Research Papers: Evaporation, Boiling, and Condensation

An Iterative Solution Approach to Coupled Heat and Mass Transfer in a Steadily Fed Evaporating Water Droplet

[+] Author and Article Information
Yigit Akkus

Lyle School of Engineering,
Southern Methodist University,
Dallas, TX 75205;
Ankara 06172, Turkey
e-mail: yakkus@aselsan.com.tr

Barbaros Çetin

Mechanical Engineering Department,
İ.D. Bilkent University,
Ankara 06800, Turkey
e-mail: barbaros.cetin@bilkent.edu.tr

Zafer Dursunkaya

Department of Mechanical Engineering,
Middle East Technical University,
Ankara 06800, Turkey
e-mail: refaz@metu.edu.tr

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received June 21, 2018; final manuscript received December 21, 2018; published online January 30, 2019. Assoc. Editor: Milind A. Jog.

J. Heat Transfer 141(3), 031501 (Jan 30, 2019) (10 pages) Paper No: HT-18-1410; doi: 10.1115/1.4042492 History: Received June 21, 2018; Revised December 21, 2018

Inspired by the thermoregulation of mammals via perspiration, cooling strategies utilizing continuously fed evaporating droplets have long been investigated in the field, yet a comprehensive modeling capturing the detailed physics of the internal liquid flow is absent. In this study, an innovative computational model is reported, which solves the governing equations with temperature-dependent thermophysical properties in an iterative manner to handle mass and heat transfer coupling at the surface of a constant shape evaporating droplet. Using the model, evaporation from a spherical sessile droplet is simulated with and without thermocapillarity. An uncommon, nonmonotonic temperature variation on the droplet surface is captured in the absence of thermocapillarity. Although similar findings were reported in previous experiments, the temperature dip was attributed to a possible Marangoni flow. This study reveals that buoyancy-driven flow is solely responsible for the nonmonotonic temperature distribution at the surface of an evaporating steadily fed spherical water droplet.

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Fig. 2

Flowchart of the computational scheme

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Fig. 3

Measured surface temperatures [30] and computed counterparts simulated with and without thermocapillarity

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Fig. 4

Temperature distribution, streamlines, and velocity vectors without thermocapillarity: (a) case 1, (b) case 2, and (c) case 3

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Fig. 5

Temperature distribution, streamlines, and velocity vectors with thermocapillarity: (a) case 1, (b) case 2, and (c) case 3

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Fig. 6

Velocity distribution and velocity vectors in the droplet with and without Marangoni convection: (a) case 3 w/o Ma convection and (b) case 3 with Ma convection

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Fig. 7

Distribution of interface temperature for different droplet radii and flow rates: (a) case 3 and (b) case 3

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Fig. 8

Energy balance on a sample control volume beneath the interface

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Fig. 9

Distribution of surface velocities for case 3 at 50 μm from the interface: (a) w/o thermocapillarity and (b) with thermocapillarity

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Fig. 10

Distribution of conduction rates for case 3 with and w/o thermocapillarity (Δr = 50 μm)



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