensitivity increases dramatically from 188.8 to 362.4 Hz/°C, respectively. In addition, the largest value of Q-factor was investigated at periodicity number = 4. Moreover, in this regard, the Q-factor has the value of 3708 at 25 °C and it reaches to the value of 896.6 at 100 °C. That is to say, the obtained results may be useful in designing thermal sensors with a high sensitivity value.

Ca 9 MgLi(PO 4 ) 7 : 4%Tb 3+ , 4%R + (R = Li, Na, K) phosphors were synthesized by a solid-state reaction method. The crystal structure, morphology, composition and luminescent properties of as-prepared samples were characterized by X-ray diffraction (XRD), high-resolution transmission electron microscopy (HRTEM), energy dispersive spectrometer (EDS), high-angle annular dark field (HAADF) and spectroscopy technique. The effect of a small concentration of charge compensators like Li + , Na + , K + on Ca 9 MgLi(PO 4 ) 7 : Tb 3+ phosphor has also investigated. Ca 9 MgLi(PO 4 ) 7 : Tb 3+ , R + (R = Li, Na, K) exhibit superior blue-green luminescence around 5 D 4 → 7 F 5 (543 nm) to Ca 9 MgLi(PO 4 ) 7 : Tb 3+ and can be effectively excited by 370 nm light, which implies that efficient charge compensation can promote the emitting of Tb 3+ in Ca 9 MgLi(PO 4 ) 7 . The CIE coordinates and decay lifetimes of typical samples were also studied. The Ca 9 MgLi(PO 4 ) 7 : Tb 3+ , R + (R = Li, Na, K) have promising application as a blue-green phosphor for near-ultraviolet chip excited white LEDs.

The purpose of this work is to study the influence of thermal effect on the surface morphology of the Fe–Cr–Al (Kh15Yu5) alloy foil and the elemental composition of the surface layers. Also, studies have been carried out on the physicochemical characteristics of the primary support with the deposited secondary support in the initial state and within the temperature range from 25 to 900 °C. The research was carried out on a JSM 6610 LV, JEOL scanning electron microscope with an installed INCA Energy 450 energy-dispersive microanalysis system. Before depositing secondary support (aluminum oxide), for a stronger adhesion to the foil metal, the foil surface was pretreated with a phosphating solution. It was found that during heating up the elemental composition of the surface layer of the Kh15Yu5-alloy foil does not remain constant and depends on the mode of thermal effect. This implies the possibility of changing the adhesion and adsorption properties of the foil surface, as well as the need to take this into account when depositing secondary support and an active phase to the foil. Studies have shown that the applied methods for phosphatizing and depositing secondary support to the foil surface make it possible to obtain a quite resistant coating. No peeling of the secondary support from the foil surface is observed during high-temperature treatment in the air.

Manganese-ion doped cobalt ferrite with the composition Mn 0.1 Co 0.9 Fe 2 O 4 was synthesized by the self-combustion method and sintered at 800 °C, 900 °C and 1000 °C, represented as MCF-800, MCF-900 and MCF-1000, respectively. X-ray methods observed a single-phase cubic spinel formation. XPS analysis revealed the distribution of Mn 3+ and Mn 2+ ions in the tetrahedral A and octahedral B sites. Optical absorption studies confirmed an energy bandgap of 1.2505 eV for the sample MCF-1000, corresponding to near IR absorption useful for catalytic and water-splitting applications. The VSM measurements revealed a maximum magnetization ( Ms ) of 79.612 emu/g for the sample MCF-1000. The maximum entropy method (MEM) electron density distribution studies revealed different strengths of electron density for the cation tetrahedral site A and octahedral site B depending on sintering temperature variation. The sample sintered at 1000 °C with the A–O covalent and B–O ionic bonds with mid-bond densities of 1.903 e/Å 3 and 0.381 e/Å 3 may be useful for ferromagnetic applications. The magnetic, optical, and electronic analyses confirm that the sample MCF-1000 may be best suited for low-cost catalytic, water splitting and ferrite applications.

The use of titanium dioxide (also known as titania) in solar cells, biomaterials, and photocatalytic processes has generated an ever-increasing amount of interest. Titania is widely used in a variety of applications because it is nanocrystalline, chemically stable, has a high refractive index, is mechanically hard, and transmits visible light well. In this work, titania nanoparticles were formed via sol–gel synthesis, wherein the effect of varying pH values such as 3, 5, 7, 9, and 11 has been investigated on the synthesized nanoparticles by studying their structural characteristics and analyzing their optical transmittance. Structural analysis of the synthesized TiO 2 shows formation of the brookite phase at all pH values under as-synthesized conditions. Moreover, structural parameters including crystallite size, dislocation density, and unit cell volume were also calculated. Cell volume was calculated at various pH levels and measured between 255.7 and 257.2 Å 3 . Optical analysis shows a transmission increase with a pH increase, and maximum transmission has been observed above 80% for a pH value of 11.