The evolution of a binary star system by various analytical and numerical approximations of mass transfer rate normalized to the equilibrium rate and its stability conditions are investigated. We present results from investigations of mass transfer and stability in close binary star systems using the different orbital parameters. The stability and instability of mass transfer in binary star evolution depends on the exchange of material which the response of the binary to the initial Roche lobe overflow causes the donor to loose even more material. Our work is mainly focused on basic mathematical derivations, analytical and numerical solutions in order to explain the mass transfer system in different orbital parameters as well as the results are compared with previous studies in both cases. Mass transfer is usually stable, as long as the winds specific angular momentum does not exceed the angular momentum per reduced mass of the system. This holds for both dynamical and thermal time scales. Those systems which are not stable will usually transfer mass on the thermal time scale. The variation of Roche lobe radius with mass ratio in the binary, for various orbital parameters in the conservative and non-conservative mass transfer, as well as the evolution equations, orbital angular momentum of the binary system and the corresponding analytical and numerical solutions for different cases, under certain restrictive approximations is derived, simulated and discussed.

In this study, we have investigated the stellar parameters of Algol-type eclipsing binaries in the range of primary and secondary masses between 0.2 and 8 M ⊙ , which were obtained from the catalog of approximate photometric and absolute elements of eclipsing variable stars. We examined those parameters for classical Algols and hot semidetached binaries. We have made a statistical analysis of Algol-type eclipsing binaries' stellar parameters and constructed the mass-luminosity and mass-radius relations for the primary and secondary components of classical Algols and hot semidetached binaries.

In this paper, we investigate the orbital and stellar parameters of low- and intermediate-mass close binary systems. We use models, presented in the catalogue of (Han et al. 2000) and calculate parameters of accretors. We also construct distributions of sys- tems along luminosity, semi-major axis and angular momentum, and make some conclusions on their evolution with time. We made a comparison of the results with observational data and it shows a good agreement. The set of theoretical models published in (Han et al. 2000) quite adequately describes the observational data and, consequently, can be used to determine the evolutionary path of specific close binary systems, their initial parameters values and final stages.

We applied the basic dynamical evolution equations of orbit for nonconservative mass transfer to compute the absolute parameters of Algols and incorporate their decreasing orbital periods. The lists contain the parameters of 59 Algols. The accretors of those systems are almost all located in the main sequence region, while their donors are evolved off the main sequence region, and they are located in a giant or subgiant region. We investigated the evolutionary computations of nonconservative mass transfer with the observed parameters of Algols, which has been designed to consistently examine the statistical analysis of both single‐ and double‐lined Algols. Then, we numerically determined the spin and the specific angular momentum of the accretor and the donor and also computed the rate of change of the orbital angular momentum and period of these systems. In addition, we calculated the semimajor axis, the fractional radius of a ring, the actual Roche lobe radius, and the critical mass ratio of the system. We also examined the stability of mass transfer in those systems. Finally, we made a comparison between the theoretical computations for the dynamical evolution equations of orbit and the observed parameters of Algols.

In this study, we have investigated the stellar evolution models using the open-source software instrument Modules for Experiments in Stellar Astrophysics. We examine the evolution of angular momentum and the stability of mass transfer in the evolution of Algol-type binaries through the inner Lagrangian point via the Roche lobe overflow. Also, we have determined the ongoing challenge of chemical mixing and exhibit improvements that make easier the simulation of Algol-type binaries evolution.