Abstract
The linear stability of flow of fluid with temperature-dependent viscosity through a channel with heated walls is considered. The resulting sixth-order eigenvalue problem is solved numerically using high-order finite-difference methods for four different viscosity models. For all the viscosity models considered a non-uniform increase of the viscosity in the channel always stabilises the flow whereas a non-uniform decrease of the viscosity in the channel may either destabilise the flow or, more unexpectedly, stabilise the flow. We discuss our results in terms of three physical effects, namely bulk effects, velocity-profile shape effects and thin-layer effects.
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