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Analytical solutions of some contact problems are infinite functional series according to the system of basic functions. When constructing such solutions, it becomes necessary to represent the kernels of integral equations describing the process of interaction in the form of two-dimensional series on a given basis. Often the kernels have a rather complex appearance, therefore, the process of finding the decomposition coefficients is a rather complex and labor-intensive process, on which the accuracy and speed of obtaining final results depend. The paper proposes a calculation method that allows calculating the coefficients of decomposition of the kernels of plane contact problems according to a special orthonormal basis that takes into account the features of contacting bodies. Other approximate formulas are also derived for the special case when coating characteristics are constant. Based on the received presentation, conclusions and recommendations are formulated.

In this paper, theoretical and numerical analysis of a~transonic flow field of critical flow Venturi nozzles according to the ISO~9300 standard is performed. Deviations of the flow field from an estimate based on one dimensionality are clarified. While the theoretical analysis allows prediction of these deviations, the numerical analysis allows quantification of their influence. The main studied phenomena include the local supersonic compression in transonic expansion and the Prandtl-Meyer expansion. The tendency of the flow field to spatial oscillations is shown, alongside the ability of the system to damp these oscillations.

This research focuses on utilizing numerical simulation to analyse how modifications in the air jet diffuser shape impact the cooling efficiency of electronic parts. The main aim of this study is to understand the physical and thermal mechanisms involved in the process. The study consists in numerically predicting the physical and thermal field of a cubic-shaped obstacle placed in the centre of a square subjected to a resulting flow field created by a transverse flow and a perpendicularly oriented impacting jet. The computations were done at a Reynolds number of 3 410, analyzing three perpendicular impinging jets with the ratio of impinging and cross flow Reynolds numbers α = Rej /ReH having the values of 0.5, 1, and 1.5. The k–ω SST turbulence model was used in this investigation. The effectiveness of the methodology that was put into action was evaluated by referring to the findings derived from the experiments conducted by Masip and his team. Once the methodology was validated, we studied the effect of changing the geometric shapes of the impinging jet diffusers on the cooling efficiency. Three geometrical shapes of air diffusers were tested (circular, swirling and lobed). We noted that there is a direct correlation between flow morphology and cooling efficiency. The impact of the ratio α was analysed and found to have a significant effect on the cooling efficiency. As this ratio increases, the quantity of heat transfer increases in all three air jet diffuser cases. In relation to the lobed air jet, it was observed that the Nusselt number exhibits greater values when compared to the other air jet diffuser cases. Moreover, it was noted that the lobed air jet diffuser can enhance the heat transfer efficiency for α = 1.5 by more than 16.3 % compared to the circular air jet diffuser.

Optimization is getting more and more important due to its application in real engineering problems. Recently, the vibrating particles system algorithm has been developed as an efficient method for mono-objective optimization. However, in multi- and many-objective design problems, the vibrating particles system method is unable to handle simultaneously the conflicting objectives. The second drawback of the vibrating particles system algorithm is the~variability of the obtained results at each independent test, due to its inability to balance exploitation and exploration capabilities. To address these issues, this paper proposes an enhanced vibrating particles system algorithm called the many-objective vibrating particles system algorithm. The proposed many-objective vibrating particles system algorithm uses the Pareto principle to store the non-dominated solutions of multiple conflicting functions. Moreover, the implementation of the particle position enhancement mechanism to boost this algorithm's exploitation and exploration capabilities is another distinctive aspect of the suggested method. A variety of high-dimensional test functions and engineering design problems are used to evaluate the efficiency of the many-objective vibrating particles system algorithm. The obtained results show that the proposed algorithm outperforms other popular methods in terms of convergence characteristics and global search ability.

The application of nanofluids in the presence of a magnetic field holds promise for advanced drug delivery sys tems, where controlled manipulation of magnetic nanoparticles within nanofluids can enhance targeted and local ized drug delivery. This study explores the instability of a viscous fluid-nanofluid interface arranged in a planar configuration influenced by a tangential magnetic field using the irrotational flow theory. When the nanofluid is positioned above a viscous fluid, the interface is susceptible to the Rayleigh-Taylor instability. Employing lin ear stability theory, an explicit relationship connecting the perturbation growth parameter with the wavenumber is derived. Different dimensionless quantities such as the Atwood number, Weber number, Froude number, and Reynolds number are analyzed using stability plots. These plots provide valuable information about the behavior of interfaces. Increased magnetic field strength is observed to delay instability onset. Surface tension is found to stabilize the interface, whereas inertial forces destabilize it. This investigation contributes to understanding and controlling the interface dynamics in nanofluid systems.

The objective of this paper is to evaluate the dynamic stress intensity factors (DSIFs) of a cracked body using the bond-based peridynamics (BBPD) formulation. The peridynamics theory offers advantages over the classical continuum theory for solving partial differential equations in fracture mechanics. Nevertheless, some problems remain, such as its dispersion characteristics and constant micromodulus used in the classical BBPD. In this study, a Gaussian function is used to define the non-constant micromodulus. A wave dispersion analysis for a 1D problem was carried out and the influence of the horizon, mesh size and the kernel function on the dispersion properties were analyzed. On the other hand, a new approach to evaluate the DSIFs of a cracked body using the BBPD coupled with the displacement extrapolation technique is presented. Parameters that reduced the wave dispersion were kept for the DSIFs estimation. The proposed method is applied to analyze some benchmark examples. The obtained results are compared with the exact ones and they showed that the proposed approach can be used as an alternative method to evaluate DSIFs.

In the triangle relation among Austria-Hungary and Italy with their mutual focus on Albania, there can be seemingly depicted a long linear process, but internally viewed as a phase which passed through constant ups and downs. They reflected stability in case when both Great Powers accepted their mutual interest in the Adriatic Sea, thanks to cooperation on a paritarian basis, it was also included their attitude toward the Albanians and their national state. This article analyses the Austro-Italian parietal attitude toward Albania on two main aspects: First, in the diplomatic aspect, which mainly focused on the Conference of Ambassadors in London (1912–1913), where the newly founded Albanian state was recognized and organized internationally. Secondly, considering the finance projects of the Adriatic Powers in Albania and the efforts to concretize their commitment with the Provisional Government of Vlora, founded as a political will of the Albanians, but not recognized by the Great Powers. In its entirety, this article places the Austro-Italian relationship in confrontation with the policy of other Great Powers, evidencing their role in bypassing the Austrian–Italian parity in both ways of how the Albanian state was organized and functioned. This article was drafted using a comparative and chronological approach based on the archival sources and relevant literature.

Warfare was a common concern among the people of precolonial Nigeria because most of their states thrived on military conquest. States paid adequate attention to the military to ensure internal and external security through offensive and defensive strategies. This study explores the force structure of the Ilorin emirate army in the 19th century. The study employed a historical research method, which comprised oral interview as the primary source, and the use of textbooks, journal articles, and other written materials as the secondary sources. Due to cultural and historical connections, the old Oyo military tradition influenced Ilorin. However, the Ilorin military became more elaborate after the establishment of her emirate system in the 1820s. The Ilorin emirate military force comprised of infantry and cavalry, while the fighting troops included professional soldiers, elites, freeborn volunteers and slaves. In the military force structure, there were four military commanders, known as Baloguns. Each of the Baloguns was required to keep a contingent of soldiers under his watch including their logistics and a mild training to prepare them for campaigns. Such regiment comprised other distinguished warriors, usually made up of professional soldiers, elite volunteer soldiers, mercenaries, and soldier-slaves. Indeed, military service and loyalty were important considerations in the access to land and political positions in the Ilorin emirate in the 19th century. The Baloguns were the major military commanders, while titles like Maiyaki (warriors) and Ubandawaki (cavalry commander) and Ajia were regimental warlords. There were ancillaries of the military in the Ilorin emirates such as smiths, singers, drummers, charms-makers, and Islamic spiritualists