Stability analysis of thin film flow on a heated cylindrical surface with effects of heat flux and exponentially varying viscosity

In paper production, a hollow, uniformly heated Yankee cylinder is often used to dry thin films of paper pulp. To model this drying process, we analyze the gravity-driven, axisymmetric flow of an incompressible Newtonian thin film outside of a vertically oriented, hollow cylindrical wall. An infinitely long wall of small thickness is considered, with a small heater inserted into the inner side to maintain a uniform temperature. The temperature gradient between the heated wall and the liquid generates a steady radial heat flux. Heat loss from the inner surface to the ambient air influences the thermal gradient, a vital aspect overlooked in previous studies. Since viscosity is temperature-dependent, it is assumed to vary exponentially with the local temperature gradient. Using the long-wave expansion approach, we derive a Benny-type nonlinear partial differential equation governing the leading-order evolution of film thickness. A normal mode linear stability analysis determines the complex growth rate of disturbances, employing viscosity variation, heat flux, and heat dissipation at the wall–liquid and wall–air interfaces. The analysis confirms the stabilizing role of the wall Biot number, Bw, and cylinder radius R, while the viscosity coefficient Kμ exerts a destabilizing effect. The effects on steady traveling wave profiles are also analyzed.