Open AccessRemark On Optimal Homotopy Method: Application Towards Nano-Fluid Flow Narrating Differential Equations
Author(s) -
Khalil Ur Rehman
Publication year - 2019
Publication title -
journal of mechanical engineering research
Language(s) - English
Resource type - Journals
ISSN - 2630-4945
DOI - 10.30564/jmer.v1i1.465
Subject(s) - homotopy analysis method , nanofluid , mathematics , flow (mathematics) , convergence (economics) , homotopy , advection , reliability (semiconductor) , mechanics , heat transfer , pure mathematics , physics , geometry , thermodynamics , power (physics) , economics , economic growth
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.