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Fluid flow and heat transfer in the evaporating thin film region

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Abstract

The evaporating thin film region is an extended meniscus beyond the apparent contact line at a liquid/solid interface. Thin film evaporation plays a key role in a highly efficient heat pipe. A detailed mathematical model predicting fluid flow and heat transfer through the thin film region is developed. The model considers the effects of inertial force, disjoining pressure, surface tension, and curvature. Utilizing the order analysis, the model is simplified and can be numerically solved for the thin film profile, interfacial temperature, meniscus radius, heat flux distribution, velocity distribution, and mass flow rate in the evaporating thin film region. The prediction shows that while the inertial force can affect the thin film profile, interfacial temperature, meniscus radius, heat flux distribution, velocity distribution, and mass flow rate, in particular, near the non-evaporating region, the effect can be neglected. It is found that a maximum velocity, a maximum heat flux, and a maximum curvature exist for a given superheat, but the locations for these maximum values are different.

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Abbreviations

A :

constant (J)

C T :

constant

dx :

differential length (m)

f :

friction factor, \({f = \frac{{4\tau_{w}}}{{\frac{1}{2}\rho_{l} u^{2}}}}\)

h lv :

latent heat of vaporization (J/kg)

k :

thermal conductivity (W/m K)

K :

curvature (m−1)

\({\dot{m}}\) :

mass flow rate (kg/s)

p :

pressure (N/m2)

P R :

reference pressure (N/ m)2

q :

heat transfer (W)

q′′:

heat flux (W/ m2)

Re :

Reynolds number, \({Re = \frac{{\rho_{l} u\delta}}{{\mu_{l}}}}\)

t :

time (s)

T :

temperature (K)

u :

velocity in the x-direction (m/s)

\({\bar{u}}\) :

mean velocity in the x-direction (m/s)

v :

velocity in the y-direction (m/s)

x :

coordinate (m)

y :

coordinate (m)

δ:

film thickness (m)

δ0 :

non-evaporating film thickness (m)

μ:

viscosity (N s/m2)

ρ:

density (kg/m3)

σ:

surface tension (N/m)

τ:

shear stress (N/ m2)

d :

disjoining

l :

liquid

lv :

liquid–vapor interface

n :

node value

v :

vapor

w :

wall

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Authors and Affiliations

  1. Department of Mechanical and Aerospace Engineering, University of Missouri, Columbia, Columbia, MO, 65211, USA

    H. B. Ma, P. Cheng & B. Borgmeyer

  2. Foxconn Thermal Technology, Austin, TX, 78753, USA

    Y. X. Wang

Authors
  1. H. B. Ma
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  2. P. Cheng
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  3. B. Borgmeyer
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  4. Y. X. Wang
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Corresponding author

Correspondence to H. B. Ma.

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Ma, H.B., Cheng, P., Borgmeyer, B. et al. Fluid flow and heat transfer in the evaporating thin film region. Microfluid Nanofluid 4, 237–243 (2008). https://doi.org/10.1007/s10404-007-0172-5

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  • DOI: https://doi.org/10.1007/s10404-007-0172-5

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