Abstract We provide a 2.5-dimensional solution to a complete set of viscous hydrodynamical equations describing accretion-induced outflow and then plausible jet around black holes/compact objects. We prescribe a self-consistent advective disk-outflow coupling model, which explicitly includes the information of vertical flux. Inter-connecting dynamics of inflow-outflow system essentially upholds the conservation laws. We provide a set of analytical family of solutions through the self-similar approach. The flow parameters of the disk-outflow system depend strongly on viscosity parameter $\alpha$ and cooling factor $f$.
Keywords accretion, accretion disk, black hole physics, hydrodynamics, galaxies: jets
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