Stability of non-isothermal annular Poiseuille flow with viscosity stratification

Abstract

The non-isothermal annular Poiseuille flow widely appears in many engineering applications related to the annular passage. This paper reports the linear stability analysis of a viscous flow of water between two differentially heated concentric cylinders with temperature-dependent viscosity. The viscosity variation with temperature is described by an Arrhenius-type model in the flow. The instability properties are examined numerically with a spectral collocation method for axisymmetric disturbance. The stability results are simulated for two different reference temperatures (294.4 and 323 Kelvin (K)) at the outer cylinder. The results show that the basic velocity profiles possess a point of inflection for some value of the curvature parameter when the temperature difference between the cylinders is larger than 80.0 K. The growth of the disturbance increases by increasing the value of the curvature parameter and temperature differences between the cylinders. The disturbance growth rate for reference temperature 323 K is larger than the reference temperature 294.4 K up to a certain value of the curvature parameter. The linear stability boundaries show that the critical value of the Reynolds number decreases with increasing the value of the curvature parameter and temperature differences between the concentric cylinders. The stability of the water flow decreases by decreasing the gap between the cylinders and the viscosity of the flow. However, in contrast to temperature-dependent channel flow, the flow stability increases by increasing the small number of temperature differences between the cylinders for the relatively lower value of the curvature parameter.