One end of a $2.35\,\text{m}$ long aluminium rod of radius $2.0\,\text{cm}$ ($K = 235\,\text{W\,m}^{-1}\text{K}^{-1}$) is held at $20\,^\circ\text{C}$. The other end is in contact with a block of ice at its melting point. The rate in $\text{kg\,s}^{-1}$ at which ice melts is [Take latent heat of fusion for ice as $3.36\times10^5\,\text{J\,kg}^{-1}$]