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, the Homotopy Analysis Method (HAM) is presented for obtaining the approximate solution of new coupled modified Korteweg-de Vries (MKdV) system. The approximate analytical solution is obtained by using this method in the form of a convergent power series with components that are easily computable. For the problems considered, only a few terms are required to obtain an approximate ...

An analysis is carried out for axisymmetric stagnation flow of a micropolar nanofluid in a moving cylinder with finite radius. The coupled nonlinear partial differential equations of the problem are simplified with the help of similarity transformations and the resulting coupled nonlinear differential equations are solved analytically by homotopy analysis method HAM . The features of the flow p...

Multispecies pollutant migration often occurs in polluted groundwater systems. Most of the multispecies problems that have been dealt literature assume constant transport parameters, primarily because analytical solutions for varying parameters become a challenge. The present study analytically solves two-species convection-dispersion equation, considering spatially dispersion coefficient and s...

This article describe the unsteady boundary layer flow over a stretching sheet. The governing boundary layer equations are transformed to a non-linear partial differential equation by applying similarity transformations. Analytic solution valid for all times is obtained using homotopy analysis method (HAM). The influence of dimensionless time and second grade material parameter is discussed on ...

The gravity-driven film flow has been analyzed along a vertical wall subjected to a convective boundary condition. The Boussinesq approximation is applied to simplify the buoyancy term, and similarity transformations are used on the mathematical model of the problem under consideration, to obtain a set of coupled ordinary differential equations. Then the reduced equations are solved explicitly ...

This work proposes an interval-based uncertain Susceptible–Infected–Recovered (SIR) epidemic model. The interval model has been numerically solved by the homotopy analysis method (HAM). SIR is proposed and under different intervals HAM to obtain numerical solution of Furthermore, ODE was transformed into a stochastic differential equation (SDE) results deterministic models were compared using s...