A time-dependent two-fluid model with thermal conduction for the solar wind

A time-dependent spherically symmetric two-fluid model for the solar wind is presented. In this model, continuity, momentum, and energy equations are simultaneously solved. Thermal conduction for both electron and proton components-with allowance for noncollisional modifications-are incorporated in the model equations. This model is used to study and compare one-fluid and two-fluid time-dependent solutions with and without consideration of thermal conduction effects. It is found that, as in the steady-state case, the unique temperature of the one-fluid time-dependent case (T^1F) represents to a good approximation the electron temperature of the two-fluid time-dependent case (T_e^2F). Second, in the two-fluid time-dependent case, a shock is formed in the interplanetary medium when higher-speed solar wind streams overtake the lower speed steady solar wind. Finally, the time-dependent solutions of the two-fluid model provide proton to electron temperature ratios which may be larger or smaller than unity.