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An Experimental Investigation of the Reynolds Analogy and its Modifications Applied to Annular Condensation Laminar Flow of R134a in a Vertical Tube

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Abstract

The Reynolds analogy and its modifications are applied to forced convection laminar in-tube condensation to predict the heat transfer coefficient of R134a by means of well-known two-phase friction factors and agreed void fraction models and correlations explained in the authors’ previous works. The vertical test section is a 0.5 m long countercurrent flow double tube heat exchanger with refrigerant flowing in the inner smooth copper tube (8.1 mm i.d.) and cooling water flowing in the annulus (26 mm i.d.). The test runs are performed at average saturated condensing temperatures of 40 °C (Pr = 0.92) and 50 °C (Pr = 0.97). The heat fluxes are between 10.16 and 66.61 kW m−2 while the mass fluxes are between 260 and 515 kg m−2 s−1 for the vertical test sections. The Reynolds’ model is modified by various two-phase flow models and correlations to account for the partial condensation inside the tube. The refrigerant side heat transfer coefficients are determined within ±30% using the two-phase friction factors of Wallis, Moeck, Fore et al., while all the proposed friction factor correlations for the Reynolds analogy, Prandtl and Taylor analogy, and Colburn analogy predict the experimental friction factor within a ±20% deviation band. The importance of altering the Prandtl number to the Reynolds analogy (Pr = 1) is also shown in the paper.

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Abbreviations

A:

Inside surface area, m−2

C p :

Specific heat, J kg−1 K−1

d :

Internal tube diameter, m

f :

Friction factor

G :

Mass flux, kg m−2 s−1

h :

Heat transfer coefficient, W m−2 K−1

i :

Enthalpy, J kg−1

i fg :

Latent heat of condensation, J kg−1

L :

Length of test tube, m

k :

Thermal conductivity, W m−1 K−1

m :

Mass flow rate, kg s−1

P :

Pressure, MPa

Pr :

Prandtl number

r :

Internal tube radius, m

Re :

Reynolds number

S :

Slip ratio

T :

Temperature, °C

u :

Velocity, m s−1

Q :

Heat transfer rate, W

q :

Mean heat flux, kW m−2

x :

Mean vapor quality

y :

Wall coordinate

ΔP :

Pressure drop, Pa

ΔT :

Vapor side temperature difference, T sat−T wi, K

\({\varepsilon_{\rm c}}\) :

Conductive diffusivity/viscosity, m2 s−1

\({\varepsilon_{\rm m}}\) :

Eddy momentum diffusivity/viscosity, m2 s−1

\({\varepsilon_{\rm q}}\) :

Eddy heat diffusivity/viscosity, m2 s−1

ρ :

Density, kg m−3

μ :

Dynamic viscosity, kg m−1 s−1

δ :

Film thickness, m

δ + :

Dimensionless film thickness

α :

Void fraction

τ :

Shear stress, N m−2

ν :

Kinematic viscosity, m2 s−1

corr:

Correlation

exp:

Measured

f:

Fluid

g:

Gas/vapor

H:

Homogeneous

i:

Inlet

l:

Liquid

o:

Outlet

ph:

Preheater

ref:

Refrigerant

sat:

Saturation

SG:

Superficial

TS:

Test section

w:

Water

wi:

Inner wall

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Author information

Authors and Affiliations

  1. Heat and Thermodynamics Division, Department of Mechanical Engineering, Yildiz Technical University (YTU), Yildiz, Besiktas, Istanbul, 34349, Turkey

    A. S. Dalkilic

  2. Department of Mechanical Engineering, Jadavpur University, Kolkata, 700032, India

    B. Kundu

  3. Fluid Mechanics, Thermal Engineering and Multiphase Flow Research Lab. (FUTURE), Department of Mechanical Engineering, Faculty of Engineering, King Mongkut’s University of Technology Thonburi, Bangmod, Bangkok, 10140, Thailand

    S. Wongwises

  4. Academy of Science, The Royal Institute of Thailand, SanamSuea Pa, Dusit, Bangkok, 10300, Thailand

    S. Wongwises

Authors
  1. A. S. Dalkilic
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  3. S. Wongwises
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Correspondence to A. S. Dalkilic.

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Dalkilic, A.S., Kundu, B. & Wongwises, S. An Experimental Investigation of the Reynolds Analogy and its Modifications Applied to Annular Condensation Laminar Flow of R134a in a Vertical Tube. Arab J Sci Eng 38, 1493–1507 (2013). https://doi.org/10.1007/s13369-013-0595-0

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