Estimation of the onset of longitudinal vortices in a laminar boundary layer heated from below

Numerical study of the onset of longitudinal vortices in a boundary layer flow over a horizontal flat plate heated from below is presented. The onset position is determined as long as the gradually growing disturbances are large enough to be detected by measurements. Various experimental techniques, such as flow visualization, thermo-couple temperature reading, LDA, hot-wire velocity anemometry, and heat transfer measurement, are carefully examined for evaluating the onset criteria in the numerical solution. The governing parameters on the onset position x* of longitudinal vortices are Prandtl number, wave number a, and the ratio of Grashof number and Reynolds number Gr(L)/Re-L(1.5). The obtained onset position (Gr(X)/R(X)(1.5))* and corresponding wave number a*x*(1/2) are independent of the values of Gr(L)/Re-L(1.2) = 500, 1000, and 1500 used, and weakly depend on the applied initial temperature t(0) = 10(-4), 5 X 10(-5), 10(-5) and 10(-6), and the different onset criteria. The results of present numerical study are in good agreement with the previous experimental data.