This thesis describes the heating rate of a small liquid droplet in a developing boundary layer wherein the boundary layer thickness scales with the droplet radius. Surface tension modifies the nature of thermal and hydrodynamic boundary layer development, and consequently the droplet heating rate. A physical and mathematical description precedes a reduction of the complete problem to droplet heat transfer in an analogy to Stokes' first problem, which is numerically solved by means of the Lagrangian volume of fluid methodology.For Reynolds numbers of order one, the dispersed phase Prandtl number significantly influences the droplet heating rate only in the transient period when the thermal boundary layer first reaches the droplet surface. As the dispersed phase Prandtl number increases, so does the duration of the transient. At later times, when the the droplet becomes fully engulfed by the boundary layer, the heating rate becomes a function of only the constant heat flux boundary condition. This characteristic holds for all Peclet and Weber numbers, but the spatial behavior of the droplet differs for small and large Peclet and Weber numbers.Simulation results allow for the development of a predictive tool for the boiling entry length of dilute systems in channel flow. The tool relies on an assumption of temperature equivalency between the droplet and the thermal boundary layer evaluated in absence of the dispersed phase, which is supported by the computational results. Solutions for plug and fully developed flow do not differ appreciably, suggesting a precise description of the fluid mechanics is not necessary for an approximation of the boiling entry length. Future experimental work is required to validate the predictive models derived in this thesis.
University of Minnesota Master of Science thesis. August 2014. Major: Mechanical Engineering. Advisor: Professor Francis A. Kulacki.
Heat transfer to droplets in developing boundary layers at low capillary numbers.
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