Effects of wall-heating on the linear instability characteristics of pressure-driven two-layer channel flow

The linear stability analysis of a pressure-driven two-layer channel flow of two immiscible, Newtonian and incompressible fluids is considered. The walls of the channel are maintained at different constant temperatures and Nahme's law is applied to model the temperature dependence of the fluid viscosity. A modified Orr–Sommerfeld equation for the disturbance streamfunction coupled to a linearized energy equation is derived and solved using a spectral collocation method. Our results indicate that increasing the dimensionless top wall temperature has a non-monotonic effect on the linear stability characteristics. We also found that increasing the thermal conductivity and density ratios stabilise the flow for the set of parameter values considered; the viscosity ratio has a non-monotonic effect on the maximal growth rate. An energy ‘budget’ analysis shows that the most dangerous mode is of ‘interfacial’ type.

► Increasing the dimensionless top wall temperature has a non-monotonic effect on the linear stability characteristics.
► We found that increasing the thermal conductivity and density ratios stabilise the flow.
► The viscosity ratio has a non-monotonic effect on the maximal growth rate.
► Energy ‘budget’ analysis shows that the most dangerous mode is of ‘interfacial’ type.