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This study introduces a methodology to compute spray cooling in the nucleate boiling regime. It examines the cooling of a horizontal circular tube, although the approach is not restricted to this geometry. While numerous investigations have considered nucleate boiling in the past, these are usually restricted to spray impingement onto a flat plate and not onto more complex surfaces. Furthermore, most prior studies are highly empirical in nature. The present study circumvents both of these restrictions. On the one hand, with more complex surfaces additional factors must be considered, in particular the influence of the local impingement angle on the number flux of impinging drops. On the other hand, the heat transfer for single droplets is first computed using existing theoretical solutions and then the principle of superposition is used to compute the global heat transfer from the surface over which the spray impinges. Accompanying this computation, a drop size distribution is specified in order to also investigate the influence of not only one representative drop size, but also the variance of drop size distribution on the heat transfer, an influence seldom reported on. Furthermore, the probability of drop-drop interaction on the surface has been estimated and the heat transfer correspondingly adjusted. This approach of computing total net heat transfer on a surface is first validated using available measurements in which the heat transfer in the nucleate boiling regime from a flat plate were used for comparison. The heat transfer from a circular tube was then computed as a function of mass flow rate, drop size distribution (expectation and variance) and wall temperature. Conditions for maximum heat transfer, corresponding to the critical heat flux, were identified. In all cases the net heat transfer was limited by the onset of drop-drop interaction on the substrate, i.e. the net coverage of liquid on the surface. The results of these parametric studies indicate clearly how the mass flow rate can be adjusted to maximize heat transfer while avoiding excess fluid consumption. Furthermore, the Sauter mean diameter is shown to be an appropriate drop size to use, if no further information is available concerning the size distribution. • A non-empirical methodology to computing heat transfer in the nucleate boiling regime. • Spray cooling computation taking into account explicitly the size distribution of drops. • Insight into spray conditions, which maximizes heat transfer while minimizing liquid consumption. • Consideration of highly varying number density of drops when cooling a surface of complex geometry. [ABSTRACT FROM AUTHOR]

This study examines spray cooling of horizontal, circular tubes when the surface temperature exceeds the Leidenfrost point, and the individual drop impacts are in the film boiling regime. Although film boiling is not an optimal condition for heat transfer, it is encountered in transient cooling processes or when high temperatures persist along the tube. The goal of the study is to apply existing models for drop impact and heat transfer to surfaces more complex than flat plates and to determine the overall steady state heat removal rate as an essential parameter for heat exchanger design. The spray characteristics are prescribed by a local number flux and drop size, assuming a random distribution in space and a uniform velocity of all drops. The angle of individual drop impingement on the cylindrical tube is accounted for through the maximum spreading diameter of the drop on the surface and the normal component of impact velocity. Furthermore, drop-drop interaction on the heated surface is accounted for at high local number flux values through an effective coverage area coefficient. The results are expressed in the form of a local heat transfer coefficient. These results confirm that the most influential parameters regarding heat transfer are the liquid mass flow rate in the nozzle and the drop diameter; however, they also indicate that the non-normal impact of drops over portions of the cylindrical tube leads to a highly reduced number flux; hence heat transfer. This oblique impact angle arises for one from the local spray angle, but more drastically from the curved, cylindrical surface; the latter leading to a dramatic sharp decrease in heat transfer. This is important information when considering the use of multiple spray nozzles, either circumferentially or longitudinally along the tube, since it dictates the optimal spacing between neighbouring nozzles. [Display omitted] • A methodology for predicting spray cooling in the film boiling regime is introduced. • The predication of heat transfer is based on theoretical analysis; only one empirical factor is introduced. • The local impingement angle of drops has been considered in the hydrodynamics of impact and in the influence on the local number flux. • Parametric studies indicate the influence of droplet size, substrate temperature, and mass flow rate on the heat transfer. • This study lays the basis for simulation of practical spray cooling scenarios involving multiple nozzles and/or nozzle arrays. [ABSTRACT FROM AUTHOR]