This paper was prepared by students of Academician V. L. Rvachev, the creator of non-Archimedean calculus. Structurally, the paper is divided into three sections. The first section examines the relativistic formula for n-ary addition. Transformations of this formula yield four results: two pairs of mutually inverse functions which, given their properties, define the construction of non-Archimedean calculus; the structure of a relativistic series; and two mappings between the sets ℜ=(-∞, ∞) and ӿ=(-c, c). The second section presents relativistic trigonometry, including formulas for addition, the conversion of a sum of trigonometric functions into a product, and the conversion of a product of trigonometric functions into a sum. In the third section, relativistic hyperbolic functions are derived with the use of the relativistic exponential function, and their properties are outlined.
Under the current operating conditions of the Integrated Power System of Ukraine, the reliability and operational safety of thermal power plant equipment are of critical importance. Ensuring long-term operation and evaluating the individual service life of critical turbine components following mechanical damage and repair restorations require a comprehensive investigation of their thermomechanical state. The aim of this study is to perform computational research of the spatial thermal state of the low-pressure rotor of the K-200-130 steam turbine to provide scientific and technical justification for extending its reliable operational life. The research methodology is based on the fundamental principles of transient heat conduction and continuum mechanics, utilizing the finite element method within the SolidWorks environment. A spatial 3D model of the symmetric half of the LPR (approximately 6.2 million elements) was developed with adaptive mesh refinement in stress concentration zones. The model incorporates actual post-repair geometric modifications, specifically a reduction in the shaft journal diameter in the bearing No. 5 area from 435 mm to 420 mm. Second- and third-kind boundary conditions for heat transfer were determined using similarity theory criterion equations, accounting for the thermodynamic and hydrodynamic characteristics of the steam flow in the flow path. Three-dimensional temperature fields of the rotor were obtained for the rated 200 MW load regime and during a transient cold start-up. It was found that under steady-state operation, the metal reaches a thermally stabilized state, with temperatures ranging from 160–170 °C in the steam inlet region to 40–65 °C in the last stages. During cold start-up, significant transience was observed: during rotor rolling and speed acceleration, an extreme radial temperature gradient occurs, with the outer surface heating up to 130–150 °C while inner layers warm up only to 30–40 °C. A notable thermal lag in the warming of the shaft symmetry axis was recorded, resulting from the massive rotor dimensions and the thermophysical properties of 25Cr1Mo1V steel. The resulting temperature fields and gradients provide a foundational basis for subsequent numerical analysis of the rotor’s stress-strain state, evaluation of cumulative low-cycle fatigue damage, and prediction of the power unit's remaining individual service life.
A schematic design for a hybrid power plant based on a solid oxide fuel cell (SOFC) and Stirling engines, which involves the cascaded recovery of the thermal potential of the SOFC exhaust streams, is proposed. The objective of this study is to enhance the efficiency of fuel energy utilization in the SOFC–Stirling engine hybrid power plant by developing a configuration that employs the energy potential of the SOFC exhaust streams in a cascade, recovering waste heat sequentially across Stirling engines operating at different temperature levels. A mathematical model of the system has been developed, accounting for the material and energy balances of its core components, as well as regenerator efficiency, dead volumes, and temperature differences within the Stirling engines. A parametric analysis was conducted to examine the impact of regeneration efficiency and the temperature difference between the gas stream and the working fluid on the plant’s energy performance. For a configuration featuring a single Stirling engine, it was found that increasing the regenerator efficiency from 0.5 to 0.8 raises the thermal efficiency from 16.32–16.33% to 28.41–28.54%, and the electrical power output – from 116 kW to 202.72 kW. Under these conditions, the hybrid power plant achieves a maximum energy efficiency of 77.30% among the studied operating modes. It has been shown that after the first stage of waste heat recovery and the regenerative preheating of the cathode air, the temperature of the exhaust gas stream remains in the range of 474–528 °C. To utilize this thermal potential, the installation of a second Stirling engine – operating at a lower heat-input temperature level – is proposed. Calculations indicate that its electrical power output ranges from 103.29 to 108.17 kW, bringing the total electrical power output of the hybrid power plant to 810.85 kW. Among the analyzed operating modes, the highest calculated energy efficiency for the two-stage plant is 89.19%, achieved with regenerator efficiencies of e1=e2=0.8 and temperature differences of ΔTh,1=20 К and ΔTh,2=50 K. These results confirm the viability of using a cascaded approach to recover the thermal potential of SOFC exhaust streams via Stirling engines operating at different temperature levels, thereby generating additional electrical energy.
This paper investigates the isothermal drying kinetics and effective moisture diffusivity of cylindrical Shorea robusta (Sal) wood particles dried in a hot air oven at 75 °C, 90 °C, and 105 °C. Sal wood, one of the most ecologically and commercially significant hardwood species of the Indian subcontinent, holds considerable promise as a biomass fuel feedstock, yet its drying characteristics have not been systematically characterized. Five established thin-layer drying models; Lewis, Page, Modified Page, Wang & Singh, and Henderson & Pabis, were fitted to the experimental moisture ratio (MR) data using MATLAB curve fitting. The Page model provided the best statistical fit, yielding coefficients of determination (R²) of 0.9971, 0.9988, and 0.9983; sum of squares of error (SSE) values of 0.003618, 0.001854, and 0.003047; and root mean square error (RMSE) values of 0.01608, 0.01151, and 0.01425 at 75°C, 90°C, and 105°C, respectively. Effective moisture diffusivity, calculated via the analytical solution of Fick’s second law for cylindrical geometry, increased from 7.92×10⁻8 to 26.0×10⁻8 m²/s over the experimental temperature range. Activation energy, estimated using an Arrhenius-type equation, was found to be 4.42×10⁴ J/mol, consistent with values reported for analogous lignocellulosic biomasses. The findings provide fundamental kinetic data for rational dryer design and optimisation of biomass pre-treatment systems.
This study focuses on volumetric sensible enthalpy formulation of ethylene glycol-based nanofluids that replaces the conventional temperature-based energy equation. The nanofluid contains Al2O3 nanoparticles with volume fractions in the range (0.01≤φ≤0.05), consistent with experimentally investigated concentrations. Unlike conventional temperature-based energy formulations, the present approach describes thermal transport through volumetric sensible enthalpy, representing the sensible energy stored per unit volume of the nanofluid. This framework enables the analysis of coupled momentum, enthalpy, and nanoparticle transport in electrically conducting Casson nanofluids involving thermophoresis, viscous dissipation, and Joule heating. The governing momentum, enthalpy, and nanoparticle concentration equations were transformed into coupled nonlinear ordinary differential equations using similarity transformations and solved numerically using an adaptive collocation scheme (SciPy’s solve_bvp). Parameter effects are systematically evaluated, including the Casson parameter, magnetic field parameter, Schmidt number, Biot number, thermal and solute Grashof numbers, Brinkman number, Eckert number and thermophoresis parameter. The results show that the magnetic field parameter and Casson rheological effects strongly influence the momentum characteristics of the flow. Increasing the magnetic field parameter suppresses the velocity distribution through the Lorentz force while enhancing the volumetric sensible enthalpy due to Joule heating. The Eckert number produces a significant increase in volumetric sensible enthalpy owing to viscous dissipation, whereas the Schmidt number primarily controls nanoparticle concentration transport with only a weak influence on the enthalpy field. Thermal and solutal buoyancy parameters enhance fluid motion through buoyancy-driven convection, while thermophoresis promotes nanoparticle migration and moderately increases thermal energy storage within the boundary layer. In contrast, the Biot and Brinkman numbers exhibit limited influence on the velocity, volumetric sensible enthalpy, and concentration profiles within the considered parameter ranges. The proposed volumetric sensible enthalpy formulation provides an alternative framework for quantifying internal energy storage and redistribution in MHD non-Newtonian nanofluids. Potential applications include thermal energy storage, electronic cooling with nanofluids, polymer extrusion, magnetohydrodynamics (MHD) pumping, biomedical flows, solar thermal collection, and nuclear reactor cooling.
