Some well established observational facts about most wind-type astrophysical outflows are the following: (i) they are strongly nonspherically symmetric and at least two-dimensional; fast solar wind streams from polar coronal holes and jets from stars and galaxies are two representative and characteristic examples, (ii) some kind of nonthermal heating is required, at least during the initial acceleration stage of the outflow; therefore, the flow is far from beeing adiabatic and the assumption of polytropicity with an arbitrarily specified index γ, although useful from the mathematical point of view to solve the governing equations and provide some physical insight into the problem, is nevertheless artificial. (iii) the ubiquitous magnetic field seems to play a decisive direct, or at least, indirect role in heating stellar coronae and driving stellar winds. Nevertheless – perhaps for the sake of simplicity – most studies on astrophysical outflows and winds so far have neglected to incorporate the above three basic features of nonspherical expansion, nonpolytropic equation of state and magnetohydrodynamic description of the problem. We have recently embarked in an effort to model wind-type outflows by incorporating those basic physical constraints (Low and Tsinganos, 1986; Tsinganos and Low, 1989; Tsinganos and Trussoni, 1990, 1991; Tsinganos and Sauty, 1992a,b).