I discuss a recent application of homotopy perturbation method to a heat transfer problem. I show that the authors make infinity equal five and analyze the consequences of that magic. There has recently been great interest in the application of several approximate procedures, like the homotopy perturbation method (HPM), the Adomian decomposition method (ADM), and the variation iteration method ...

In this paper, the nonlinear free vibrations of thin symmetric and non-symmetric cross-ply composite plates subjected to biaxial initial stresses are investigated. Because of their excellent properties such as specific strength and specific stiffness, composite plates have wide applications in aerospace and mechanical structures. Based on Von-Karman's strain-displacement relations and using Gal...

Thermal recovery involves well-known processes such as steam injection (cyclic steam stimulation, steam drive, and steam-assisted gravity drainage), in situ combustion, and a more recent technique that consists of heating the reservoir with electrical energy. When high frequency is used for heating, it is called electromagnetic (EM) heating. The applications of EM heating for heavy-oil reservoi...

The steady three-dimensional flow of condensation or spraying on inclined spinning disk is studied analytically. The governing nonlinear equations and their associated boundary conditions are transformed into the system of nonlinear ordinary differential equations. The series solution of the problem is obtained by utilizing the homotopy perturbation method HPM . The velocity and temperature pro...

An analytical method, called homotopy perturbation method HPM , is used to compute an approximation to the solution of the nonlinear differential equation governing the problem of two-dimensional and steady flow of a second-grade fluid in a converging channel. The table and figures are presented for influencing various parameters on the velocity field. The results compare well with those obtain...

An analysis has been performed to study the natural convection of a non-Newtonian fluid between two infinite parallel vertical flat plates and the effects of the non-Newtonian nature of fluid on the heat transfer are studied. The governing boundary layer and temperature equations for this problem are reduced to an ordinary form and are solved by Homotopy perturbation method (HPM) and numerical ...

This paper investigates the numerical solution of imprecisely defined fractional order dynamic system, subjected to an unit impulse load. A mechanical spring mass system having fractional damping of order 1/2 with fuzzy initial condition is taken into consideration. Fuzziness appearing in the initial conditions is modelled through different types of convex normalised fuzzy sets viz. triangular,...

In recent years, many more of the numerical methods were used to solve a wide range of mathematical, physical and engineering problems linear and nonlinear. In this article, we shall use the homotopy perturbation method (HPM) to solve some systems of partial differential equations viz. the systems of coupled Burgers’ equations in oneand twodimensions and the system of Laplace’s equation. This a...

In this article, we present the fuzzy Adomian decomposition method (ADM) and modified Laplace (MLDM) to obtain solutions of fractional Navier–Stokes equations in a tube under derivatives. We have looked at turbulent flow viscous fluid tube, where velocity field is function only one spatial coordinate, addition time being dependent variables. Furthermore, investigate Elzaki transform, (EDM) appl...

The main goal of this paper is to introduce a new scheme, known as the Aboodh homotopy integral transform method (AHITM), for approximate solution wave problems in multi-dimensional orders. (AIT) removes restriction variables recurrence relation, whereas perturbation (HPM) derives successive iterations using initial conditions. convergence analysis provided study equation with multiple dimensio...