Yang transform–homotopy perturbation method for solving a non‐Newtonian viscoelastic fluid flow on the turbine disk

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.

A Novel Hybrid Approach Leveraging Shehu Transformation, Akbari-Ganji’s Method, and Padé Approximant for the Resolution of Diffusive Prey-Predator Systems

“…Despite the evident importance of studying this system via various simulation techniques, the nonlinearity of these equations poses a challenge to their resolution using integrative transformation methods. Existing knowledge indicates that combining integrative transformations with analytical methods can reduce computational operations and complexity [21][22][23].…”

The Fractional Series Solutions for the Conformable Time‐Fractional Swift‐Hohenberg Equation through the Conformable Shehu Daftardar‐Jafari Approach with Comparative Analysis

“…Various integral transforms are used with other analytical, numerical, or homotopy-based methods to handle FODEs. The Laplace transform (LT) [18], the Elzaki transform (ET) [19], the traveling wave transform (TWT) [20], the Yang transform (YT) [21], the Aboodh transform (AT) [22], the fractional complex transform (FCT) [23], and the natural transform (NT) [24] are all transformations that can be used to solve FODEs. The Shehu transform (ST), which has been used by numerous academics for the solutions of FODEs, has recently piqued the curiosity of many mathematicians [25][26][27].…”