Value Of Auxiliary Parameter Research Articles

The influence of magnetic field on the fluid flow in the entrance region of channels: analytical/numerical solution

The present paper investigates the steady laminar development flow of a Newtonian incompressible electrically conducting fluid in a plane channel subjected to a uniform transverse external magnetic field. In order to solve the problem, the analytical integral momentum method and numerical finite volume method (FVM) are conducted. In integral momentum solution, the Pohlhausen’s fourth-degree velocity profile is assumed. Applying the boundary conditions leads to the appearance of a new dimensionless parameter named auxiliary parameter (AP). It is shown that the value of AP depends on the magnitude of magnetic intensity and the pressure gradient. For each specified value of AP, distinct velocity distribution and as a result, a correlation for computing the magnetic development length is obtained. Besides, the FVM is applied to solve the same problem and the correlation for estimating the magnetic development length is obtained. It can be concluded that for a particular engineering application of magnetohydrodynamics channel flows, the associated value of AP can be determined by the numerical investigation. The results of numerical solution are compared with the analytical results and it can be concluded that the results for AP = − 6 are in agreement with the numerical results. Further, the effect of Hartmann and Reynolds number on the magnetic development length and Lorentz force are illustrated. It was shown that as the Hartmann number increases, the value of development length and Lorentz force are reduced.

An efficient computational approach for time-fractional Rosenau–Hyman equation

In this work, we concentrate on the analysis of the time-fractional Rosenau–Hyman equation occurring in the formation of patterns in liquid drops via q-homotopy analysis transform technique and reduced differential transform approach. The q-homotopy analysis transform algorithm can provide rapid convergent series by choosing the appropriate values of auxiliary parameters ħ and n at large domain. The reduced differential transform technique gives wider applicability due to reduction in computations and makes the calculation much simpler and easier. The proposed techniques are realistic and free from any assumption and perturbation for solving the time-fractional Rosenau–Hyman equation.

Approximate Analytical Solutions of Fractional Coupled mKdV Equation by Homotopy Analysis Method

In this paper, the approximate analytical solutions of the fractional coupled mKdV equation are obtained by homotopy analysis method (HAM). The method includes an auxiliary parameter which provides a convenient way of adjusting and controlling the convergence region of the series solution. The suitable value of auxiliary parameter is determined and the obtained results are presented graphically.