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Hybrid integral transform analysis of supercooled droplets solidification.

Igor S Carvalho1,2, Renato M Cotta2,3, Carolina P Naveira-Cotta2

  • 1Petrobras S.A., Rio de Janeiro, Brazil.

Proceedings. Mathematical, Physical, and Engineering Sciences
|February 14, 2022
PubMed
Summary

This study presents a novel mathematical model for freezing supercooled droplets, crucial for developing ice-repellent surfaces. The hybrid numerical-analytical solution accurately predicts freezing times and temperatures, aiding engineering applications.

Keywords:
GITTicingintegral transformsmoving boundarysupercooled droplet

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Area of Science:

  • Thermodynamics and Fluid Mechanics
  • Heat and Mass Transfer
  • Materials Science

Background:

  • Freezing of supercooled liquid droplets is critical for engineering applications, including designing ice-repellent surfaces.
  • Understanding droplet freezing dynamics informs strategies to reduce ice adhesion and accretion.
  • Existing models often require complex numerical simulations for transient heat and mass transfer.

Purpose of the Study:

  • To develop a robust mathematical model for the freezing of supercooled droplets in a cold air stream.
  • To implement hybrid numerical-analytical solutions for accurate prediction of droplet freezing phenomena.
  • To analyze the impact of convective heat transfer, mass transfer, and thermal radiation on droplet freezing.

Main Methods:

  • Development of a mathematical model incorporating convective heat and mass transfer, and thermal radiation.
  • Application of the generalized integral transform technique (GITT) for solving the transient partial differential equations.
  • Utilizing a nonlinear eigenfunction expansion for the interface temperature and solving the moving boundary problem.

Main Results:

  • The hybrid numerical-analytical solution accurately captures the moving boundary heat transfer problem.
  • The model successfully accounts for nonlinear boundary conditions at the droplet interface.
  • Analysis reveals the influence of key physical parameters on droplet temperatures and freezing duration.

Conclusions:

  • The developed hybrid GITT approach provides an efficient and accurate method for analyzing supercooled droplet freezing.
  • The findings offer valuable insights for designing surfaces with tailored icephobicity.
  • This model serves as a foundation for further research in droplet phase change phenomena and anti-icing technologies.