The Graetz-Nusselt problem is the classical framework for laminar forced convection, describing the balance between axial convection and transverse heat conduction. However, this balance breaks down at the nanoscale, where axial conduction and viscous dissipation become comparable to bulk transport terms. In this work, we first examine this modified balance using molecular dynamics simulations of water convective heat transfer in graphene nanochannels. The simulations show that thermal development is not determined by the inlet Péclet and Brinkman numbers alone. Nanoscale effects become a leading contribution to the energy balance and can even drive the bulk temperature above the wall temperature in heating cases, causing heat flux reversal and an apparent singularity in the local $\mathit{Nu}$. We then develop a generalized extended Graetz model that incorporates all key nanoscale effects, including axial conduction, bulk and interfacial dissipation, velocity slip, temperature jump, and thermal conductivity anisotropy. The model accurately predicts the evolution of local $\mathit{Nu}$ from the developing to the fully developed state. Using this model, we further analyze the effects of key nanoscale parameters and find that velocity slip affects heat transfer mainly through dissipation, while temperature jump directly weakens wall-fluid heat transfer and lowers $\mathit{Nu}$. Furthermore, we propose a dimensionless resistance ratio $\mathrm{\Pi }=Nu{\mathrm{\Lambda }}_{\mathrm{k}}$ that quantifies the interfacial contribution to total thermal resistance and distinguishes bulk-controlled, transition, and interface-controlled regimes.

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• Convection
• Heat transfer
• Nanofluidics
• Noncontinuum effects
• Thermal transport
• Navier-Stokes equation