layer is unaffordable even with an enlarged energy flux. We can only consider the lower part of the convection zone. The computed box has a shorter radial extension ($d=0.1R$) and the top is placed at the middle of the convection zone. $r_{\rm b}$ is at $0.6R$. Consequently, the unstable layer is about $2.7$ PSHs thick and the whole computed domain contains about $6.6$ PSHs. To suppress the significant thermal adjustment caused by truncating the convection zone, an artificial thermal control layer is introduced near the upper boundary. This is a slightly sub-adiabatic layer with an artificial conductivity set to $-F_{\rm rad}/(d T/d z)$ so that radiation carries all of the energy flux. The corresponding layer is indicated by the dashed line in Fig. [\[init\]]{}.

The dimensionless input energy flux ($F_{\rm btm}$) for intermediate mass star model is very small (see the last column in Table \[dpm\]). To reduce the thermal relaxation time several values of $a_{\rm f}$ around $10^4$ are used. In constructing the initial model, the flux and geometry were modified through the controlling parameters $a_{\rm f}$, $c_{\rm r}$, $d$, and $r_{\rm
b}$. Among the modifications, we care most about the effects caused by $a_{\rm f}$. Three intermediate mass 