Solution of model equation of completely passive natural convection by improved differential transform method

In this paper we investigate the natural convection which exists under the Boussinesq approximation and completely passive boundary conditions. This phenomenon is applicable to the cooling of a heated body and heating and cooling of rooms and buildings and etc. The model equations of momentum and energy are solved by using improved differential transform method. This method is an iterative way for obtaining Taylor series coefficients. The convergence of the Taylor series is obtained by combining the method with the Least Square method for the problem first time here. The combination of these two powerful methods yields semi analytical solutions in the form of a polynomial through a straightforward manner. The efficiency and applicability of the algorithm are assessed and tested and error calculations have been presented.