Yang transform–homotopy perturbation method for solving a non‐Newtonian viscoelastic fluid flow on the turbine disk
Takia Ahmed J. Al‐Griffi, Abdul‐Sattar J. Al‐Saif
Abstract
Abstract In this paper, a new method is suggested and implemented to find an analytical approximate solution for a non‐Newtonian viscoelastic fluid flow on the turbine disk, used to cool the axisymmetric channel that has a porous wall. The new method depends on combining the algorithms of Yang transform and the homotopy perturbation method (HPM) named Yang transformation–homotopy perturbation method (YTHPM). To ensure the correctness of the method, we compared the results of YTHPM with the ones obtained by the numerical method (Runge–Kutta 4th order) and by other methods as reported in the literature; a good agreement was observed. Additionally, the effect of the power‐law index, Prandtl and Reynolds numbers on the velocity, and heat transfer was studied. The results that we obtained by using the new method confirm that this method has high accuracy and efficiency compared with other methods, used to find the analytical approximate solution for the current problem. Furthermore, the graphs and tables of error show the validity, utility, and necessity of this method.