  Understanding the explosion mechanism of type Ia supernova is among the most
challenging issues in astrophysics. Accretion of matter on a carbon-oxygen
white dwarf from a companion star is one of the most important keys in this
regard. Our aim is to study the effects of WD composition on various parameters
during the accretion of helium rich matter at a slow rate. We have used the
computer simulation code Modules for Experiments in Stellar Astrophysics (MESA)
to understand the variations in the properties such as specific heat
(\textit{$C_P$}) and degeneracy parameter (\textit{$\eta$}). The profile of
specific heat shows a discontinuity and that of the degeneracy parameter shows
a dip near the ignition region. As expected, the size of WD decreases and
\textit{g} increases during the accretion. However, a red-giant-like expansion
is observed after the rapid ignition towards the end. Our study explains the
reason behind the delay in onset of helium ignition due to the difference in
carbon abundance in a CO-WD. We find that white dwarfs of the lower abundance
of carbon accrete slightly longer before the onset of helium ignition.
