Maysoon Hasan - Department of Mathematics; College of Education for Pure Science; Basrah University, Basrah, Iraq.
Abdul-Sattar J. Ali Al-Saif - Department of Mathematics; College of Education for Pure Science; Basrah University, Basrah, Iraq.

In this paper, we propose a new technique for solving the magnetic hydrodynamic boundary layer equations after converting them to a nonlinear ordinary differential equation using the appropriate similarity transformation. This technique is based on a combination of the q-homotopy analysis method, the Laplace transform, and the Pade´ approximation, named (q-HALPM). To ensure the method's efficiency, we compared the results of q-HALPM with the ones obtained by methods (DTM-Pade´) and M-HPM . Additionally, the effect of the magnetic parameter on the velocity and heat transfer was studied. The results confirm that the new method has high accuracy and efficiency in finding the approximate analytical solution for the current problem. Moreover, the graphs of the new solutions show the validity and usefulness of the proposed method.

q-Homotopy analysis method, Laplace transform, Padé approximation, MHD, boundary layer