A very effective and accurate solution method is proposed for studying the free and the wall buoyant jets. The buoyant jets are treated as a combined system of the momentum jets and buoyant plumes, and are analyzed by introducing some dimensionless variables of proper scales over the entire range of buoyancy. An effective and rigorous finite difference scheme is developed to solve the nonsimilar equations subject to the integral constraints of momentum and heat flow conservations. Very accurate correlation equations are proposed for predicting the centerline temperature and the centerline velocity of the two-dimensional laminar free buoyant jets. Correlations of the surface temperature and the surface shear stress of the wall buoyant jets are also presented.