A physics informed neural network for mesh free modelling of conjugate heat transfer in hybrid nanofluid microchannel heat sinks

Thermal management of high-power microelectronics requires coupled design of coolant, channel geometry and operating point, yet mesh-based conjugate CFD is too costly for broad parametric search. This work develops a mesh-free surrogate for three-dimensional steady laminar conjugate heat transfer in microchannel heat sinks using a single physics-informed neural network (PINN); the contribution is primarily methodological. One fully connected network represents the field map (x, y, z, φ, Re) → (u, v, w, p, Tf, Ts). Temperature continuity at the solid–fluid interface is enforced by reading the two temperature outputs as one continuous field, and heat-flux continuity through a dedicated interface loss with an inverse-residual adaptive weight. The framework is demonstrated on a Cu-Al₂O₃/water hybrid nanofluid in a silicon sink (ks/knf ≈ 220). Against the finite-volume benchmark of Qu and Mudawar, the network reproduces velocity to within a pointwise L₂ error of 1.2% and pressure drop within the 5% experimental band. A single trained network spans Re ∈ [100, 1000], φ ∈ [0, 0.03] and aspect ratio ∈ (Vinodhan and Rajan in Energy Convers Manag 86:595-604, 2014; Chen and Ding in Int J Therm Sci 50:378-384, 2011) without retraining, evaluating a new operating point in about 0.03 s versus roughly 45 min for the equivalent finite-volume solve. At Re = 500 and 50 W cm⁻ 2 , a 2 vol.% suspension raises the average Nusselt number by 14.8% and lowers the base-wall temperature by 4.6 K; within the property model this gain is additive, so the practical case for the hybrid rests on colloidal stability with metallic conductivity. The differentiable, mesh-free surrogate suits design optimisation, real-time control and uncertainty quantification of electronics cooling.