The non-linear analysis of any physical problem is capable of predicting the qualitative and quantitative aspects of the problem. In this article, the effects of the constraints like rotation, permeability and quadratic density profile on unidirectional solidification with buoyancy and small segregation coefficient were investigated using nonlinear theory. In this study, the system consists of a fluid / fluid saturated porous layer was focused. The analysis was carried out by using a power series technique, while leading-order as well as corrections to the leading-order solutions are computed by considering higher order approximations.