Total instantaneous blockage (TIB) is a severe subassembly accident in a sodium cooled fast reactor. During such an accident, a heat generating fuel pool is formed which is bounded by six neighboring subassemblies which are force-cooled by sodium. The molten fuel pool attacks the walls of the neighboring hexcan, melting them layer by layer. The rate of propagation of such damage and the temperature rise in sodium due to heat transfer from fuel pool through hexcan wall are investigated by a two-step mathematical approach. In the first step, natural convection in the fuel pool is studied by a 2D axisymmetric computational fluid dynamic model and correlations for effective conductivity as a function of internal Rayleigh number and aspect ratio have been developed. In the second step, rate of damage propagation to the hexcan wall and sodium temperature rise are predicted by a 1D transient enthalpy model. It is found that rate of damage propagation is accelerated by natural convection inside the pool. Further, the rate of heat transfer to neighboring subassembly sodium also increases due to natural convection in the pool. Eventually, the residual thickness of hexcan at the time of reactor trip is found to be insensitive to the presence/absence of natural convection in the pool.