A New Technique to Solve Two-Dimensional Viscous Fluid Flow Among Slowly Expand or Contract Walls

Abstract

In this research, we have proposed a new technique to solve two-dimensional (2D) viscous fluid flow among slowly expanding or contracting walls. The new technique depends on combining the algorithms of Yang transform and the homotopy perturbation methods. The results, obtained from the first iteration and by using the new method, show the accuracy and efficiency of this method compared to the other methods, used to find the analytical approximate solution for the problem caused by the 2D viscous fluid flow. Moreover, the graphs of the new solutions show the validity, usefulness and necessity of the new method.

Modify homotopy perturbation method using yang transform to study the effect of magnetic field with mass and heat transfer on pulsatile blood flow in tapered stenosis arteries

“…In this study, the developed problem for 2D pulsatile blood flow in tapered stenosis arteries under the impact of a magnetic field in addition to the effect of mass and heat transfer was solved analytically by using a YTHPM. Which consider as expanding to the application of YTHPM that we proposed for the first time in Al‐Saif and Al‐Griffi 27,28 The model that we developed through adding the effect of a magnetic field on it explain the following results, when $$M$$ increases, the velocity and flow rate decrease, but in contrast when $$M$$ increases, the wall shear stress, and resistance flow increase. Also, it is concluded through the convergence analysis that the solutions obtained using YTHPM in the case of the presence of a magnetic field show faster convergence than when the field is absent, and this in turn leads to the values of error being small.…”

“…In this section, the convergence of analytical approximate solutions obtained from YTHPM for Equation (19), are studied by depending on the convergence theorems illustrated in Al‐Saif and Al‐Griffi 27,28 From these theorems and the resulting condition is defined as: $$${\gamma }^{m}=\left\{\begin{array}{c}\frac{\Vert \,{W}_{m+1}-{W}_{m}\Vert }{\Vert {W}_{1}-{W}_{0}\Vert }=\frac{\Vert {w}_{m+1}\Vert }{\Vert {w}_{1}\Vert },\Vert {w}_{1}\Vert \ne 0,m=1,2,3,\text{\unicode{x022EF}}\\ 0,\Vert {w}_{1}\Vert =0.\end{array}\right.$$$…”

“…According to the information available to us, the new system has not been studied before, and thus will be one of the new innovative points of our work. Third, we resolve the new system by using the YTHPM as proposed for first time in Al‐Saif and Al‐Griffi 27,28 Fourth, we study the effect of the magnetic field as well as the properties of blood on the axial velocity, volumetric flow rate, wall shear stress, and the flow resistance profile. Finally, we analyze the convergence of the results with and without the existence of the magnetic field and note the effect of the magnetic field on the convergence of the solutions.…”

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

“…Moreover, nowadays, studies concentrate on the combinations between analytical methods and/or numerical methods to overcome the difficulties that appear in one or both of the merging methods and the time‐consuming problem of numerical methods. All these reasons led us to suggest a new method to overcome these difficulties and reduce the number of iterations (based on our previous experience we found the solution within the first or second iterations [19, 20]); that observed when researchers try to find analytical approximate solutions to the nonlinear equations of the problem.…”

The Comparison Study of the Hybrid Method for Solving the Unsteady State Two-Dimensional Convection-Diffusion Equations

“…It has received much attention since it has been applied to solve a wide variety of problems by many authors [13][14][15][16][17][18]. The Yang transform (YT) is suggested by Yang [19] in 2016, which is applied to solve the steady heat transfer problem, and it is used by several researchers in [20,21]. Henri Padé (1863-1953) presented an approximation technique in his doctoral thesis in 1892 which is called Padé approximation.…”