= Solution
A geometrically thin <accretion disk> around a central <mass> $M$ has nearly <Keplerian orbits>, with $\Omega^2\simeq GM/r^3$. Its vertical <hydrostatic equilibrium> gives $H\sim c_s/\Omega\ll r$. The <specific angular momentum> $\ell=r^2\Omega\propto r^{1/2}$ decreases inward, so accreting matter must transfer <angular momentum> to other matter. A <viscous stress> couples neighboring annuli rotating at different <angular velocities>.
Writing $\nu$ for effective <kinematic viscosity> and $\Sigma$ for surface <mass density>, the outward <viscous torque in an accretion disk> is
$$
\mathcal G=-2\pi r^3\nu\Sigma\frac{d\Omega}{dr}>0.
$$
Steady <mass conservation> defines $\dot M=-2\pi r\Sigma u_r>0$. If the inner radius $r_{\rm in}$ has negligible applied torque, <angular momentum conservation> gives $\mathcal G=\dot M(\ell-\ell_{\rm in})$, hence
$$
\boxed{\nu\Sigma=\frac{\dot M}{3\pi}\left[1-\left(\frac{r_{\rm in}}r\right)^{1/2}\right].}
$$
Well outside that boundary, $u_r\simeq-3\nu/(2r)$ and the inward drift time is of order $r^2/\nu$, much longer than an <orbital period> in a thin disk with modest effective stress. Dissipation of orbital <energy> heats the disk. If that heat escapes locally from two faces, the radiative flux from either face is
$$
F(r)=\frac{3GM\dot M}{8\pi r^3}\left[1-\left(\frac{r_{\rm in}}r\right)^{1/2}\right].
$$
Integration over both faces gives $L=GM\dot M/(2r_{\rm in})$ in this Newtonian zero-torque model. Material can lose <angular momentum> while the disk's outer parts spread outward: outward transport does not imply that most of its <mass> moves outward. In real ionized disks, <magnetorotational instability> and magnetic stresses often provide the effective transport; molecular <viscosity> alone is generally insufficient.
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