ISBN: 978-1-56700-537-0
ISBN Online: 978-1-56700-538-7
ISSN Online: 2377-424X
International Heat Transfer Conference 17
HEAT TRANSFER IN A SOLID WALL AFTER AN IMPACT OF A LIQUID DROP OR SOLID PARTICLE
Résumé
If the initial temperatures of a drop or particle and the substrate before collision are different, an intense heat exchange takes place between both. This effect is at the heart of many industrial processes, such as spray cooling or spray lubrication, and it plays a vital role during ice accretion caused by ice crystal impact on a heated wall.
It is well known that heat transfer in the vicinity of the particle-substrate contact occurs in a very thin layer whose thickness increases with time. This layer includes the thermal boundary layer in the deforming particle as well as the thermal boundary layer in the substrate. There is currently an exact solution for heat transfer during drop spreading on a rigid substrate that does not involve boiling. Models have also been developed for heat transfer problems involving drop impact accompanied by nucleate boiling or film boiling.
In this theoretical and experimental study, a three-dimensional heat transfer problem in the substrate is modeled for times much longer than the contact time and at distances much greater than the contact radius. A time dependent asymptotic solution is obtained for the temperature field in the wall. This spherically symmetric solution satisfies exactly the heat conduction equation. The expression for temperature is singular at the initial time instant t = 0. Therefore, the initial conditions are satisfied only in an integral sense through the total thermal energy balance of particle impact. This is why this theoretical solution is considered as a remote asymptotic solution valid for long times. The solution is linear. Therefore, a superposition of the solutions can be applied for the case of a chain or spray of particles.
The solution is validated by comparison with experimental data. The experimental setup consists of a drop generator, a solid particle injector, a heated substrate and a high-speed video system. The setup allows to observe the impact of a liquid drop or a solid particle. The temperature in the thick solid substrate is measured at different positions using an array of thermocouples. In these experiments, the heat transfer associated with a single liquid drop impact, chain of drops as well as a single ice particle impact is studied.
The impact of a single water drop and chain of drops is studied at the temperatures below the boiling point of water. The impact leads to the drop spreading and rebound. The impact of an ice particle leads to a partial particle deformation, breakup and rebound. The heat transfer includes the melting of the ice volume deposited at the substrate after the particle impact. It is interesting to note that the heat transfer, initiated by these completely different phenomena, is very similar at large times. The theoretical predictions for the evolution of the temperatures in the substrate agree well with the experimental data.
It is well known that heat transfer in the vicinity of the particle-substrate contact occurs in a very thin layer whose thickness increases with time. This layer includes the thermal boundary layer in the deforming particle as well as the thermal boundary layer in the substrate. There is currently an exact solution for heat transfer during drop spreading on a rigid substrate that does not involve boiling. Models have also been developed for heat transfer problems involving drop impact accompanied by nucleate boiling or film boiling.
In this theoretical and experimental study, a three-dimensional heat transfer problem in the substrate is modeled for times much longer than the contact time and at distances much greater than the contact radius. A time dependent asymptotic solution is obtained for the temperature field in the wall. This spherically symmetric solution satisfies exactly the heat conduction equation. The expression for temperature is singular at the initial time instant t = 0. Therefore, the initial conditions are satisfied only in an integral sense through the total thermal energy balance of particle impact. This is why this theoretical solution is considered as a remote asymptotic solution valid for long times. The solution is linear. Therefore, a superposition of the solutions can be applied for the case of a chain or spray of particles.
The solution is validated by comparison with experimental data. The experimental setup consists of a drop generator, a solid particle injector, a heated substrate and a high-speed video system. The setup allows to observe the impact of a liquid drop or a solid particle. The temperature in the thick solid substrate is measured at different positions using an array of thermocouples. In these experiments, the heat transfer associated with a single liquid drop impact, chain of drops as well as a single ice particle impact is studied.
The impact of a single water drop and chain of drops is studied at the temperatures below the boiling point of water. The impact leads to the drop spreading and rebound. The impact of an ice particle leads to a partial particle deformation, breakup and rebound. The heat transfer includes the melting of the ice volume deposited at the substrate after the particle impact. It is interesting to note that the heat transfer, initiated by these completely different phenomena, is very similar at large times. The theoretical predictions for the evolution of the temperatures in the substrate agree well with the experimental data.