$\alpha$ as the viscosity (see below).

We employ the following viscosity parameter ($\alpha$) prescription in a time-dependent manner (Mineshige, Wheeler 1989): $$\label{alpha}
   {\alpha}(R,t)~=~
   {\alpha}_0~\left[{{H(R,t)}\over R}\right]^N,$$ where ${\alpha}_0$ is a constant, and $R$ and $H$ are the disk radius and height. From the hydrostatic relation, $H$ = $C_{\rm s}/{\Omega}_{\rm K}$, where $C_{\rm s}$ is the sound speed, we can rewrite equation (\[alpha\]) as $$\alpha(R,t)~=~
   \alpha_0~{\left({{{\cal R}\over \mu}{T_{\rm c}}
                    ~v_\phi^2}\right)}^{N\over 2},$$ where $\cal R$ is the gas constant, $\mu$ is the mean molecular weight, and $v_{\phi}(R)$ = $R~{\Omega}_{\rm K}(R)$, the azimuthal velocity in the Keplerian disk. This implies that $\alpha$ is a function of the mid-plane or central temperature: $\alpha$ $\propto$ ${T_{\rm c}(t)}^{N/2}$.

The boundary conditions are $${\partial T_{\rm c}\over\partial r} = 0   \quad {\rm and}\quad
  {\dot M} = {\dot M}_{\rm T}$$ at the outer edge and $$T_{\rm c} = W = 0$$ at the inner edge of the disk, where the mass-transfer rate from the companion star is taken to be constant in any particular model. Relativistic effects are not taken into account.

Methods of Calculations
-----------------------

The radially-dependent equations, (\[mass\])–(\[energy\]), are solved with the equations obtained by integration of the vertical structure of disks, $$f=f(T_{\rm c},\Sigma,R),$$ where the function $f$ 