This paper describes an analytical-numerical method for the skin and proximity effects in a system of two parallel conductors of circular cross section—a system very frequently encountered in various applications. The magnetic field generated by the current applied on each conductor is expressed by means of vector magnetic potential and expanded into Fourier series. Using the Laplace and Helmholtz equations, as well as the classical boundary conditions, the current density induced due to the proximity and skin effect is determined in each conductor. The resulting current density is expressed as a series of successive reactions. The results obtained are compared with those obtained via finite elements. Although the paper is theoretical, the considered problem has a practical significance, because transmission lines with round conductors are universally used. Besides, the results can be used to estimate errors when only the first reaction is taken into account, which gives relatively simple formulas.

This paper presents a semi-analytical method for determining the distribution of the thermal field in a system of two parallel round conductors, taking into account the skin and proximity effects. The method of a suitably constructed Green’s function was applied to find an analytical expression for the eigenfunctions describing the temperature distributions. In turn, the relevant integrals, which cannot be determined analytically, were calculated numerically. The foundation of the method is the knowledge of the current density distribution in the conductors. As a result, the steady-state distribution of the temperature field in the conductors for various parameter values can be determined. The obtained numerical results were positively verified using the finite element method. Using the developed method, the share of skin and proximity effects in the temperature rise and steady-state current rating was evaluated. Closed analytical formulas were obtained for the AC case with the skin effect taken into account. When the skin depth is smaller than the wire radius, the skin effect has quite a large impact on the conductor temperature. The impact of the proximity effect is much smaller but clearly noticeable when the distance between the wires is smaller than five times the wire radius. In addition, the influence of the value of the heat transfer coefficient on the thermal field of the conductors was also examined.

Waste tobacco stems from the tobacco industry were used to obtain activated carbon by thermal conversion and chemical activation with KOH. The aim was to investigate its adsorption ability towards Zn(II), Cd(II), and Pb(II) from aqueous solutions. Fundamental physical and chemical properties were investigated, and the point of zero charge pH was detected. The results showed that the obtained activated carbon was characterized by a high specific surface area, pore volume, and negative surface charge, which could make it an efficient metal adsorbent. In the next step, the optimal adsorption conditions were determined using Central Composite Design. Finally, the adsorption kinetics and thermodynamics were studied. The adsorption rate is very high for Pb(II) and Cd(II), whereas it is noticeably lower for Zn(II). The negative value of Gibbs free energy change (∆G) confirmed that the adsorption process of the tested metal ions is feasible and proceeds spontaneously. The thermodynamics indicate that the adsorption of zinc and lead on the tested carbon is an exothermic process, and for cadmium, this process is endothermic.

Devices for electric heating of railroad turnouts are elements of the railway infrastructure protecting railroad turnouts against blocking them by snow and ice in winter. They often operate based on the principle of resistance heating but other solutions are also emerging. In this paper, one of such new solutions using the phenomenon of electromagnetic induction was presented and tested under various conditions. In comparison with traditional resistive heaters, the inductive ones offer heat distribution directly to ice and snow without intermediation of rails. Moreover, they can use a wide range spectrum of frequency to shorten the melting time. The resistive and inductive devices were tested with respect to melting time, temperatures and energy consumption. It follows that the induction-based device offers much lower energy consumption at a level of 30%–60% of that by resistive heater. The details depend on frequency used, initial temperature and number of induction devices of action assumed equivalent to the resistive one. Inductive heating of turnouts also offers shorter times of operation, which are obtained for frequencies in the range 40–70 kHz. The inductive device was also tested with respect to magnetic field levels around it to assess its possible influence on nearby infrastructure.

The paper presents a study of the influence of magnetic hysteresis on macroscopic eddy current losses. Usually, this loss is calculated within many simplifying assumptions, of which the most striking is not only neglecting the hysteresis, but also the nonlinearity of the material. To check how such simplifications affect the results, the loss was calculated taking into account the hysteresis phenomenon for several materials. For this purpose, an algorithm for solving Maxwell’s equations with magnetic characteristics given as a family of measured hysteresis loops was constructed. A new method for conversion between H and B fields using the measured hysteresis loops was also proposed. The results of calculations for three materials show that the eddy current loss calculated with magnetic hysteresis taken into account are smaller than those calculated via the classical formula obtained for linear materials. For the tested materials, the differences reach up to around 30%, depending on frequency, magnetic flux density and thickness of electrical sheet. This may result, among others, in erroneous determination of the excess loss in Bertotti’s approach.

The removal of Pb(II), Cd(II) and Ni(II) ions from aqueous solutions by means of nonthermal plasma with a dielectric barrier discharge is investigated. Aqueous solutions with metal ion concentrations from 10 to 100 mg/dm³ in spring water were used. In the first stage, the optimization of the solution flow rate, generator modulation frequency and duty cycle was made in terms of the removal efficiency of the considered metals. The removal was then investigated as a function of the number of passes of the solution through the cold plasma reactor. The effect of the initial concentration of ions in the solution was studied. Techniques such as composite central design, least squares method and Fourier transform infrared spectroscopy were used. The physical and chemical parameters of the solutions, such as electrical conductivity, pH, temperature, concentration of metal ions and the content of other substances (e.g., total organic carbon), were measured, and the presence of microorganisms was also examined. It was found that each pass of the solution through the cold plasma reactor causes a decrease in the concentration of Cd(II) and Ni(II); the concentration of Pb(II) drops rapidly after one pass, but further passes do not improve its removal. The removal percentage was 88% for Cd(II) after six passes and 72% for Pb(II) after one pass, whereas 19% for Ni(II). The purification mechanism corresponds to the precipitation of metal ions due to the increasing pH of the solution after exposure to cold plasma.