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

Abstract

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 (Formula presented.) representing (Formula presented.) 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 ((Formula presented.)) using residual connections, adaptive collocation, and curriculum learning—overcoming standard PINN divergence (errors (Formula presented.)). The model is validated against analytical ((Formula presented.)) and RK4 numerical ((Formula presented.)) solutions, achieving (Formula presented.) errors (Formula presented.) and (Formula presented.) errors (Formula presented.). Results show that stable stratification (Formula presented.) suppresses convective transport, significantly reduces local Nusselt number ((Formula presented.)) by up to (Formula presented.) (driving (Formula presented.) towards zero at both boundaries), and induces sign reversals and gradient inversions in thermally developing regions. Conversely, destabilizing buoyancy (Formula presented.) enhances vertical mixing, resulting in an asymmetric response: (Formula presented.) increases markedly (by up to (Formula presented.)) at the lower wall but decreases at the upper wall compared to neutral forced convection. At (Formula presented.) 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).