A global 2.5-dimensional three fluid solar wind model is presented. Two ion species, namely protons and alpha particles, are heated by an empirical energy flux while electrons are heated by the classical heat flux and Coulomb coupling with ions. It is found that for a reasonable relative speed between alpha particles and protons at 1 AU to be achieved, the alphas need to be preferentially heated in the inner corona. No external heating is applied in the streamer base, the closed magnetic field region. A hot coronal boundary, the electron heat flux, and Coulomb coupling keep plasma species in equilibrium inside the streamer, and a nonisothermal streamer is found. The abundance of alpha particles varies within the streamer base. It is small in the streamer core compared with streamer legs, and alphas continuously drain out of the streamer core along magnetic field due to gravitational settling. The settling operates over a timescale of several days. Alpha particles in the slow wind have a smaller abundance than in the fast wind at 1 AU, in agreement with observations. This is mainly determined in the near-Sun region. For the coronal alpha abundances in the range 0.015--0.15, it is found that alpha particles play a negligible role in determining the magnetic field. In this sense, treating alphas as test particles is justified. However, alphas have an important impact on solar wind parameters. Coulomb collisions and heating drag alphas into the solar wind. The Coulomb friction with protons by itself is, however, unable to drive into the slow solar wind a flux of alphas flowing at roughly the same speed of protons as observed by in situ measurements at 1 AU.