Modal decomposition and surrogate modelling of non-Newtonian flow in corrugated channels with linearly varying entrance amplitude

This study presents a thermo-hydraulic performance and entropy generation analysis of non-Newtonian power-law fluid flow through wavy channels with linearly varying entrance amplitude. Proper Orthogonal Decomposition (POD) and a Gaussian Process Regression (GPR) surrogate reduced order model are coupled to link flow dimensionality with thermodynamic irreversibility. Finite element simulations span Reynolds number, Re 10–400, power-law index, n = 0.5–1.5, and dimensionless entrance length (EL) = 0, 5.5, 11.5, and 22.5. A regime-dependent reversal in hydraulic penalty is identified and explained: shear-thinning fluids (n < 1) exhibit the lowest pressure ratio at low Re but the highest at Re = 400, where intense recirculation vortices form. At low Re, thermal irreversibility dominates (volume-averaged Be > 0.999). At Re = 400, the local Bejan number falls below 0.5 in the shear layers of shear-thinning fluids. EL = 22.5 yields the highest performance factor (PF ≈ 0.92 at Re = 25). POD of 40 velocity and temperature snapshots reveals the flow is intrinsically low-dimensional: six modes reconstruct the velocity field within 0.8% L2 error. Mode 2, carrying only 0.63% of total energy, encodes spatially concentrated recirculation zones whose modal coefficient quantifies rheology-dependent recirculation intensity and is associated with the hydraulic penalty reversal. The GPR surrogate, trained on 100 computational fluid dynamics cases and validated at two withheld Re of 150 and 300, achieves test-set Mean Absolute Percentage Error (MAPE) below 2.3% for all seven outputs. The low R2 (0.18) for PF at EL = 5.5 reflects near-flat test-set topology (MAPE = 0.55%), not surrogate failure. The surrogate identifies EL = 22.5 as globally optimal when both EL and n are simultaneously optimized, across the full Re range, establishing a PF envelope from 0.92 at Re = 25 to 0.72 at Re = 400. These results establish a quantitative design envelope for managing pressure drop and heat transfer in compact thermal systems handling rheologically complex fluids.