Heat convection length for boundary-layer flows

In analyses of heat convection problems, it is traditional to introduce the heat transfer coefficient, h, such that the average heat flux at the solid surface can be conveniently calculated. To find h, one has to simultaneously solve governing equations for conservations of mass, momentum, and energy. This task may prove too challenging for contemporary undergraduate students. In the present study, we propose a heat convection length, Δs, which can greatly simplify the analysis, yet allow the convection characteristics to be retained. Classical examples for laminar boundary-layer air flows driven by forced convection or free convection over flat plates with length L are presented. For forced convection, Δs/L is found to be 2.026 for a wide range of Re; for free convection, Δs/L is found to be 2.511 for various Gr values.