Instability of a vapor layer on a vertical surface at presence of nanoparticles

Based on the linear perturbation technique, an equation was derived for the prediction of hydrodynamic stability criteria in vapor layers formed at boiling of nanofluids in the inverse annular-dispersed regime. The equations were obtained in two-dimensional and three-dimensional approximations. A solution of the eigenvalue problem enabled determining criteria of hydrodynamic stability. For the first time, a complete analysis of the thermalhydrodynamic instability of a vapor layer near a vertical surface has been performed based on the Orr-Sommerfeld approach, where not only the perturbed momentum equation, but also the perturbed energy equation and the perturbed convective-diffusion equation for the nanoparticle concentration were analyzed. This approach accounts for the influence of the unperturbed 'velocity, temperature, and nanoparticle concentration profiles. The analytical solution for the vapor film stability criteria was validated against experimental studies of the effects of nanoparticles on formation and destruction of a vapor film emerged in nanofluid boiling on the surface of a metal probe during unsteady cooling. In experiments, nanoparticles caused destabilizing influence on the vapor film during boiling.