The College of Education for Pure Sciences at the University of Basrah  discussed a master's thesis on a comparison between analytical methods - approximate equations for convection - thermal diffusion
The thesis presented by the researcher (Zeina Abdel-Kadhim Hassan) included a comparative study between a new approach we proposed to improve and develop the reduced differential transfer algorithm and other methods found in the literature to solve some linear and nonlinear two-dimensional load-diffusion equations. The new approach was based on the combination of the method of reduced differential transformation, Yang transformation, and a paddle approximation to produce an efficient hybrid algorithm, which was applied to solve the linear 2D load-diffusion equation, biological population model equations, system of 2D Berger equations, and 2D Navier-Stokes equations.
The results obtained by using this approach were compared with the standard method: reduced differential transfer and other methods available in the literature. The results are consolidated in tables and graphs. The graphs and tables of the new analytical approximate solutions indicate the validity, usefulness and importance of the new approach. Moreover, the accuracy and convergence of the new solutions were discussed, as the results showed that the proposed approach led to clear improvements in accuracy and convergence.
Finally, it can be concluded that the proposed approach is a powerful and useful tool that has the ability to solve the proposed two-dimensional linear and nonlinear load-diffusion equations, which reflects the realization of the main objective of this study.