We obtain a necessary and a sufficient condition expressed in terms of Wiener type tests involving the parabolic $W_{q'}^{2,1}$- capacity, where $q'=\frac{q}{q-1}$, for the existence of large solutions to equation $\prt_tu-\Delta u+u^q=0$ in non-cylindrical domain, where $q>1$. Also, we provide a sufficient condition associated with equation $\prt_tu-\Delta u+e^u-1=0$ . Besides, we apply our results to equation: $\prt_tu-\Delta u+a|\nabla u|^p+bu^{q}=0$ for $a,b>0$, $11$.