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The problem of the relaxation to a Maxwellian of the Balescu-Lenard equation is solved numerically as an initial value problem for isotropic distributions of electrons situated in a neutralizing, uniformly smeared out background of positive charge. Several different forms for the initial distribution function are chosen: a Gaussian peaked at about 0.28 of the electron thermal speed, a resonance function, and a Maxwellian coexisting with a sharply peaked Gaussian (the peak of the Gaussian being located at two thermal speeds of electrons). The Fokker-Planck equation with the Rosenbluth-MacDonald-Judd collision term is also solved numerically under the same restrictions and with the same initial distribution functions. Comparison of the solutions of the two kinetic equations shows that the difference between them is very small, and a probable reason for this is advanced. The evolution of the distribution functions with time is studied, and a relaxation time is defined.

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The authors have evaluated eco-friendly base fluids for hardening steel such as canola oil and soybean oil to identify alternative renewable quenchants using basestocks available in Ukraine. Meso- and nanofluids were prepared by the discrete-pulse input of energy (DPIE) method. It has been established that the cooling intensity of these quenchants depends not only on the composition of the base fluid and the meso- or nanoparticles but also on the methods of preparation. The influence of the DPIE method on cooling characteristics of vegetable oils was studied. High-temperature cooling properties within the temperature range of 200°C–850°C exceed the observed properties of traditional mineral oil-based quenchants.