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We apply optimal homotopy asymptotic method (OHAM) for finding approximate solutions of the Burger's-Huxley and Burger's-Fisher equations. The results obtained by proposed method are compared to those of Adomian decomposition method (ADM) (Ismail et al., (2004)). As a result it is concluded that the method is explicit, effective, and simple to use.

In this research paper we examined Darcy-Forchheimer three-dimensional micro-polar nanofluid flow of carbon nanotubes (CNTs) based on water. The nanofluid flow is examined between parallel and horizontal plates in a rotating system. The thermal radiation impact is taken to be varying in the absorption/generation for the purpose, to see the concentration as well as the temperature modifications between the nanofluid and the surfaces. The micro-polar nanofluid in permeable media is designated by assuming the Darcy-Forchheimer model where drenching permeable space obeys the Darcy-Forchheimer expression. For Skin friction coefficient it is perceived to be larger for weak concentration and smaller for strong concentration. The impacts of the porosity, rotation and inertia coefficient analysis have been mainly focused in present investigation. Plots have been presented in order to study how the velocities and temperature profile get affected by various flow parameters. The leading equations are converted to a system of nonlinear differential equations and then homotopic method is employed for solution. The other physical features of flow such as Skin friction, heat flux and mass flux have been studied. The impacts of the porosity, rotation and inertia coefficient have been mainly focused in this research.

The approximate solution of the doubly periodic wave solutions of the coupled Drinfel' d-Sokolov-Wilson equations has been considered by using the optimal homotopy asymptotic method (OHAM). We obtained the numerical solution of the problem and compared that with the OHAM solution. The obtained solutions show that OHAM is effective, simpler, easier, and explicit and gives a suitable way to control the convergence of the approximate solution.

Application of Optimal Homotopy Asymptotic Method (OHAM), a new analytic approximate technique for treatment of Falkner-Skan equations with heat transfer, has been applied in this work. To see the efficiency of the method, we consider Falkner-Skan equations with heat transfer. It provides us with a convenient way to control the convergence of approximate solutions when it is compared with other methods of solution found in the literature as finite difference (N. S. Asaithambi, 1997) and shooting method (Cebeci and Keller, 1971). The obtained solutions show that OHAM is effective, simpler, easier, and explicit.