The College of Science, in the Department of Mathematics, hosted a seminar entitled "Study of Analytical Methods for Incompressible Fluid Flow Problems" for postgraduate student Sajjad A. Khadhim. In this seminar, the problem of incompressible fluid flow consisting of the Navier-Stokes equations with heat transfer through the presence of various physical parameters is analyzed. Similarity variables are an important factor in converting the modeling of partial differential equations into ordinary differential equations for various flow parameters. The improvement of analytical solutions under consideration by hybridizing the method of q-homotopy analysis by Laplace transform (q-LTHAM) and Padé Approximation (q-PAHAM). The results obtained from these hybridizations demonstrate the efficiency of this method with the imposed transform and approximate by obtaining better accuracy.