A theory of rheological film condensation

Abstract

The article provides a theoretical investigation of the laminar film-condensation of shear-thinning fluids onto an isothermal, vertical plate in the presence of gravity, interfacial shear, wall friction, and inertia. The liquid motion occurs toward gravity, overcoming the resistances of interfacial shear, wall friction, and inertia. The liquid motion induces momentum to the adjacent stagnant saturated vapor by interfacial shear. The vapor motion, in turn, influences the liquid film’s heat transfer and fluid dynamics. For film condensation, it is well-known that the film, along the length of the plate, can be grouped in two separate heat transfer regimes, viz. conduction-dominated regime and convection-dominated regime. For the first time, we have identified three distinct fluid dynamic regions across the film (viz. R1, R2, and R3) unique to power-law fluids. R1 is bounded between the condensing surface and the locus of Newtonian shear stress. R2 is bounded between the locus of Newtonian shear stress and the locus of zero shear stress. Beyond R2, R3 is stretched up to the liquid-vapor interface. The transverse temperature gradient is subtly different in these three fluid dynamic regions. We examine flow physics on a non-dimensional platform. The critical role of the power-law index in determining wall-friction and condensate’s mass flow rate and the impact of liquid Prandtl number in achieving the degree of subcooling has been nicely illustrated. We expose various limiting conditions for simplifying the robust mathematical theory. An analytical expression for the liquid’s longitudinal velocity has been derived, neglecting inertia and interfacial shear.