A perturbation analysis for laminar free convection along a vertical plate, utilizing the classical boundary-layer solution as the zeroth-order approximation, is presented. First-order perturbations for the velocity and temperature fields have been calculated in detail for Prandtl numbers of 0.72 and 10.0. The propagation of leading-edge singularity into the first-order perturbations is examined and discussed. Good agreement is found between the present solution and experimental data.
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Yang et al. (1964) studied this question.