Deep Physics-Informed Neural Networks for Stratified Forced Convection Heat Transfer in Plane Couette Flow: Toward Sustainable Climate Projections in Atmospheric and Oceanic Boundary Layers

We use deep Physics-Informed Neural Networks (PINNs) to simulate stratified forced convection in plane Couette flow. This process is critical for atmospheric boundary layers (ABLs) and oceanic thermoclines under global warming. The buoyancy-augmented energy equation is solved under two boundary conditions: Isolated-Flux (single-wall heating) and Flux–Flux (symmetric dual-wall heating). Stratification is parameterized by the Richardson number (Ri∈ [−1,1]), representing ±2 °C thermal perturbations. We employ a decoupled model (linear velocity profile) valid for low-Re, shear-dominated flow. Consequently, this approach does not capture the full coupled dynamics where buoyancy modifies the velocity field, limiting the results to the laminar regime. Novel contribution: This is the first deep PINN to robustly converge in stiff, buoyancy-coupled flows (∣Ri∣≤1) using residual connections, adaptive collocation, and curriculum learning—overcoming standard PINN divergence (errors >28%). The model is validated against analytical (Ri=0) and RK4 numerical (Ri≠0) solutions, achieving L2 errors ≤0.009% and L∞ errors ≤0.023%. Results show that stable stratification (Ri>0) suppresses convective transport, significantly reduces local Nusselt number (Nu) by up to 100% (driving Nu towards zero at both boundaries), and induces sign reversals and gradient inversions in thermally developing regions. Conversely, destabilizing buoyancy (Ri<0) enhances vertical mixing, resulting in an asymmetric response: Nu increases markedly (by up to 140%) at the lower wall but decreases at the upper wall compared to neutral forced convection. At 5–10× lower computational cost than DNS or RK4, this mesh-free PINN framework offers a scalable and energy-efficient tool for subgrid-scale parameterization in general circulation models (GCMs), supporting SDG 13 (Climate Action).