Progress in electrical engineering puts a greater demand on the cooling and insulating properties of liquid media, such as transformer oils. To enhance their performance, researchers develop various nanofluids based on transformer oils. In this study, we focus on novel commercial transformer oil and a magnetic nanofluid containing iron oxide nanoparticles. Three key properties are experimentally investigated in this paper. Thermal conductivity was studied by a transient plane source method dependent on the magnetic volume fraction and external magnetic field. It is shown that the classical effective medium theory, such as the Maxwell model, fails to explain the obtained results. We highlight the importance of the magnetic field distribution and the location of the thermal conductivity sensor in the analysis of the anisotropic thermal conductivity. Dielectric permittivity of the magnetic nanofluid, dependent on electric field frequency and magnetic volume fraction, was measured by an LCR meter. The measurements were carried out in thin sample cells yielding unusual magneto-dielectric anisotropy, which was dependent on the magnetic volume fraction. Finally, the viscosity of the studied magnetic fluid was experimentally studied by means of a rheometer with a magneto-rheological device. The measurements proved the magneto-viscous effect, which intensifies with increasing magnetic volume fraction.

The Brownian motion (BM) is not only a natural phenomenon but also a fundamental concept in several scientific fields. The mathematical description of the BM for students of various disciplines is most often based on Langevin’s equation with the Stokes friction force and the random force modeling Brownian particle (BP) collisions with surrounding molecules. For many phenomena, such a description is insufficient, as it assumes an infinitesimal correlation time of random force. This shortcoming is overcome by the generalized Langevin equation (GLE), which is now one of the most widely used equations in physics. In the present work, we offer a simple way of solving this equation, consisting of its transformation into an integro-differential equation for the mean square displacement of the BP, which is then effectively solved using the Laplace transform (LT). We demonstrate the use of this method to solve both the standard Langevin equation and the GLE for the BP in an external harmonic field. We analyze the cases of overdamped (when frictional forces prevail over inertial forces and the BP mass is considered zero in the equation) and underdamped (inertial effects are not neglected) equations. We show under what conditions an overdamped solution can be used instead of complicated solutions of the underdamped equation. We also demonstrate the effectiveness of the use of the LT on a microscopic approach to the derivation of the GLE. Graduate students are offered several problems in which the internal shortcomings of the overdamped Langevin equations manifest themselves.

In conventional viscometry studies an additional treatment of data is necessary in order to obtain the expected linear dependence of the reduced viscosity on concentration in extremely diluted polymer solutions. This work reports on the direct measurements of this dependence using a new Couette-type viscometer. The values of intrinsic viscosity and Huggins coefficient of the studied poly(N-vinyl-2-pyrrolidone) (PVP) water solution notably differ from the previous results obtained by the traditional capillary viscometers. From the obtained data the parameters used in the bead-spring theories of polymer universal behavior, such as the gyration radius and the longest relaxation time are calculated.