Heat transfer analysis of temperature dependent viscosity Johnson–Segalman fluid film flow on a vertical heated belt

Understanding the behaviour of temperature dependent viscosity thin film flows on a vertically upward moving heated belt is crucial for improving predictive models in various engineering applications, such as in coating and lubrication processes. This paper presents the heat transfer analysis of temperature-dependent viscosity fluid flow on a vertical upward moving heated belt. The formulated coupled system of nonlinear ordinary differential equations is solved using the Adomian decomposition method. The study investigates the impact of flow controlling parameters: Stokes number S_t, Brinkmann number Br, variable viscosity parameter β, Weissenberg number We, effective viscosity ϕ and slip parameter e is observed on velocity, temperature, and stationary points. It is perceived that the temperature of the fluid decreases with the increase of S_t, Br, β, and ϕ, while it increases with the increase of We and e. Positions of stationary points relocate towards the heated belt surface by the increment of S_t, Br, β, and ϕ. On the other hand, their positions relocate away from the heated belt surface by the increment of We and e. The analysis also highlights the influence of heat generated by viscous dissipation and heat transported by thermal diffusion on the velocity, temperature, and stationary points. Moreover, the flow variables discussed for the temperature dependent viscosity Johnson–Segalman fluid are also discussed for the temperature dependent viscosity Newtonian fluid, and an analogy between both is provided.