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Concentration-dependent thermophysical properties of molten Mg-Pb and Mg-Ga alloys at 1000 K was compared using the Redlich Kister equation by optimizing exponential interaction energy parameters based on the R-K polynomials framework. The mixing behavior was investigated by giving more emphasis to the role of temperature-dependent interaction energy parameters. Our study shows that the magnesium gallium alloy is slightly interacting than the magnesium lead alloy. The surface tension and viscosity of both alloys was compared using the Butler equation as improved by Kaptay and KRP (Kozlov-Ronanov-Petrov) approach respectively. The surface tension of Mg-Pb liquid alloy increases but decreases in Mg-Ga alloy with an increase in the concentration of Mg. The viscosity has a nonlinear variation for both alloys with the increase in the concentration of magnesium.

A sudden application of sources results in time-varying currents and voltages in the circuit known as transients. This phenomenon occurs frequently during switching. A simple circuit constituting a resistor, an inductor, and a capacitor is termed an RLC circuit. It may be in parallel or series configuration or both. Different values of damping factors determine the different nature of the transient response. We applied different numerical solution methods such as explicit (forward) Euler method, third-order Runge-Kutta (RK3) method, and Butcher's fifth-order Runge-Kutta (BRK5) method to approximate the solution of second-order differential equation with initial value problem (IVP). We thoroughly compared the numerical solutions obtained by these methods with the necessary visualization and analysis of error. We also examined the superiority of these methods over one another and the appropriateness of numerical methods for different damping conditions is explored. With high accuracy of the approximation and thorough analysis of the observation, we found Butcher's fifth-order Runge-Kutta (BRK5) method to be the best numerical technique. Regarding the different values of damping factors, we considered the further possibility of discussion and analysis of this iterative method.

Theoretical study of thermodynamic properties of binary liquid Potassium-Thallium alloy at temperatures 798 K, 1000 K, 1200 K and 1400 K have been analyzed as a function of concentration by considering temperature dependent exponential interaction parameters in the framework of R-K polynomials. The viscosity and surface tension of the alloy have been studied by BBK model and improved derivation of Butler equation respectively. The study provides the information of moderately interacting as well as segregating nature at the low concentration of Thallium and ordering nature at high concentration of Thallium and the viscosity and surface tension of the alloy decrease with increase in temperature.

The thermodynamic and structural properties of binary alloy Ag- Sb at temperature 1250K have been reported theoretically using quasi lattice model. The interchange energy has been considered a function of a temperature and thus various thermodynamic quantities are calculated at elevated temperature. The theoretical values of free energy of mixing, heat of mixing, entropy of mixing and chemical activity are reasonable agreement with experimental values in all concentrations of antimony from 0.1 to 0.9. The theoretical analysis tells that the alloy shows both ordering nature in Ag rich end and segregating nature in Sb rich end .The study reveals that the properties of alloy are asymmetric around equi-atomic composition. The Ag_3 Sn complexes are most likely to exist in the liquid state and are moderately interacting.

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We have extended a computational model used to research the thermodynamic properties of binary liquid alloys to study chemical short-range order parameters and diffusion coefficients. Numerous simulations have also been employed for surface properties such as surface concentration and surface tension. The propensities for phase separation of the Pb–Sb alloy were also observed with a temperature rise. The structural and thermodynamic properties of the alloys were measured using the same interaction parameters that are suitable for the free energy of mixing and mixing enthalpy. The interaction parameters are discovered to be temperature-dependent but concentration-independent. Our results indicate that the liquid alloy Pb–Sb has a weakly interacting composition. According to the surface property review, the element Sb having a higher surface concentration than its bulk concentration segregates over the surface of the alloy.

A theoretical model based on the assumption of compound formation in binary liquid alloy has been used to investigate the thermodynamic properties (free energy of mixing, enthalpy of mixing and entropy of mixing), microscopic properties (concentration fluctuation in long wavelength limit and chemical short range order parameter), surface properties (surface tension and surface composition) and dynamic properties ( viscosity and diffusion coefficient). All the properties of Al2Fe binary melt have been measured using the same energy parameters configured for experimental values of free energy of mixing. The energy parameters are detected as independent of concentration, but depend on temperature. The findings are well consistent with the experimental standards.

Thermodynamic properties of compound forming binary liquid sodium-mercury alloy at temperature 673 K have been analyzed as a function of concentration by considering NaHg 2 complex using quasi chemical approximation. The surface tension of the alloy has been studied by the compound formation model, Butler equation as improved by Kaptay, and Statistical mechanical approach. The mixing behavior of the alloy is studied in detail with more emphasis on the interaction energy parameters between neighboring atoms of the alloy. The study provides the information of moderately interacting as well as ordering nature on the entire range of concentration of the liquid alloy and the computed theoretical thermodynamic data are in good agreement with the corresponding experimental data at 673 K. The surface tension of the alloy computed predicts deviation from the ideal case.