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Numerical investigation of an evaporating meniscus in a heated capillary slot

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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.

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Abbreviations

A :

Dispersion constant (Hamaker constant), (J)

C :

Thermal conductance, (W m−1 ° C−1)

C p :

Specific heat, (J kg−1K−1 )

f :

Accommodation coefficient

h :

Wicking height, (m)

h fg :

Latent heat of evaporation, (J kg−1)

h l :

Length of liquid column, (m)

h v :

Length of vapor column, (m)

h dip :

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

h amb :

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

h res :

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

H :

Height of capillary slot, (m)

k l :

Liquid conductivity, (W m−1 K−1)

k v :

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)

P c :

Capillary pressure, (N m−2)

P d :

Disjoining pressure, (N m−2)

P l :

Liquid pressure, (N m−2)

P sat :

Saturation pressure, (N m−2)

P v :

Vapor pressure, (N m−2)

∆P c :

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

∆P l :

Liquid pressure drop, (N m−2)

∆P v :

Vapor pressure drop, (N m−2)

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

Interface net heat flux, (W m−2)

Q mic :

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

Q mic, w :

Cumulative heat transfer, (W)

R c :

Meniscus radius of curvature, (m)

R g :

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)

x men :

Meniscus height, (m)

y :

Ordinate, (m)

δ :

Liquid film thickness, (m)

δ 0 :

Non-evaporating film thickness, (m)

μ l :

Liquid viscosity, (N s m−2)

μ v :

Vapour viscosity, (N s m−2)

ρ l :

Liquid density, (kg m−3)

ρ v :

Vapour density, (kg m−3)

σ :

Surface tension, (N m−1)

θ :

Apparent contact angle, (deg)

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

References

  1. Potash M, Wayner PC Jr (1972) Evaporation from a two-dimensional extended meniscus. Int J Heat Mass Transf 15:1851–1863

    Article  Google Scholar 

  2. Wayner PC Jr, Yao YK, LaCroix LV (1976) The interline heat-transfer coefficient of an evaporating wetting film. Int J Heat Mass Transf 19:487–492

    Article  Google Scholar 

  3. Holm FW, Goplen SP (1979) Heat transfer in the meniscus thin film transition region. J Heat Transf 101:543–547

    Article  Google Scholar 

  4. DasGupta S, Schonberg JA, Wayner PC Jr (1993) Investigation of an evaporating extended meniscus based on the augmented young-Laplace equation. J Heat Transf 115:201–208

    Article  Google Scholar 

  5. DasGupta S, Kim IY, Wayner PC Jr (1994) Use of the kelvin-Clapeyron equation to model an evaporating curved microfilm. J Heat Transf 116:1007–1015

    Article  Google Scholar 

  6. Ha JM, Peterson GP (1996) The interline heat transfer of evaporating thin films along micro grooved surface. J Heat Transf 118:747–755

    Article  Google Scholar 

  7. Wang H, Garimella SV, Murthy JY (2007) Characteristics of an evaporating thin film in a microchannel. Int J Heat Mass Transf 50:3933–3942

    Article  Google Scholar 

  8. Jasvanth VS, Ambirajan A, Kumar D, Arakeri JH (2013) Effect of heat pipe figure of merit on an evaporating thin film. J Thermophys Heat Transf 27(4):633–640

    Article  Google Scholar 

  9. Troung JG, Wayner PC Jr (1987) Effect of capillary and van der Waals dispersion forces on the equilibrium profile of a wetting fluid: theory and experiment. J Chem Phys 87(1):4180–4188

    Article  Google Scholar 

  10. Zheng L, Plawsky JL, Wayner PC Jr (2002) Accuracy of measurements of curvature and apparent contact angle in a constrained vapor bubble heat exchanger. Int J Heat Mass Transf 45:2021–2030

    Article  Google Scholar 

  11. Zheng L, Plawsky JL, Wayner PC Jr, DasGupta S (2004) Stability and oscillations in an evaporating corner meniscus. J Heat Transf 126:169–178

    Article  Google Scholar 

  12. Panchamgam SS, Gokhale SJ, Plawsky JL, DasGupta S, Wayner PC Jr (2005) Experimental determination of the effect of disjoining pressure on shear in the contact line region of a moving evaporating thin film. J Heat Transf 127:231–243

    Article  Google Scholar 

  13. Panchamgam SS, Chatterjee A, Plawsky JL, Wayner PC Jr (2008) Comprehensive experimental and theoretical study of fluid flow and heat transfer in a microscopic meniscus in a miniature heat exchanger. Int J Heat Mass Transf 51(21):5368–5379

    Article  Google Scholar 

  14. Migliaccio CP, Dhavaleswarapu HK, Garimella SV (2011) Temperature measurements near the contact line of an evaporating meniscus V-groove. Int J Heat Mass Transf 54:1520–1526

    Article  Google Scholar 

  15. Stephan PC, Busse CA (1992) Analysis of the heat transfer coefficient of grooved heat pipe evaporator walls. Int J Heat Mass Transf 35(2):383–391

    Article  Google Scholar 

  16. Schonberg JA, DasGupta S, Wayner PC Jr (1995) An augmented young-Laplace model of an evaporating meniscus in a microchannel with high heat flux. Exp Thermal Fluid Sci 10:163–170

    Article  Google Scholar 

  17. Wang H, Pan Z, Garimella SV (2011) Numerical investigation of heat and mass transfer from an evaporating meniscus in a heated open groove. Int J Heat Mass Transf 54:3015–3023

    Article  Google Scholar 

  18. Du S-Y, Zhao Y-H (2012) Numerical study of conjugated heat transfer in evaporating thin-films near the contact line. Int J Heat Mass Transf 55:61–68

    Article  Google Scholar 

  19. Khrustalev D, Faghri A (1996) Fluid flow effects in evaporation from liquid–vapor meniscus. J Heat Transf 118:725–730

    Article  Google Scholar 

  20. Ma HB, Peterson GP, Pratt DM (1998) Disjoining pressure effect on the wetting characteristics in a capillary tube. Microscale Thermophys Eng 2(4):283–297

    Article  Google Scholar 

  21. Jasvanth VS, Ambirajan A, Arakeri JH (2016) Experimental study on evaporation of pentane from a heated capillary slot. Int J Heat Mass Transf 95:466–476

    Article  Google Scholar 

  22. Peles YP, Yarin LP, Hetsroni G (2000) Thermohydrodynamic characteristics of two-phase flow in a heated capillary. Int J Multiphase Flow 26:1063–1093

    Article  Google Scholar 

  23. Bertossi R, Lataoui Z, Ayel V, Romestant C, Bertin Y (2009) Modelling of thin liquid film in grooved heat pipes. Num Heat Transfer, Part A 55:1075–1095

    Article  Google Scholar 

  24. Morris SJS (2001) Contact angles for evaporating liquids predicted and compared with experiments. J Fluid Mech 432:1–30

    Article  Google Scholar 

  25. Patankar SV (1980) Numerical heat transfer and fluid flow, McGraw–Hill Companies Inc

  26. Recktenwald GW (2003) The control-volume finite-difference approximation to the diffusion equation. Technical report, Portland State University, Department of Mechanical Engineering, Portland, OR

  27. Recktenwald GW (2006) One dimensional convection: interpolation models for CFD,” Technical report, Portland State University, Department of Mechanical Engineering, Portland, OR

  28. Yang WY, Cao W, Chung T-S, Morris J (2005) Applied numerical methods using MATLAB. John Wiley & Sons, Inc, New Jersey

    Book  Google Scholar 

  29. Reference Fluid Thermodynamic and Transport Properties (REFPROP) (2007) NIST standard reference database 23, Version 7:0

  30. Wee SK (2004) Microscale observables for heat and mass transport in sub-Micron scale evaporating thin film, Ph.D. thesis, Texas A&M University

  31. Holman JP (2001) Experimental methods for engineers, 7th edn. McGraw Hill Companies Inc, New York

    Google Scholar 

  32. Peles YP, Yarin LP, Hetsroni G (2001) Steady and unsteady flow in a heated capillary. Int J Multiphase Flow 27:577–598

    Article  Google Scholar 

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Acknowledgements

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

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Authors and Affiliations

  1. Thermal Systems Group, U R Rao Satellite Centre, Bangalore, 560017, India

    Jasvanth V. S., Amrit Ambirajan & Abhijit A. Adoni

  2. Department of Mechanical Engineering, Indian Institute of Science, Bangalore, 560012, India

    Jaywant H. Arakeri

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  1. Jasvanth V. S.
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  2. Amrit Ambirajan
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  4. Jaywant H. Arakeri
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Correspondence to Jasvanth V. S..

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V. S., J., Ambirajan, A., Adoni, A.A. et al. Numerical investigation of an evaporating meniscus in a heated capillary slot. Heat Mass Transfer 55, 3675–3688 (2019). https://doi.org/10.1007/s00231-019-02672-4

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