Abstract: Numerical solutions are given for inward solidification of a high Prandtl number fluid with temperature-dependent viscosity in an isothermally cooled horizcntal pipe. The high prandtl number fluid, which was housed in a pipe with a uniform surface temperature lower than the solidification temperature of the fluid, was initially in liquid phase. Transient flow patterns associated with free convections of the liquid and their effects on the development of the solid-liquid interface are presented in full. Variations of temperature distribution for both the liquid and the solid, and the interface position in the radial and axial directions are illustrated with time. The changes of bulk temperature of the liquid and the relevant Nusselt number with time are shown as a function of the Grashof number. The rate of development of the solidification interface is also given as a function of the Grash of number.