A two-dimensional, time-dependent mathematical model has been developed to investigate the flow and temperature stratification phenomena in a liquid thermal storage tank for a solar energy system. This model is based on the principles of both natural and forced convective heat transfer. To obtain the numerical solution for this set of nonlinear partial differential equations, an improved Alternative Direction Implicit (ADI) scheme was developed, which enables us to obtain solutions for very large Grashof and Reynolds numbers for the first time. In this analysis, we present the numerical results on the flow patterns and temperature distributions in a liquid storage tank for various Reynolds and Grashof numbers together with the numerical scheme.