Rarefied Flow and Heat Transfer of Thermo-Responsive Al₂O₃/TiO₂/Ag–PNIPAm Tri-Hybrid Nanofluids in Microchannels: An MRT-LBM Study

Abstract

The rapid miniaturization of thermal-management systems and microfluidic devices has intensified the need to understand fluid transport at scales where classical continuum assumptions break down. This paper presents the first comprehensive investigation of rarefied flow and heat transfer in microchannels laden with a novel smart thermo-responsive tri-hybrid nanofluid composed of aluminium oxide (Al₂O₃), titanium dioxide (TiO₂), and silver (Ag) nanoparticles dispersed in an aqueous poly(N-isopropylacrylamide) (PNIPAm) solution. PNIPAm undergoes a well-characterized lower critical solution temperature (LCST) transition at approximately 32°C, inducing a reversible coil-to-globule conformational change that dramatically alters the suspension viscosity and thermal conductivity in a temperature-driven, self-regulating manner. This work addresses the unexplored coupling between stimuli-responsive rheology, tri-hybrid nanoparticle synergy, and rarefaction-induced velocity slip and temperature jump at the solid–fluid interface. Knudsen-number-corrected Navier–Stokes equations, augmented with second-order Maxwell–von Smoluchowski slip/jump boundary conditions, are coupled with FENE-P viscoelastic constitutive equations that incorporate a temperature-dependent relaxation time λₚ(T) capturing the PNIPAm LCST transition. Tri-hybrid effective thermophysical properties are computed via extended Hamilton–Crosser and modified Krieger–Dougherty mixture models accounting for nanoparticle morphology, interfacial nanolayer resistance, and Brownian diffusion contributions from all three nanoparticle species. Numerical simulations are performed using a Multiple-Relaxation-Time Lattice Boltzmann Method (MRT-LBM) with polymer stress forcing and cross-validated against finite-volume CFD (ANSYS Fluent with user-defined functions). Parametric studies span Knudsen numbers Kn = 0.001–0.1 (slip-flow regime), total nanoparticle volume fractions φ = 0–6%, PNIPAm concentration cₚ = 0–2000 ppm, Reynolds numbers Re = 1–100, and wall temperatures Tᴄ = 25–45°C, which straddle the PNIPAm LCST. Results reveal a pronounced non-monotonic Nusselt number response to wall temperature: below the LCST (Tᴄ < 32°C), PNIPAm chains remain hydrophilic and extended (high viscosity, moderate thermal conductivity), while above the LCST (Tᴄ > 32°C), the collapsed globular conformation reduces viscosity and activates a self-regulating heat-transfer enhancement mechanism. The tri-hybrid combination delivers a 41.6% higher effective thermal conductivity than single-component Al₂O₃ at φ = 3%, owing to phonon-scattering complementarity between the three nanoparticle species. Net thermal performance gains of up to 47.3% relative to the pure-liquid slip-flow baseline are demonstrated at optimum conditions (Kn = 0.01, φ = 3%, cₚ = 600 ppm, Tᴄ = 36°C). These findings establish design guidelines for smart, self-regulating polymer-nanofluid-cooled MEMS, microreactors, and biomedical lab-on-chip platforms.