A rivulet of perfectly wetting fluid with temperature-dependent viscosity draining down a uniformly heated or cooled slowly varying substrate

Uses the lubrication approximation to analyze the steady locally unidirectional gravity-driven draining of a thin rivulet of a perfectly wetting Newtonian fluid with temperature-dependent viscosity down a slowly varying substrate that is either uniformly hotter or uniformly colder than the surrounding atmosphere, and hence highlight the similarities and differences between the perfectly wetting and the nonperfectly wetting cases.