Machine learning analysis of oscillatory-turbulent heat transfer using carbon-based diamond nanofluids over MHD nonlinear wavy surfaces

This study presents a comprehensive numerical analysis of the oscillatory heat transfer and of turbulent-flow dynamics of carbon-based diamond-water nanofluids on a vertical nonlinear wavy surface under magnetohydrodynamic (MHD) effects. The work highlights the pivotal role of nanodiamonds, a class of carbon nanomaterial characterized by ultra-high thermal conductivity (1,000 W/m·K) and exceptional stability, in enhancing thermal performance. The resulting governing flow model, derived using similarity transformations, is solved by the Keller-box method (KBM) and validated with exceptional accuracy (MSE ≈ 10−7) using an artificial neural network (ANN) for machine learning (ML). Aggregated (ANP) and non-aggregated nanoparticle (NANP) configurations are systematically studied under the rising magnetic field strengths (M = 1.0–5.0) and sinusoidal conditions ($ {\varepsilon }_{T} $= 0.1–0.3). The results show that the formation of ANPs leads to a substantial increase in thermal conductivity due to the formation of conductive clusters, which increase the Nusselt number Nu by 30%, albeit at the considerable cost of a 25% increase in viscous dissipation and skin friction Cf. Conversely, non-aggregated nano-diamonds promote smooth velocity profiles that yield moderate enhancement in Nu (up to 22%) and high hydrodynamic functionality. Surface undulations generate oscillatory thermal dynamics and turbulent mixing structures, resulting in a 15%–20% reduction in the overall Nu due to boundary layer discontinuity. However, this negates the reduction resulting from the increase in overall thermal bridging. An optimal nanoparticle volume fraction Cf of 2%–3% is identified, balancing the thermal enhancement against the pumping power requirements. These results provide important design insights for advanced thermal management systems, especially in the cooling of electronics and high-performance heat exchangers, where magnetic field control and surface geometry optimization are critical for operational efficiency.