A two-dimensional mathematical model is presented to describe the solidification and cooling of liquid steel. The liquid steel is poured into a mold to obtain a solid mass of desired shape called an ingot. After cooling of the steel in the mold for some time, the mold is removed. Then the leftover ingot mass is cooled in air. This article is concerned with the above process. Nevertheless, the technique can be very applicable to other processes such as continuous casting. Partial differential equations describing the process have been discretized using control-volume (or (finite-volume) technique. The discretization equations obtained are of tridiagonal matrix form, which have been solved using the well-known tridiagonal matrix algorithm (TDMA) and the alternate direction implicit (ADI) solver The model has been validated by measuring surface temperatures of molds and ingots using an infrared thermo-vision scanner. This is then used to compute temperature distribution and solidification status of the ingot as a function of time and type of ingot.