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Numerical investigation of an evaporating meniscus in a heated capillary slot

  • Jasvanth V. S.Email author
  • Amrit Ambirajan
  • Abhijit A. Adoni
  • Jaywant H. Arakeri
Original
  • 23 Downloads

Abstract

This paper numerically studies heat transfer and fluid flow from an evaporating meniscus of a wetting fluid within a heated capillary. A simplified steady state mathematical model is developed for predicting the wicking height of the meniscus and the evaporation mass flow rate which includes: (1) one-dimensional flow and energy equations for the liquid and vapor regions, (2) one-dimensional model for the evaporating meniscus region, and (3) two-dimensional energy equation for the capillary wall. Three parameters, namely, apparent contact angle, cumulative heat transfer, and evaporating meniscus height characterize the evaporating meniscus region. In this paper, the apparent contact angle in the evaporating meniscus is uniquely deduced from the meniscus curvature at the centre of the capillary using the thickness profile obtained from standard extended meniscus theory (which includes the evaporating thin film and bulk meniscus regions). Correlations are obtained for the cumulative heat transfer, apparent contact angle and evaporating meniscus height as a function of the difference between the wall and saturation temperatures from the evaporating thin film theory for the meniscus region, which is called as micromodel. The macroscopic model accounts for wall heat conduction and heat transfer with fluid flow in the liquid and vapor regions. The micromodel deals with heat transfer and fluid flow in the evaporating meniscus region. In this paper, a novel scheme to link the “macroscopic” momentum and energy equations in the capillary slot and the evaporating meniscus through the correlations developed above is proposed. Using this numerical model, the wicking height and the evaporation mass flow rate are estimated and the results are compared with previously conducted experiments. The trends in the numerical results of the mathematical model correlate reasonably well with the experimental data.

Nomenclature

Alphabets

A

Dispersion constant (Hamaker constant), (J)

C 

Thermal conductance, (W m−1 ° C−1)

Cp

Specific heat, (J kg−1K−1 )

f 

Accommodation coefficient

h 

Wicking height, (m)

hfg

Latent heat of evaporation, (J kg−1)

hl

Length of liquid column, (m)

hv

Length of vapor column, (m)

hdip

Length of the column immersed in the reservoir, (m)

hamb

Convective heat transfer coefficient with air, (W m−2 K−1)

hres

Convective heat transfer coefficient with liquid, (W m−2 K−1)

H 

Height of capillary slot, (m)

kl

Liquid conductivity, (W m−1 K−1)

kv

Vapor conductivity, (W m−1 K−1)

K

Interface curvature, (m−1)

\( \dot{m} \)

Evaporation mass flow rate, (kg s−1)

\( {m}_{evap}^{\prime \prime } \)

Interface net mass flux, (kg s−1 m−2)

Pc

Capillary pressure, (N m−2)

Pd

Disjoining pressure, (N m−2)

Pl

Liquid pressure, (N m−2)

Psat

Saturation pressure, (N m−2)

Pv

Vapor pressure, (N m−2)

∆Pc

Sum of disjoining pressure and capillary pressure, (N m−2)

∆Pl

Liquid pressure drop, (N m−2)

∆Pv

Vapor pressure drop, (N m−2)

\( {q}_{evap}^{\prime \prime } \)

Interface net heat flux, (W m−2)

Qmic

Cumulative heat transfer per unit depth, (W m−1)

Qmic, w

Cumulative heat transfer, (W)

Rc

Meniscus radius of curvature, (m)

Rg

Specific gas constant, (J kg−1 K−1)

t 

Capillary wall thickness, (m)

T 

Temperature, (°C)

∆T

Temperature drop (Tw − Tsat), (°C)

u 

Velocity in x-direction, (m s−1)

2w 

Slot width, (m)

W 

Depth of capillary slot, (m)

x 

Abscissa, (m)

xmen

Meniscus height, (m)

y

Ordinate, (m)

Greek symbols

δ

Liquid film thickness, (m)

δ0

Non-evaporating film thickness, (m)

μl

Liquid viscosity, (N s m−2)

μv

Vapour viscosity, (N s m−2)

ρl

Liquid density, (kg m−3)

ρv

Vapour density, (kg m−3)

σ

Surface tension, (N m−1)

θ

Apparent contact angle, (deg)

Subscripts

0

Initial condition for adsorbed film or ambient condition

cap 

Capillary

i 

= l or v, liquid or vapor

in

Inlet

l 

Liquid

lv

Liquid-vapor interface

m 

Meniscus

mic

Micro or meniscus

res 

Reservoir

sat 

Saturation condition

v 

Vapor

w

Wall

Notes

Acknowledgements

The authors gratefully acknowledge the support and encouragement of Dr. Anand Kumar Sharma, Deputy Director, Mechanical Systems Area.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Jasvanth V. S.
    • 1
    Email author
  • Amrit Ambirajan
    • 1
  • Abhijit A. Adoni
    • 1
  • Jaywant H. Arakeri
    • 2
  1. 1.Thermal Systems GroupU R Rao Satellite CentreBangaloreIndia
  2. 2.Department of Mechanical EngineeringIndian Institute of ScienceBangaloreIndia

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