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 $Nu=AR{e}^{\gamma }P{r}^{\lambda }$, where $\lambda <\gamma$ for moderate-to-high-Pr fluids, whereas $\lambda =\gamma$ 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.