Sathyamoorthy Sivasankari - Research Scholar, Research Centre and PG Department of Mathematics, The Madura College (Affiliated to Madurai Kamaraj University), Madurai, Tamil Nadu, India.
Vembu Ananthaswamy - Research Scholar, Research Centre and PG Department of Mathematics, The Madura College (Affiliated to Madurai Kamaraj University), Madurai, Tamil Nadu, India.

An analytical study is carried out to obtain the approximate solution for the Magnetohydrodynamic (MHD) flow issue of Darcy-Forchheimer nanofluid containing motile microorganisms having viscous dissipation effect through a non-linear extended sheet employing a new approximate analytical method namely Ananthaswamy-Sivasankari Method (ASM) and also Modified Homotopy Analysis method (MHAM). The derived analytical solution is given in explicit form and is compared with the numerical solution. The graphical results are interlined to reflect the effects of various physical parameters involved in the problem. The numerical computation of the Nusselt number, the local skin friction parameter, and the Sherwood number are compared and shown in the table. Faster convergence is acquired using this strategy. The solution obtained by this method is closer to the exact solution. Also, the solution is in the simplest and most explicit form. It is applicable for all initial and boundary value problems with non-zero boundary conditions. This method can be easily extended to solve other non-linear higher order boundary value problems in physical, chemical, and biological sciences.

Darcy-Forchheimer nanofluid flow, Viscous dissipation, Gyrotactic Microorganisms, Ananthaswamy-Sivasankari method (ASM), Modified Homotopy analysis method (MHAM)