Journal of Theoretical and Applied Mechanics, Sofia, vol. 53 Issue 4 (2023)

We are delighted to announce that this issue of the Journal of Theoretical and Applied Mechanics is dedicated to Prof. Zapryan Zapryanov, honouring him on his 90th birthday.

The aim of this study is to perform a stability analysis of a thermo-capillary flow in a steady-state evaporating/condensing liquid layer applying the statistical rate theory expression for the mass flux across the interface. In the general mass, momentum and energy balance equations, the effects of gravity, temperature gradients in the surface tension, the interfacial momentum and energy loss due to the net mass flux are taken into account. Assuming a non-deformable surface and low dynamic viscosity and thermal conductivity of the vapor, the stability problem of the liquid phase is separated from that for the vapor. The exact solution is found and the dispersion relationship is solved numerically for water. The numerical results show that the interfacial instability mode always takes place in spite of the direction of the mass flux across the interface. The main physical reason for this kind of instability is the strong dependence of the mass flux on the vapor pressure predicted from the statistical rate theory. Other internal instability modes are described as a function of the Rayleigh and Marangoni numbers. The stability diagrams are discussed in the light of the available experiments for controllable water steady-state evaporation and condensation.

Mathematical model of the deformation and drainage of film between interacting drops is presented in the case when dispersed or continuous phases are viscoelastic fluids. The model is based on the assumptions of a gentle collision at small Reynolds numbers and small deformation at small capillary numbers. It consists of lubrication approximation in the film and creeping flow equation in the dispersed phase. The equations in the continuous and dispersed phases are coupled by continuity of the velocity and stress boundary conditions at the interface. Generalizations of the Maxwell-type rheological constitutive relation are used to model the viscoelastic effects: upperconvected Maxwell model in the drop and fractional Maxwell model in the film phase. Predictions of the effect of the extra elastic stresses on the film drainage are given.

This paper is a review of recent studies of the present authors related to the modeling of hydrodynamic and heat transfer processes in waterfilled glazing chambers exposed to sunlight. Due to the absorption properties of water, solar visible and near-infrared irradiance induces a volumetric heat source with exponential decay. Three different scenarios of mixed natural and forced convection are discussed: two fully-developed flows in vertical flat and rectangular channels and a developing flow in a slender channel with a rectangular cross-section (similar to a Hele-Shaw cell). Three cases of temperature boundary conditions are studied for the lighted and the opposite walls, whereas in the case of the rectangular channel, linear declination of the side wall temperatures is applied. Analytical solutions for fully-developed flows in both flat and rectangular channels are reported and discussed. Some physical characteristics of the flows such as bulk liquid temperature and Nusselt number are calculated. The problem of developing flows in the slender rectangular channel is formulated in a "stream function-vorticity" version. The main conclusion is that the presented models predict quite well the average physical parameters of the mixed convection flows in the glazing chamber under solar radiation.

Complex flow instabilities including wall slip and shear banding occur in many industrial applications, such as in polymer extrusion processes, thus affecting the throughput and the quality of the final product. The modelling of rheological data is a key point when studying different polymeric flows. The present survey incorporates three different ways to model the shear stress of shear thinning polymers as nonlinear functions of shear stress: generalized Newtonian model (Carreau-Yasuda model), wall shear slipping and banding with yield (Herschel–Bulkley model). Based on these models, the flow in the nozzle tube of a 3D printer is analyzed by a numerical model and two analytical models: the classical Weissenberg–Rabinowitsch–Mooney (WRM) model with slip; a simple model in three different regions in the tube (including yield, parabolic and band, which match their boundaries). The real data of measured shear stress by a plate–plate rheometer for three nanocomposites is used to compare the three models. The experimentally measured flow rates during the extrusion of the same nanocomposites are used to give insight into the corresponding flow structures in the nozzle tube.

The paper presents statistical analysis of air pollutants in the Bulgarian part of trans-border BG–RO area. Air contamination charcteristics and norms are also presented and commented in the present survey. Ecological monitoring system in the BG–RO trans-border area is described. Particulate matter (PM), nitrogen dioxide (NO₂) and ground-level ozone (O₃), are now generally recognised as the three pollutants that most significantly affect human health. Because of this, further in the paper concentration levels of these three pollutants are statistically studied, based on official monitoring data. Results are graphically presented and commented. Ambient air quality in the BG–RO trans-borer area is better today than it was two decades ago, but despite improvements, pollutant levels still show significant adverse effects on human health and the environment. To improve air quality in the future, it will be necessary to increase the use of "green" and more efficient technologies in terms of thermal insulation of buildings, as well as the use of alternative sources of fuel in the household and transport, use of best available technology in the industry, green roofs in urban areas and more. Also it is nessessary more precise mathematical modeling of the data series, which take into account more factors to be developed and used for better understanding and forecasting the air contamination processes.

In this work, the possibilities of the magnetosheath-magnetosphere model for describing the plasma parameters in the magnetosheath are demonstrated. We consider the problem of a flow around a body (the Earth’s magnetosphere) with two movable boundaries – the bow shock (BS) and the magnetopause (MP). The grid-characteristic method is applied to describe an ideal gas flow in the transition region (magnetosheath). A theoretical finite element model and the semi-empirical Tsyganenko model are used to describe the magnetic field in the magnetosphere. The model allows a self-consistent determination of the magnetosheath boundaries for a given momentary state of the solar wind. For these input parameters the three-dimensional solution in the transition region is calculated. An analysis of the ion flux was made based on the model and the data measured by the Interball-1 satellite in several cases of magnetosheath crossings. The advantages and limitations of the model for describing the magnetosheath flow are analyzed.