scholarly journals Numerical and asymptotic analysis to the cartesian Graetz problem with viscous dissipation

2021 ◽  
Vol 10 ◽  
pp. 100144
Author(s):  
Marco Rosales-Vera
Keyword(s):  
Asymptotic Analysis ◽  
Viscous Dissipation ◽  
Graetz Problem

On thin evaporating drops: When is the -law valid?

2016 ◽  
Vol 792 ◽  
pp. 134-167 ◽  
Author(s):  
M. A. Saxton ◽  
J. P. Whiteley ◽  
D. Vella ◽  
J. M. Oliver
Keyword(s):  
Mass Transfer ◽  
Asymptotic Analysis ◽  
Numerical Simulations ◽  
Viscous Dissipation ◽  
Square Root ◽  
Vapour Transport ◽  
Asymptotic Results ◽  
Rate Of Evaporation ◽  
And Diffusion ◽  
Matched Asymptotic Analysis

We study the evolution of a thin, axisymmetric, partially wetting drop as it evaporates. The effects of viscous dissipation, capillarity, slip and diffusion-dominated vapour transport are taken into account. A matched asymptotic analysis in the limit of small slip is used to derive a generalization of Tanner’s law that takes account of the effect of mass transfer. We find a criterion for when the contact-set radius close to extinction evolves as the square root of the time remaining until extinction – the famous $d^{2}$-law. However, for a sufficiently large rate of evaporation, our analysis predicts that a (slightly different) ‘$d^{13/7}$-law’ is more appropriate. Our asymptotic results are validated by comparison with numerical simulations.

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