Cell biology uses flagella and cilia for mobility. The dense flagellar carpets that pump fluid mammals’ brains to the solitary flagella of swimming algae have similar structures but execute distinct functions. Understanding the relevance of this finding, unique computational modeling of this mechanism was done by investigating the physical parameters of a non-Newtonian magnetic nanofluid with a Darcy flux framework, internal flagellated membrane, and undulating wall. The current study examines heat transmission in a two-dimensional malleable tube with flagellated walls of magnetic Oldroyd 4-constant nanofluid. The Brownian motion as well as the thermophoresis of Buongiorno’s nanofluid method are taken into consideration. The channel can be affected by non-linear radiation flux, ciliary pattern motion, Joule thermal effects, and viscous dissipation, among other things. The approach to addressing the problem is first converting the system into a dimensionless form. Next, f luctuating boundary value problems are normalized and linearized using lubrication approximation. Using the computer program Mathematica, a suitable technique known as built-in command ND-Solve is developed to accomplish numerical calculations and generate graphical results. Axial movement velocity is maximal in the channel center and falls towards walls when the irregular parameter of the elliptic path and flagella length changes. As the non-Newtonian parameter and magnetic field parameter are elevated, the trapped bolus grows and streamlines change emphasizing their significance in peristaltic flow control.