A Phenomenological Boundary Layer Approach to Interpret the Structure of the Heat Transfer Correlations for Laminar Forced Convection over Isothermal Flat Plates

Forced convection heat transfer is commonly described by a correlation of the type Nu=AReγPrλ, where λ<γ for moderate-to-high-Pr fluids, whereas λ=γ for low-Pr fluids. Yet, the phenomenological basis of this structure is seldom examined. This work shows that such a correlation can be interpreted from purely physical intuition, without employing scaling arguments or solving the governing equations. Focusing on laminar flow over an isothermal flat plate, we introduce a new phenomenological boundary layer approach in which, by assessing how each independent variable qualitatively affects the thickness of the boundary layer, we construct the proportionality of Nu on Re and Pr. The approach provides a physical interpretation of why the exponents of established forced convection correlations fall within certain ranges. This perspective may help both educators seeking intuition-based explanations and researchers exploring alternative formulations of forced convection heat transfer.