= Solution
For a Newtonian <circular orbit>, $v_\phi^2=GM/r$, so the specific orbital <energy> is $e=v_\phi^2/2-GM/r=-GM/(2r)$. Half of the released potential <energy> remains in circular orbital motion. The binding-energy estimate between the specified edges is therefore
$$
L_{\rm bind}\simeq\frac{GM\dot m}{2}\left(\frac1{r_{\rm in}}-\frac1{r_{\rm out}}\right)=\frac{GM\dot m}{2R_s}\left(\frac16-\frac1{30}\right)=\frac{\dot m c^2}{30}.
$$
Using $M_\odot=1.98847\times10^{30}\,\mathrm{kg}$ and one Julian year $=3.15576\times10^7\,\mathrm s$ gives $\dot m=6.30\times10^{22}\,\mathrm{kg\,s^{-1}}$. Thus \b[the radiative <luminosity> scale is $L\sim1.9\times10^{38}\,\mathrm W$], approximately $1.9\times10^{45}\,\mathrm{erg\,s^{-1}}$ or $4.9\times10^{11}L_\odot$. The black-hole <mass> cancels because both edge radii scale with $M$. The specified inner edge is $6R_s$; it must not be silently replaced with a different relativistic orbit radius.
For a finite viscous disc, the precise radiated power also depends on boundary work: <torque transport of energy in a steady accretion disk> means that orbital binding-energy release need not all be radiated inside the two stated edges. If the intended model is a radiatively efficient steady <Keplerian accretion disk> with a <zero-torque inner boundary condition>, integrate the one-face flux $F=3GM\dot m[1-\sqrt{r_{\rm in}/r}]/(8\pi r^3)$ over both faces. It gives
$$
L_{\rm diss}=\frac{GM\dot m}{2r_{\rm in}}\left[1-3\frac{r_{\rm in}}{r_{\rm out}}+2\left(\frac{r_{\rm in}}{r_{\rm out}}\right)^{3/2}\right]\simeq\boxed{1.37\times10^{38}\,\mathrm W}.
$$
The difference from $L_{\rm bind}$ is the outward <torque> power at the outer edge. The question supplies neither boundary <torque> nor the external material-supply <energy> budget, so the two calculations state their assumptions explicitly: about $2\times10^{38}$ W is the binding-energy estimate, while $1.37\times10^{38}$ W is the finite-disc zero-inner-torque dissipation result. Both neglect <radiation> advection, winds and relativistic corrections as required for this model.<Dynamics of Astrophysical Discs, Lecture 5: Boundary Conditions and Steady Accretion by Gordon I. Ogilvie>[§5.2, printed pp.3–4: steady-disc surface flux and outward torque transport of energy]{ref}
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