Radial profiles of number density (top), radial speed (middle), and temperature (bottom) for a slow (left column) and a fast solar wind (right column) in the range from 1 R_⊙ to 1 AU. These solutions were obtained using a heating function as given in Eq. (3). The color-coding distinguishes the discontinuous analytical solutions from the numerical ones. The slow wind solutions are computed for different widths of the heating function with corresponding different critical distances, where ϵ and ΔR = r_c − r₀ are given in units of solar radii. For the fast wind, a solution with an extremely narrow heating function is shown (ϵ = 1/64 R_⊙, r_c ≈ 6 R_⊙).