The numerical solution of fluid flows problems with heat transfer requires the solution of a set of coupled non- linear partial differencial equations. The major computational effort in solving these equations is due to the solution of the algebraic systems resultant from the discretization of the conservation equations. The convergence rate of iterative methods is sensitive to the nature of the problem being solved. Therefore, no one method may be claimed to be the best for all problems. Along with the development of new iterative methods, the development of technics for accelerating the convergence of known iterative methods presents a considerable interest from a practical standpoint. The primary objective of the present work was to analise a class of algorithms for the solution of algebraic systems resulting from the discretization of transport phenomena conservation equations. The second objective was to select an adequate and efficient method which lead an increase of the convergence rate. For this purpose a multigrid additive correction scheme was selected and implemented. This is a novel technique in which the same differential problem is approximated on several grids whose mesh sizes are usually integral multiples. It was investigated its performance to improve the convergence rate in combination with the iterative line-by-line TDMA as well as its performance with the use of block correction algorithm.