In this paper, the analytical solution of a viscous and incompressible fluid towards an exponentially stretching porous sheet with surface heat flux in porous medium, for the boundary layer and heat transfer flow, is presented. The equations of continuity, momentum and the energy are transformed into non-linear ordinary differential by using similarity transformation. The solutions of these hig...

The homotopy analysis method (HAM) is a useful to derive analytical approximate solutions of black holes in modified gravity theories. In this paper, we study the Einstein–Weyl coupled with Maxwell field and obtain approximation for charged by using HAM. It found that are sufficiently accurate entire spacetime outside hole’s event horizon also consistent numerical ones Einstein–Maxwell–Weyl gra...

The steady boundary layer flow of nanofluid over an exponential stretching surface is investigated analytically. The transport equations include the effects of Brownian motion parameter and thermophoresis parameter. The highly nonlinear coupled partial differential equations are simplified with the help of suitable similarity transformations. The reduced equations are then solved analytically w...

In this study, accurate analytical solution for the nonlinear free vibration of an oscillator with inertia and static type cubic nonlinearities is derived. This solution is called He’s Variational Iteration Method (VIM). Comparing this method with numerical integration solutions using a built-in ODE-solver in MATLAB and He’s Homotopy Analysis Method (HAM) is shown its drastic approximation. By ...

In this paper, we consider the giving up smoking model. First, we present the giving up smoking model in fractional order. Then the homotopy analysis method (HAM) is employed to compute an approximate and analytical solution of the model in fractional order. The obtained results are compared with those obtained by forth order Runge-Kutta method and nonstandard numerical method in the integer ca...

In this paper, an iterative scheme based on the homotopy analysis method (HAM) has been used to solve nonlinear integral equations. To check the numerical method, it is applied to solve different test problems with known exact solutions and the numerical solutions obtained confirm the validity of the numerical method and suggest that it is an interesting and viable alternative to existing numer...

As we know, the homotopy analysis method (HAM) provides us with a convenient way to adjust and control the convergence region and rate of the obtained series solutions. This great advantage of method is possible by finding a proper value of the so-called control parameter 0 c . In this paper, an efficient way of obtaining 0 c is proposed. Such value of parameter can be determined at the any ord...

In this paper, mixed convection flow of couple stress fluid in circular annulus is studied. First order chemical reaction, Soret and Dufour effects are taken into consideration. The governing partial differential equations are transformed into a system of ordinary differential equations and solved by Homotopy Analysis Method (HAM). The effects of Soret number, Dufour number, chemical reaction p...

In this article an analytical technique, namely the homotopy analysis method (HAM), is applied to solve the momentum and energy equations in the case of a two-dimensional incompressible flow passing over a wedge. The trail and error method and Padé approximation strategies have been used to obtain the constant coefficients in the approximated solution. The effects of the polynomial terms of HAM...

In this paper, an analytical technique based on the global residue harmonic balance method (GRHBM) is applied in order to obtain higher-order approximate solutions of electrostatically actuated micro-beam. To illustrate applicability and accuracy method, a high level was established for by comparing results with numerical solution as well already published literature, such variational approach ...