An innovative approach to peristaltic flow is presented in this study using a couple-stress fluid and a ternary hybrid nanofluid of titanium dioxide \((Ti{O}_{2})\) , copper \((Cu)\) , and alumina \(\left(A{{l}_{2}O}_{3}\right)\) coupled with blood as the base fluid under magnetohydrodynamic conditions and compliant walls. The compliant walls in the study play a crucial role in mimicking the natural flexibility of biological vessels, thereby enabling more accurate simulation of blood flow dynamics. A combination of homogeneous-heterogeneous chemical reactions, viscous dissipation, and thermal radiation is also examined in this study. According to the long-wavelength, small-Reynolds-number hypothesis, the model’s governing equations are valid. Using a fourth-order Runge–Kutta (RK4) method for accurate and efficient results, this problem was numerically solved in Mathematica using ND-solve. Additionally, graphs are used to discuss and examine the outcomes of different parameters. A first study investigated the combined effects of ternary hybrid nanoparticles, steady MHD, and couple-stress fluids on peristaltic motion accompanied by homogeneous-heterogeneous chemical reactions. These findings provide new insights into the optimization of thermal and fluid transport processes for advanced biomedical devices and industrial heat transfer systems. This research aims to create advanced peristaltic pump systems for drug delivery, waste removal, and fluid transfer within biophysiological environments.
