CLARIFICATION ON THE DEFINITION OF AVERAGE NUSSELT NUMBER IN LINEARLY VARYING WALL TEMPERATURE BOUNDARY CONDITIONS

In studies of natural convection from a vertical surface with a linear wall temperature distribution, the mean Nusselt number is often misapplied. Several recent publications in high-quality journals have defined the mean Nusselt number by integrating only the local Nusselt number over the surface length without accounting for the variation in the reference temperature. This work rectifies this oversight and clarifies the mean Nusselt number under such boundary conditions. The practical implications of this oversight are discussed, particularly for the design of systems such as vertical radiators and microchannel heat exchangers. A more consistent formulation is proposed for future studies. To support the theoretical findings, numerical simulations using COMSOL Multiphysics are conducted, verifying the corrected definition and highlighting discrepancies with conventional approaches.