Spatial Stability of Stagnation Water Boundary Layer with Heat Transfer

Abstract

Neglecting temperature fluctuations, assuming viscosity is only temperature dependent, and assuming all other fluid properties are constant, the two-dimensional linearized parallel flow stability problem is adequately treated by modifying the Orr-Sommerfeld equation to include viscosity variations with temperature. The resulting equation is used to study the spatial stability of stagnation water boundary layer with heat transfer. The mean flow with free-stream temperature T∞ = 60°F and wall temperature Tw ranging from 32 to 200°F is computed numerically, from the boundary layer equations with variable fluid properties. It is found that heating stabilizes the boundary layer and cooling destabilizes it. At Tw≅196°F the neutral curve degenerates to a singular point at frequency ω = 5×10−7 and Reynolds number Rδ* = 30.7×103. All disturbances become completely damped for Tw>196°F. It appears that the effect of viscosity μ is larger than the effect of its first derivative μ′ on stability, and that the effect of μ″ is negligible compared with the effect of μ′.