Abstract
The method of multiple scales is used to determine three partial differential equations describing the modulation of the amplitude and complex wavenumbers of three-dimensonal (3-D) waves propagating in two-dimensional (2-D) heated liquid layers. These equations are solved numerically along the characteristics subject to the condition that the ratio of the complex group velocities in the streamwise and transverse directions be real. A new criterion for the most dangerous frequency is proposed. For an n factor of 9, F=25×10−6 is found to be the most dangerous frequency for the Blasius flow. Three-dimensional waves yield lower n factors than 2-D waves, irrespective of the heating distribution. For a power-law heating distribution of the form T=Te+AxN, one cannot make a general statement on the effect of N on the stability. Numerical results are presented that show the n factor to increase with an increase or a decrease in N.
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