Remark On Optimal Homotopy Method: Application Towards Nano-Fluid Flow Narrating Differential Equations

Abstract

The short communication is devoted to validate the reliability and convergence of Optimal Homotopy Analysis Method (O-HAM). Owing the importance of present validation of O-HAM one can implement this method towards nanofluid flow narrating differential equations at larger scale for better description. To be more specific, the fractional order differential equation due to vertically moving non-spherical nano particle in a purely viscous liquid and an advection PDE is take into account. The corresponding homotopy for both cases are constructed and solutions are proposed by means of O-HAM. The obtained values are compared with numerical benchmarks. We observed an excellent match which confirms the O-HAM conjecture. Therefore, it can be directed that the utilization of O-HAM towards nanofluid flow regime may provide relief against some non-attempted problems.