Heat transfer at film condensation of stationary vapor with nanoparticles near a vertical plate

•A model is presented for heat transfer at film of nanofluid near a vertical plate.•Expressions were obtained for mass flow rate and the Nusselt number in the film.•Fluid flow and heat transfer are influenced by three non-dimensional parameters.•An increase in each of these parameters leads to heat transfer enhancement.

Processes of momentum, heat and mass transfer at the condensation of the stationary vapor with nanoparticles near a vertical plate were investigated using an approximate analytical model. This model extends the classical model of Nusselt by way of the inclusion of an equation for the nanoparticle concentration and a dependence of the nanofliud density on the nanoparticles concentration. Thus, mechanisms of the Brownian and thermophoretic diffusion are incorporated. The essential novelty lies in the identification of three main dimensionless parameters, which describe the influence of nanoparticles on heat transfer and fluid flow. They are (i) the parameter A that denotes the relation between the mechanisms of the thermophoretic and Brownian diffusion, (ii) the concentration ϕ∞ of nanoparticles in the vapor, and (iii) the ratio R of the densities of the nanoparticles and the fluid. Novel analytical solutions were derived that describe velocity profiles, the mass flow rate and the thickness of the film as the functions of the parameters A, ϕ∞ and R. Finally, a novel analytical solution for the normalized Nusselt number was obtained as a function of the aforementioned three dimensionless parameters. An increase in each of these parameters causes an increase in the normalized Nusselt number.