Aim. We consider the rheological behavior of a nanofluid obtained on the basis of titanium oxide nanoparticles in water and ethylene glycol.

Methodology. The experimental data are approximated using equations of the structural rheological model on separate intervals of the shear rate.

Results. A relationship is obtained between the coefficients of rheological equations and the nature of changes in the structure of the nanofluid, namely, the formation and destruction of nanoparticle aggregates.

Research implications. Equations are derived that make it possible to approximate experimental data at individual shear rate intervals corresponding to a certain structural state of the nanofluid.

Aim. For a blunt body of revolution with a power generatrix and spherical, parabolic, and hyperbolic bluntnesses, we calculate the drag force in a gas flow.

Methodology. We determine the degree of minimum resistance and the bluntness radius in the generatrix of the body as functions of the elongation in a wide range of Reynolds numbers.

Results. For a blunt body of revolution with a power generatrix and spherical, parabolic, and hyperbolic bluntnesses, the drag force in a high-speed rarefied gas flow is calculated based on several local gas flow models.

Research implications. The results obtained in this work are of great importance for optimizing the aircraft geometry.

Aim. We simulate the behavior of several bodies with Newtonian interaction potential and identify two bodies in this system in order to study their convergence.

Methodology. A system of second-order differential equations is constructed. These equations are translated into a system of algebraic equations. In a system of several bodies, two bodies are distinguished. The mutual behavior of these bodies is investigated by varying the masses of the remaining bodies of the system. All research is based on the Python language.

Results. The trajectories of motion of bodies in an inhomogeneous gravitational field formed by these bodies themselves are found. The approach trajectories of two selected bodies are obtained. The stability of such a trajectory is studied.

Research implications. In a system of several bodies interacting through gravitational potentials, a subsystem of two bodies is singled out. The stability of the orbit of rendezvous of two bodies in the field of action of other bodies of the chosen system is considered. The practical significance is expressed in the study of the security of the Earth.

Aim. The aim of the paper is to construct an effective solution in practical application to the problem of ultrasonic wave propagation in rectangular-section pores filled with a rarefied gas. 

Methodology. The solution to unsteady two-dimensional gas dynamics equations in the creeping flow approach is constructed in the form of infinite series of eigenfunctions, in which zero terms of expansions are predefined functions. The Knudsen number, defined as the ratio of the free path length in a gas to the characteristic transverse pore size, is assumed to be less than or on the order of unity. Therefore, boundary conditions taking into account the effects of sliding and temperature jump on the inner surfaces of the pores are used.

Results. A modified solution to the problem of ultrasonic wave propagation in rectangular-section pores filled with a rarefied gas is presented. In contrast to the previously published results, the solution is represented by rapidly converging series of eigenfunctions. Verification by numerical methods shows that only two terms of expansions are needed to ensure a relative accuracy of calculations not exceeding 1%. Approximate relations for eigenvalues and coefficients of two-term expansions convenient for computer calculations are obtained. Several general mathematical results are also presented.

Research implications. The results of the work can be used for engineering assessments of the acoustic characteristics of porous materials operated at low pressures, as well as provide a basis for further theoretical studies of the acoustic properties of porous materials. 

Aim. The purpose of this work is to consider the historical circumstances of the discovery of the Stefan‒Boltzmann law of thermal radiation.

Methodology. Use is made of a content analysis of the historical circumstances of the discovery of the Stefan‒Boltzmann law of thermal radiation.

Results. It is shown that the discovery of the Stefan‒Boltzmann law was one of the important episodes in the prehistory of the discovery of the universal Kirchhoff function. The discovery of this function by M. Planck in December 1900 led to the gradual formation of quantum theory and predetermined the development of the main direction of theoretical physics of the twentieth century, namely, quantum mechanics, and then quantum electrodynamics, quantum field theory, etc., which actually was the beginning of a new physical era, i.e. the era of quantum physics.

Research implications. Generalization and addition of information about the theory of thermal radiation study will be useful in the study of quantum theory, including the creation of a special course “History of Quantum Theory”.