The stability of a vertical natural convection boundary layer with temperature dependent viscosity

The two-dimensional stability theory of a laminar natural convection boundary layer adjacent to a vertical isothermal surface is extended to include the variation of viscosity with temperature. In particular, the appropriate Orr-Sommerfeld equations are derived to include the linear variation of viscosity with temperature. The analysis is applied to the case of flows over both heated plates (positive buoyancy) and cooled plates (negative buoyancy). Numerical calculations of the stability characteristics for a surface in ethylene glycol are performed for each of the following situations: (a) heated plate with T_w = 115 °F and T_∞ = 75 °F and (b) cooled plate with T_w = 75 °F and T_∞ = 115 °F. The numerical results indicate that a heated plate is more stable than a cooled plate for the same ΔT and film temperature. Calculated results for both heating and cooling are also compared to those which use the film temperature. It is found that the constant property assumption is more reasonable for the heated plated than for the cooled plate.