Hybrid semi-analytical and machine learning approach for modeling squeezing flow in couple-stress nanofluids with applications to biosensing

The dynamics of time-dependent squeezing flows involving complex fluids are critical to the performance of modern engineering systems, ranging from lubrication in heavy machinery to micro-scale transport in biosensors. However, accurately modeling the non-linear interaction between microstructural couple-stress continuum effects – governed by higher-order spin gradients and the couple-stress parameter δ c , and variable transport properties remains a significant modelling challenge. To address this, the present study investigates the unsteady squeezing flow of a couple-stress nanofluid over a straining sensory surface, incorporating temperature-dependent viscosity and thermal conductivity, Brownian motion, thermophoresis, and Arrhenius reaction kinetics. By employing similarity transformations, the highly nonlinear governing equations are reduced to a coupled ordinary differential system and solved using the perturbation-based semi-analytical Homotopy Renormalization (HTR) method, whose convergence is verified through explicit low-order approximate solutions and monotonically decreasing residual norms across successive perturbation orders. The robust semi-analytical solutions obtained through HTR serve as high-fidelity training data for a compact Artificial Neural Network (ANN) surrogate implemented in Python/PyTorch, forming a hybrid HTR–ANN framework. This trained ANN demonstrates exceptional accuracy in predicting flow, thermal, and concentration fields with coefficients of determination R 2 > 0.99 across all field variables significantly reducing computational overhead. Key findings indicate that increasing the squeezing parameter reduces the momentum boundary layer thickness, while the couple-stress parameter δ c and variable viscosity suppress velocity gradients and wall shear stress. Furthermore, the study underscores the dominant influence of variable transport properties on heat and mass transfer rates. Ultimately, the developed hybrid HTR–ANN surrogate accurately predicts crucial wall metrics – including skin-friction coefficient, Nusselt number, and Sherwood number – providing a powerful surrogate framework for rapid parametric analysis in nanofluid-based heat exchangers, microfluidic systems, and energy-efficient thermal management technologies.