Variable-viscosity flows in heated and cooled channels

An asymptotic description is given of Newtonian fluid flow in a channel which is suddenly heated or cooled. The viscosity is assumed to be purely a function of temperature. The asymptotic approximation is that the downstream viscosity at the channel wall differs by an order of magnitude from that in the upstream flow. Although we make the drastic assumption that viscous dissipation is negligible, we can analyse flows where the viscosity depends either algebraically or exponentially on the temperature.