This article investigates the heat and mass transfer process in a biomagnetic couple-stress fluid. The fluid under study is a hybrid nanofluid, consisting of silver nanoparticles immersed in gold-blood nanofluid. The fluid flows through a horizontal pair of squeezing plates with a microcantilever porous sensor positioned at the centre of the channel. A transient magnetic field and Brownian motion additionally affect the flow. The nonlinear dimensional primary flow-field equations are recast into dimensionless coupled equations with similarity variables. The equations are computed numerically through a shooting approach combined with the Runge–Kutta scheme. Flow responses are evaluated by adjusting dominant factors, such as the Hartmann number and the couple stress parameter. The results demonstrate that incorporating Au–Ag nanoparticle composites significantly enhances thermal conductivity and improves localised heat transfer, which is beneficial for biomedical applications. Furthermore, the combined effects of magnetic forces and squeezing motion offer precise control over fluid dynamics and nanoparticle transport. When the squeezing flow index increases from 0.5 to 2, the primary velocity increases by 4.36% within the boundary layer, indicating that the squeezing motion enhances the fluid transport. Meanwhile, the temperature at the sensor surface decreases by approximately 49% under other fixed parameters. The controlled squeezing flow helps transport biomolecules toward the sensor and regulates heat removal, which has potential applications in thermal management, advanced cooling systems, and even tumour hyperthermia therapy. Further, we observed a remarkable effect of couple stress on the temperature distribution across the sensor surface. An increase of one unit in the couple stress parameter leads to an approximate 44% rise in temperature, demonstrating that stronger microstructural resistance intensifies thermal energy within the fluid domain. This helps with faster heat diffusion near the sensing element. In the absence of couple stress, surface drag decreases when the distance between plates increases. The present results are in good agreement with previously reported studies.
Kumar et al. (Thu,) studied this question.