Simple relations for the stability of heated-water laminar boundary layers

Dunn-Lin theory (1955) is shown to be applicable in the estimation of minimum critical Reynolds number for heated boundary layers. A parameter is defined to reflect the curvature of the velocity profile between wall and critical layer, and includes the variable kinematic viscosity. The value of the parameter is determined by assuming a linear viscosity profile, a parabolic velocity profile, and by calculating a dominant viscous term in the asymptotic solution of the Orr-Sommerfeld equation. The inclusion of the curvature permits accurate results for the laminar velocity profiles in the wall region. Comparisons are made between the obtained values and those derived from a numerical computation using the Orr-Sommerfeld equation for exact boundary layer profiles. Agreement is noted in predicting the location of the maximum attainable critical Reynolds number in certain cases, and the method is considered reliable within experimentally available pressure gradients and surface overheats.