For the sperm to have the best chance of reaching the egg, the ciliated walls of the uterine tube must be meticulously monitored. Recognizing the significance of this investigation, a novel mathematical simulation of this process has been performed by analyzing the dynamics of a non-Newtonian magnetized fluid adopting a Darcy flow framework with an undulating wall and an interior ciliated membrane. In the present investigation, the transmission of heat in a two-dimensional flexible conduit with ciliated walls of magnetic Sutterby nanofluids is investigated by considering all of these variables concurrently. Buongiorno’s nanofluid approach, that involves Brownian motion and thermophoresis aspects is considered. The channel is susceptible to ciliary wave motion, Joule heating effects, viscous dissipation, non-linear radiation flux, and other circumstances. The suspension’s electrical conductivity has been identified as a variable that is dependent on concentration distributions and the surrounding temperature. The problem-solving strategy depends on first transforming the system into a dimensionless form, after which using the lubrication approximation, the evolving boundary value problems has been normalized and linearized form. To carry out the numerical computations and produce graphical solutions, an appropriate algorithm is created and is referred to as the built-in command ND-Solve via computational software known as Mathematica. The most important findings pointed out that the gradients of the pressure are higher in the case of dilatant fluid (B > 0) comparing to the case of pseudoplastic fluid (B < 0). Additionally, when the metachronal waves variable gets bigger, the peristaltic ciliary motility has a more optimal axial ve locity than peristaltic flow along the walls within the entire area [ ± 0.5,±1]. The findings revealed a thorough grasp of biomimetic energy frameworks that utilize nanotechnology, magnetism, and ciliary peristalsis flow. Besides that, they provide a useful baseline for multi-physics simulations that are both experimental and numerical.