adopt $\alpha$ -prescription for viscosity of rotating gas in accretion flow. The convection, outflow and magnetic field and its correspond resistivity are important to transfer of energy and angular momentum in disc.

The equation of continuity gives:

$$\frac{\partial}{\partial r}(r \Sigma V_r )+\frac{1}{2\pi}\frac{\partial \dot{M}_\mathrm{w}}{\partial r}=0$$

where $V_{r}$ is the accretion velocity ($V_{r}<0$) and $\Sigma=2\rho H$ is the surface density at a cylindrical radius $r$. $H$ is the disc half-thickness and $\rho$ is the density. Mass-loss rate by wind/outflow is represented by $\dot{M}_\mathrm{w}$. So

$$\dot{M}_\mathrm{w}=\int 4\pi r'\dot{m}_\mathrm{w}(r')dr',$$

where $\dot{m}_\mathrm{w}(r)$ is the mass-loss per unit area from each disc face. Similar to Blandford & Begelman (1999) and AM12, we write the dependence of accretion rate as follows,

$$\dot{M}=-2\pi r \Sigma V_r =\dot{M}_{out}(\frac{r}{r_{out}})^{s}
$$

where $\dot{M}_{out}$ is the mass accretion rate at the outer adge of the disc ($r_{out}$) (Blandford & Begelman 1999) and $s$ is a constant with order of unity. Considering equation (1-3), we can write $$\dot{m}_\mathrm{w}=\frac{s \dot{M}_{out}}{4 \pi r_{out}^{2}}(\frac{r}{r_{out}})^{s-2}
$$ The equation of motion in the radial direction is:

$$V_r \frac{\partial V_r}{\partial
r}=\frac{V_{\varphi}^{2}}{r}-\frac{GM_{\star}}{r^2}-\frac{1}{\Sigma}\frac{d}{dr}(\Sigma
c_\mathrm{s}^{2})$$

$$-\frac{c_\mathrm{\varphi}^{2}}{r}-\frac{1}{2\Sigma}\frac{d}{dr}(\Sigma c_\mathrm{\varphi}^{2}+\Sigma c_\mathrm{z}^{2})$$

where $V_{\varphi}$, $G$ and $c_\mathrm{s}$ are the rotational velocity of the flow, the gravitational constant and sound speed respectively. The sound speed is defined 