Analytical solutions of single and multi-phase models for the condensation of nanofluid film flow and heat transfer

Classical Nusselt's condensate falling film theory is extended in this paper to the case when the base fluid is added ingredients of some frequently used popular nanoparticles. The resulting mixture, i.e, nanofluids, is analytically investigated either when the nanoparticles are uniformly distributed across the condensate boundary layer which is the most used model (single phase) in the literature, or when the concentration of nanoparticles through the film is allowed to vary from the wall to the outer edge of the condensate film in the light of modified Buongiorno's nanofluid model (multi-phase) incorporating mechanisms of the Brownian and thermophoretic diffusion. In both theoretical cases, momentum and energy equations are solved analytically to deduce the flow and heat transport phenomena. As a result, the influences of employed nanofluids on the flow and heat of the condensate film are determined exactly. When the concentration of nanoparticles is assumed constant both models are shown to coincide. Otherwise, effects of nanofluids as compared to the regular fluid on the velocity profiles, the mass flow rate, the thickness of the condensate film and the Nusselt number are easy to conceive from both single and multi-phase models. In particular, the theoretical treatment in both models enables us to understand the heat transfer enhancement feature of the nanofluids models. When the diffusion parameter is increased in the multi-phase model, more enhancement in the rate of heat transfer is observed. In agreement with the experimental evidences, the water-based nanofluid with nanoparticles Ag is the best heat transferring mixture.