THE STABILITY AMD TRANSITION OF HEATED AND COOLED INCOMPRESSIBLE LAMINAR BOUNDARY LAYERS

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Abstract
The linearized governing equation for the stability of two-dimensional incompressible, laminar boundary layer in water flows with heat transfer, is the Orr-Sommerfeld equation modified to include the effect of viscosity variation with temperature. The resulting equation is solved using the method of Wazzan, Okamura, and Smith. Stability characteristics are presented for flat plate and Hartree β = −0.1988 flows for the case of Froude number larger than unity. Stability is enhanced with heating, whereas the reverse is true with cooling. The critical Reynolds number exhibits a maxima with increased wall temperature. The velocity profiles for cooled flat plates are inflected and exhibit inviscid instability. In β = −0.1988 flows, the variation of inflexion point with wall temperature does not completely account for the calculated enhanced stability; the effect of heating on viscosity and its first and second derivatives that appear in the governing equation must be considered. Charts suitable for predicting the variation of the transition Reynolds number with heat transfer are presented.

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