RESEARCH PAPERS: Bubbles, Particles and Droplets

Heat Transfer From a Translating Droplet at High Peclet Numbers: Revisiting the Classic Solution of Kronig & Brink

[+] Author and Article Information
Douglas L. Oliver

MIME Department, University of Toledo, Toledo, Ohio 43606doliver@eng.utoledo.edu

Adham W. Souccar

MIME Department, University of Toledo, Toledo, Ohio 43606

See Eq. (3.160) of Sadhal et al.  and Eq. (3-86) of Clift et al. 

J. Heat Transfer 128(7), 648-652 (Nov 18, 2005) (5 pages) doi:10.1115/1.2193542 History: Received April 13, 2005; Revised November 18, 2005

More than five decades ago Kronig and Brink published a classic analysis of transport from translating droplets. Their analysis assumed that the bulk of the resistance to transfer was in the droplet phase. It considered the limiting solution as the Peclet number became very large. Their work has been cited in many subsequent studies of droplet transfer. The present work revisits their solution using numerical techniques that were not then available. It was found that only the first mode of their solution is mathematically accurate. Hence, their solution is accurate only at large times.

Copyright © 2006 by American Society of Mechanical Engineers
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Grahic Jump Location
Figure 1

First two eigenfunctions, present versus Kronig and Brink

Grahic Jump Location
Figure 2

Bulk temperature, Θ¯(τ)

Grahic Jump Location
Figure 3

Θ(r,τ) along θ=π∕2, Kronig and Brink versus present

Grahic Jump Location
Figure 4

Nusselt number, Kronig and Brink versus present

Grahic Jump Location
Figure 5

Θ(r,τ) along θ=π∕2

Grahic Jump Location
Figure 6

Upper: locations of Θ=0.9 as a function of time; lower: contours of Θ at τ=0.01



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