Shear viscosity calculation for particle-based flow

A particle-based method called multi-particle collision (MPC) dynamics is considered, and the shear viscosity is calculated theoretically. As part of the particle-based mechanism, velocities of particles change due to collisions and due to an applied external force used to create flow. The system's temperature increases due to the external force, and a thermostat is used to remove this excess temperature so as to maintain constant temperature (isothermal) flow conditions. A theoretical expression for the shear viscosity is derived and compared to existing viscosity expressions. Additionally, results for MPC flow through a local constriction are assessed. The novelty of the numerical results in this Thesis come from using a local thermostat rather than a global thermostat that had been used in the past.

Shear viscosity calculation for particle-based flow

A particle-based method called multi-particle collision (MPC) dynamics is considered, and the shear viscosity is calculated theoretically. As part of the particle-based mechanism, velocities of particles change due to collisions and due to an applied external force used to create flow. The system's temperature increases due to the external force, and a thermostat is used to remove this excess temperature so as to maintain constant temperature (isothermal) flow conditions. A theoretical expression for the shear viscosity is derived and compared to existing viscosity expressions. Additionally, results for MPC flow through a local constriction are assessed. The novelty of the numerical results in this Thesis come from using a local thermostat rather than a global thermostat that had been used in the past.

The interaction between mantle plumes and lithosphere and its surface expressions: 3-D numerical modelling

SUMMARY The rise of mantle plumes to the base of the lithosphere leads to observable surface expressions, which provide important information about the deep mantle structure. However, the process of plume–lithosphere interaction and its surface expressions remain not well understood. In this study, we perform 3-D spherical numerical simulations to investigate the relationship between surface observables induced by plume–lithosphere interaction (including dynamic topography, geoid anomaly and melt production rate) and the physical properties of plume and lithosphere (including plume size, plume excess temperature, plume viscosity, and lithosphere viscosity and thickness). We find that the plume-induced surface expressions have strong spatial and temporal variations. Before reaching the base of the lithosphere, the rise of a plume head in the deep mantle causes positive and rapid increase of dynamic topography and geoid anomaly at the surface but no melt production. The subsequent impinging of a plume head at the base of the lithosphere leads to further increase of dynamic topography and geoid anomaly and causes rapid increase of melt production. After reaching maximum values, these plume-induced observables become relatively stable and are more affected by the plume conduit. In addition, whereas the geoid anomaly and dynamic topography decrease from regions above the plume centre to regions above the plume edge, the melt production always concentrates at the centre part of the plume. We also find that the surface expressions have different sensitivities to plume and lithosphere properties. The dynamic topography significantly increases with the plume size, plume excess temperature and plume viscosity. The geoid anomaly also increases with the size and excess temperature of the plume but is less sensitive to plume viscosity. Compared to the influence of plume properties, the dynamic topography and geoid anomaly are less affected by lithosphere viscosity and thickness. The melt production significantly increases with plume size, plume excess temperature and plume viscosity, but decreases with lithosphere viscosity and thickness.

Features of using linear graphs in developing mathematical model of metal melting process in induction crucible furnace

The use of linear graphs in the development of a mathematical model of metal melting in an induction crucible furnace allows to determine the metal melting temperature and control the excess temperature in the main parts of the furnace. In addition, if it is necessary to optimize the thermal mode of operation of the furnace according to the presented graph conversion method, a graph model of any part of the furnace with the desired thermal parameters can be obtained.

Dynamics of the Thermal Uplifting in the Atmosphere Under a Continuous Supply of Heat: Practical Application Examples

The author has earlier considered the dynamics of an isolated thermic arising from an instant heat release. The rigorous analytical, as well as simplified, solutions describing the dynamics of the uplifting of a spherical thermic have been obtained. Such a thermic appears during a short-term release of heat, e.g., during an explosion. The uplifting of a meteoroid thermic has also been studied. The theory of the thermic has found applications in the magnetic precursors of earthquakes. At the same time, the heat can be supplied during many hours or even days when big forest fires occur, peat fires burn, volcano eruptions occur for a long time, and during the release of heat before earthquakes. The dynamics of the uplifting of a thermal under these circumstances is considerably different from an instantaneous energy release. Employing the cylindrical model of a thermic, the dynamics of the thermic has been studied in the case of the continuous supply of heat. Within the model, the analytical solutions to the set of equations governing the temporal dependences of the velocity of a parcel of the heated air and the position of the upper bound of the thermic, as well as the excess temperature in the heated parcel have been obtained. The upper thermal boundary speed and location has been shown to increase with uplifting, while the excess temperature to gradually decrease. The numerical estimation has been performed for characteristic situations. The ecological consequences of large-scale fires, as well as the mechanisms for generating gravity waves by the thermals, are discussed. The physics-based mechanisms for generating acoustic wide-band emissions by the thermals have been analyzed; the wave periods have been estimated to be 1–103 s. The energy of acoustic emissions from a big fire has been estimated to be approximately 1014 J. At the same time, the energy of acoustic emissions from all fires that occurred in the Russian Federation in 2020 amounts to 7∙1016 J, while in Ukraine it is three orders of magnitude lower.

Intelligent non-colorimetric indicators for the perishable supply chain by non-wovens with photo-programmed thermal response

Spoiled perishable products, such as food and drugs exposed to inappropriate temperature, cause million illnesses every year. Risks range from intoxication due to pathogen-contaminated edibles, to suboptimal potency of temperature-sensitive vaccines. High-performance and low-cost indicators are needed, based on conformable materials whose properties change continuously and irreversibly depending on the experienced time-temperature profile. However, these systems can be limited by unclear reading, especially for colour-blind people, and are often difficult to be encoded with a tailored response to detect excess temperature over varying temporal profiles. Here we report on optically-programmed, non-colorimetric indicators based on nano-textured non-wovens encoded by their cross-linking degree. This combination allows a desired time-temperature response to be achieved, to address different perishable products. The devices operate by visual contrast with ambient light, which is explained by backscattering calculations for the complex fibrous material. Optical nanomaterials with photo-encoded thermal properties might establish new design rules for intelligent labels.

FEM-Analysis of 2D Micromachined Flow Transduers based on aGe-Thermistor Arrays and a Double Bridge Readout

This paper reports on a design and simulation study aiming at high-accuracy 2D micromachined thermal flow transducers. The scope is restricted to micromachined devices featuring a square-shaped membrane incorporating central symmetric thin-film devices. A microthermistor array probed spatial excess temperature variations while the main heat supply was alternatively established by optional heating resistors or by pronounced self-heating of the thermistor devices. Proper device designs enable leading edge transducer performance without sophisticated signal conditioning schemes. We found that a high azimuthal uniformity of flow magnitude transduction is tantamount to a precise azimuthal accuracy. The most advanced result gave a maximum azimuthal aberration of 0.17 and 1.7 degrees for 1 m/s and 10 m/s, respectively, while the corresponding magnitude uniformity amounted to 0.07% and 0.5%. Such excellent specifications exceed the need of ordinary meteorological applications by far. However, they are essential for, e.g., precise non-contact measurements of 2D relative movements of two quasi-planar surfaces via the related Couette flow in intermediate air gaps. The simulations predicted significantly better device characteristics than achieved by us in first experiments. However, this gap could be attributed to imperfect control of the flow velocity field by the measurement setup.

Dynamics of convective upwelling of large-scale weakly heated atmospheric aggregates

Equations for the center-of-mass speed of the parcel of heated air, the mass of the entrained cool air, and the resulting buoyancy of the entire air aggregate have been used to obtain exact and approximate relations for describing height and temporal dependences of the characteristic radius, the excess relative temperature, and a weakly heated large-scale (hundreds of meters and greater) air aggregate convective upwelling. It is shown that the excess temperature relaxation in the air aggregate occurs quickly, the aggregate radius increases slowly and insignificantly. The variations in the center-of-mass speed of the aggregate are not monotonous. First, the speed increases from zero to a maximum value, and then it decreases to zero. Numerical simulations have been performed for the case of interest to practical applications.