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


  • Khalil Ur Rehman Department of Science and Humanities, National FAST University, Islamabad Pakistan
  • Asif Mehmood Department of Mathematics, Air University E-9 Islamabad 44000 Pakistan
  • Khalil Ur Rehman Department of Mathematics, Air University E-9 Islamabad 44000 Pakistan



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.


Non-Spherical Nano-Particle; Viscous Fluid Regime; Convergence Control Parameters.


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