Hybrid integral transform analysis of supercooled droplets solidification

Author:

Carvalho Igor S.12ORCID,Cotta Renato M.23ORCID,Naveira-Cotta Carolina P.2ORCID,Tiwari Manish K.45ORCID

Affiliation:

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

2. Laboratory of Nano and Microfluidics and Microsystems, LabMEMS, Mechanical Engineering Department, POLI and COPPE, UFRJ, Federal University of Rio de Janeiro, Brazil

3. General Directorate of Nuclear and Technological Development, DGDNTM, Brazilian Navy, Rio de Janeiro, Brazil

4. Nanoengineered Systems Laboratory, UCL Mechanical Engineering, University College London, London WC1E 7JE, UK

5. Wellcome/EPSRC Centre for Interventional and Surgical Sciences (WEISS), University College London, London W1 W 7TS, UK

Abstract

The freezing phenomena in supercooled liquid droplets are important for many engineering applications. For instance, a theoretical model of this phenomenon can offer insights for tailoring surface coatings and for achieving icephobicity to reduce ice adhesion and accretion. In this work, a mathematical model and hybrid numerical–analytical solutions are developed for the freezing of a supercooled droplet immersed in a cold air stream, subjected to the three main transport phenomena at the interface between the droplet and the surroundings: convective heat transfer, convective mass transfer and thermal radiation. Error-controlled hybrid solutions are obtained through the extension of the generalized integral transform technique to the transient partial differential formulation of this moving boundary heat transfer problem. The nonlinear boundary condition for the interface temperature is directly accounted for by the choice of a nonlinear eigenfunction expansion base. Also, the nonlinear equation of motion for the freezing front is solved together with the ordinary differential system for the integral transformed temperatures. After comparisons of the solution with previously reported numerical and experimental results, the influence of the related physical parameters on the droplet temperatures and freezing time is critically analysed.

Funder

Royal Society Wolfson Fellowship

Conselho Nacional de Desenvolvimento Científico e Tecnológico

Fundação Carlos Chagas Filho de Amparo à Pesquisa do Estado do Rio de Janeiro

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior

European Research Council

Publisher

The Royal Society

Subject

General Physics and Astronomy,General Engineering,General Mathematics

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