Stone et al. 1999; Narayan et al. 2000) there are some debates about whether convection exists in hot accretion flow or not. Some of them have clearly shown that convection in an MHD accretion flow likely does not exist (Pen et al. 2003; Narayan et al. 2012; Yuan et al. 2012b). But some other series of numerical simulations reveal that the convection instability likely occurs in hot accretion flows (Igumenshchev, Chen & Abramowicz 1996, Igumenshchev & Abramowicz 1999, 2000, Stone, Pringle & Begelman 1999, Yuan & Bu 2010). Of course, some uncertainties still exist and we can’t conclude the non-existence of convection (see discussion in Yuan & Narayan 2014), thus it is still feasible to study convection and it worth to study CDAFs. Narayan, Igumenshchev & Abramowicz (2000) and Quataert & Gruzinuv (2000) introduced analytical model based on self-similar solution which was called convection dominated accretion flows (CDAFs). In particular, Igumenshchev, & Abramowicz (1999, 2000) have been point out that the ADAFs becomes convectively unstable whenever the viscous parameter $\alpha \le 0.1$. On the other hand, Narayan et. al (2000), Quataret & Gruzinuv (2000) based on self-similar solutions have shown that CDAF consist of a hot plasma about virial temperature 