Mixed convection on a vertical plate with an unheated starting length

The effect of an unheated starting length on combined forced and natural convection adjacent to a vertical plate has been investigated by solving the nonsimilar laminar boundary layer equations. The solutions were carried out numerically for prescribed values of the governing parameters which include the starting length Reynolds number Re₀, a mixed convection parameter gβ(ΔT)v/U_∞³, and the Prandtl number (which was assigned a value of 0.7). The local heat transfer results show that the presence of the unheated starting length can significantly accentuate the effects of buoyancy relative to the case of no starting length. The degree of accentuation of the buoyancy effects is strongly influenced by the magnitude of gβ(ΔT)v/U_∞³. When this parameter is on the order of 10⁻³, the natural convection contribution to the heat transfer coefficient is markedly increased owing to the starting length. On the other hand, when gβ(ΔT)v/U_∞³ is about 10^{− 5}, the buoyancy contribution is essentially unaffected by the starting length. The shape of the velocity profile is also found to be highly responsive to the interaction between the buoyancy and the starting length. As a by-product of the research, the accuracy of a wellknown integral momentum/energy solution for pure forced convection with a starting length was established. In addition, velocity profiles for mixed convection without a starting length were compared with those of experiment in order to appraise a proposed explanation for a disparity that had been previously identified in the literature.