The College of Education for Pure Sciences at the University of Basrah in the Department of Mathematics discussed a PhD thesis on (New Approximate Analytical Techniques for Solving Fluid Flow Problems)
The thesis, which was conducted by the researcher (Yasser Ahmed Abdel-Amir), included proposals for new techniques to find approximate analytical solutions to various forms of non-linear fluid flow issues. The first technique represents a hybrid approach that combines the homotopic perturbation method (HPM) and the Fourier transform (FT), which is represented by the symbol (FT-HPM). In the second technique, the Fourier transform was used with convolution theory to develop the homotopic perturbation method, and this technique was denoted by the symbol (FTC-HPM). The third technique, during which the homotopic perturbation method was developed using the Fourier transform and Laplace transform (LT), denoted by the symbol (FLT-HPM), during this method, the Fourier transform is applied to one of the two variables and then the Laplace transform is applied to the other variable. In addition, Fourier transform was used for two consecutive times on two different variables to improve the method of homotopic disorder and devising a new method referred to as (2F-HPM).
The aforementioned methods have been used to deal with various problems such as the flow of a viscous liquid through a porous channel with contraction or expansion of permeable walls, the problem of natural two-dimensional convection (transient/steady state) between two concentric horizontal circular cylinders, and the problem of heat and mass transfer with binary pressure. Dimensionally unstable on viscous flow. The effect of non-dimensional numbers on fluid flow and heat transfer is discussed with different values. Tabulated results and graphs obtained using the proposed methods were compared with the results obtained by applying some previous methods such as HPM, YT-HPM, VPM, PIA method, Rang-Kutta method of fourth order (RK-4th), and some Other modalities mentioned in previous literature. The accuracy and efficiency of the proposed methods in finding analytical solutions was also verified by calculating absolute errors and standard errors and comparing the new results with the results of previously published methods. The results showed that the current methods are characterized by good accuracy, and that the computational time for implementation was very short compared to the computational time in other methods. In addition, the convergence of the new methods was theoretically discussed. By formulating and proving the convergence theorem, the convergence of all the analytical solutions obtained by applying this theory to different values of non-dimensional physical parameters was tested. The results confirmed that the proposed techniques represent powerful, effective and accurate analytical tools that can be relied upon to solve many difficult problems, especially nonlinear flow problems. All of the above reflects the achievement of the main objectives of the study.