An analytical theory for the forced convection condensation of shear-thinning fluids onto isothermal horizontal surfaces

摘要

We present an analytical theory for laminar forced convection condensation of saturated vapor on horizontal surfaces. The condensation produces shear-thinning film moving downstream due to the viscous-drag occurring at the vapor-liquid interface. The mathematical model is built based on a few input parameters, viz. power-law index (n), nondimensional film-thickness (ηδ,l), Prandtl number (Pr), and inertia number (Mc). A set of output parameters is used to analyze the distinct characteristics of the fluid-flow and condensation, viz. the condensate’s nondimensional mass flow rate (m^), Nusselt number, specific enthalpy ratio (Rh), thermal retention coefficient (Θ), and nondimensional wall-shear stress (τ^w). We have identified the subtlety of shear-thinning film flow when liquid’s thermophysical properties vary according to the changes in wall-shear and the interfacial drag. Contextually, we illustrate that a rise in shear-thinning effect (obtained by decreasing n), keeping Mc and ηδ,l fixed, results in a decrease of m^, Rh, τ^w, and (1/Θ). We have demonstrated that for a fixed Rh, a shear-thinning film, compared to the Newtonian film, would exhibit a greater ηδ,l but a smaller interfacial velocity (fi′). Furthermore, a greater film thickness is required for low Pr liquids to attain the same degree of subcooling compared to high Pr liquids. We perform systematic investigation over a wide range of ηδ,l. We observe that for small ηδ,l values, the vapor boundary-layer moving onto the liquid-film exhibits similar flow-features as found in the well-known Blasius boundary-layer. Conversely, at large ηδ,l, the present solution would remarkably differ from the Blasius solution. Finally, we establish an approximate theory for small ηδ,l motivated by the linearity in the cross-stream variations of velocity and temperature within the thin-film. This approximate theory gives rise to analytical correlations for Rh, Θ, τ^w, and m^, which would be useful for engineers.