Abstract

We present a mathematical model and numerical analysis of the solar wind, incorporating magnetohydrodynamic (MHD) effects. Extending Parker’s classical solar wind model, we introduce a magnetic field through the dimensionless plasma beta parameter (𝛽), defined as the ratio of thermal to magnetic pressure. The resulting model yields a nonlinear ordinary differential equation that governs the solar wind velocity profile as a function of radial distance from the Sun. Numerical solutions are obtained for a range of 𝛽values, revealing the influence of magnetic pressure on solar wind acceleration. Our analysis shows that lower values of 𝛽(indicating stronger magnetic effects) lead to earlier and more rapid acceleration through the critical point, producing higher terminal velocities. These findings underscore the importance of MHD processes in accurately describing solar wind dynamics and provide a theoretical framework for investigating solarterrestrial interactions.