<p>This study presents a numerical examination of unsteady flow and heat transfer of hydromagnetic Darcy media between plates with oscillatory thermal variations and suspended ternary nanoparticles (MWCNT + Fe₃O₄ + Au) by mixing into blood. Also considered the non-uniform heat source or sink and thermal radiation into account. The arising governing system is nonlinear partial differential system; it is transformed to ordinary system by considering the similar variables. The transformed governing equations are solved numerically using MATLAB’s bvp4c solver. The results are presented via three different kinds of oscillatory conditions and found that there are a lot of changes in different situations by varying parameters like magnetic field, porosity, squeezing parameter, thermal radiation, and non-uniform heat source or sink on velocity (tangential and azimuthal) and temperature as well as heat transfer rate at both the lower and upper plate. Also, the results are presented through 3D surface plots. It is found that the temperature ratio sets the thermal gradient for ratethe system, and thermal radiation adds to the total energy transfer, both of which are critical in controlling the heat transfer. A higher Darcy number reduces the resistance of the porous medium, allowing the fluid to move more easily. This increased flow contributes to a stronger heat transfer rate. The findings underscore the potential for precisely controlling heat transfer in these systems by carefully adjusting key parameters like magnetic field strength, squeezing rate, and porosity, facilitating progress in bio-mechanisms and other biological applications. This research provides significant insights into the performance enhancements enabled by oscillatory variations and trihybrid nanofluids, including improved thermal conductivity, facilitating progress in biological applications such as biomechanics, blood circulation, cancer therapy, and targeted drug delivery.</p>