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Handbook of Thermal Science and Engineering pp 1795–1821Cite as

Mixture Boiling

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Abstract

This chapter provides the engineer and the researcher with correlations and models for the prediction of the critical aspects of the boiling heat transfer of mixtures. This chapter offers a reliable, hands-on resource for solving common problems across pool boiling and flow boiling applications such as miscible mixtures, refrigerant/lubricant mixtures, additives, and refrigerant/nanolubricants. Fundamental heat transfer and thermodynamic principles are succinctly provided to accompany the correlations and models. This chapter was written with the busy engineer in mind by providing simple but accurate prediction methods, and guidance where neither correlations nor models exist.

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Abbreviations

a :

surface area (m2)

A c :

cross-sectional flow area inside tube (m2)

A n :

coefficients given in Eq. (26)

A i :

actual inner surface area of tube (m2)

A s :

heat transfer surface area (m)

b :

fourth-degree polynomial in wl, Eq. (27)

B n :

coefficients given in Eq. (26)

Bo:

local boiling number, \( \frac{q^{{\prime\prime} }}{G_r{i}_{fg}} \)

c p :

specific heat (J·kg−1·K−1)

c :

fourth-degree polynomial in wl, Eq. (27) (K)

C :

coefficients given in Eqs. (16) and (32)

D :

tube diameter (m)

D e :

equivalent inner diameter of smooth tube, \( \sqrt{\frac{4{A}_{\mathrm{c}}}{\uppi}} \) (m)

D h :

hydraulic diameter of microfin tube (m)

D np :

nanoparticle diameter (m)

e :

fin height (m)

E :

Reynolds number enhancement factor given in Eq. (13)

F :

exponential constant in Eq. (1)

g :

gravitational acceleration (m·s−2)

G :

total mass velocity (kg·m−2·s−1)

h fg :

latent heat of vaporization (kJ·kg−1)

h i :

ideal mixture heat transfer coefficient (W·m−2 K−1)

h m :

heat transfer coefficient of refrigerant/lubricant mixture (W·m−2 K−1)

h 2 ϕ :

local two-phase heat-transfer coefficient (W·m−2 K−1)

i m :

mass transfer coefficient (m·s−1)

k :

refrigerant thermal conductivity (W·m−2 K−1)

K :

mixture correction factor Eq. (15)

l e :

thickness of excess layer (m)

l a :

thickness of adiabatic/Van der Waals excess layer (m)

L :

tube length (m)

m :

fitting constant in Eq. (32)

\( \dot{m} \) :

mass flow rate (kg·s−1)

M w :

molecular weight (g·mole−1)

n a :

bubble site density (s−1)

Nu:

local Nusselt number based on Dh

N f :

number of fins

N np :

the number of nanoparticles

Nnp/As:

nanoparticle surface density (m−2)

p :

wetted perimeter (m)

P :

local fluid pressure (Pa)

Pr:

liquid refrigerant Prandtl number \( {\left.\frac{c_p\mu }{k}\right|}_{r,l} \)

q :

heat duty (W)

q″ :

local heat flux (W·m−2)

\( {q}_n^{{\prime\prime} } \) :

\( =\frac{q_{\mathrm{PL}}^{{\prime\prime} }}{1\mathrm{W}\cdot {\mathrm{m}}^{-2}} \)

r c :

critical site radius for bubble nucleation (m)

r b :

bubble departure radius (m)

Re:

all-liquid, refrigerant Reynolds number based on Dh = \( \frac{G_r{D}_h}{\mu_{r,l}} \)

s :

spacing between the fins (m)

S :

suppression factor given in Eq. (14)

S p :

perimeter of one fin and channel (m)

t b :

thickness of the fin at its base (m)

t w :

thickness of the tube wall (m)

T :

temperature (K)

T b :

bubble point temperature of mixture (K)

T c :

refrigerant/lubricant critical solution temperature (lower limit) (K)

T d :

dew point temperature of mixture (K)

T e :

temperature at excess layer/bulk fluid interface (K)

T ib :

temperature of the liquid–vapor interface at bottom of tube (K)

T it :

temperature of the liquid–vapor interface at top of tube (K)

T w :

temperature at roughened surface (K)

w :

bulk lubricant mass fraction

x :

mass fraction

x i :

mass fraction or mole fraction of ith component

x m :

mole fraction

x q :

thermodynamic mass quality

z :

axial distance (m)

α:

helix angle between microfin and tube axis

β:

fin-tip angle, radians

γ :

surface free energy (kg·s−2)

Γ :

excess surface density (kg·m−2)

ΔTs:

wall superheat: Tw − Ts (K)

ΔTle:

temperature drop across excess layer (K)

ζ :

fraction of excess layer removed per bubble

θ :

dimensionless thermal boundary layer temperature profile

Θ :

bubble contact angle, rad

λ :

thermal boundary constant

μ :

dynamic viscosity (kg·m−1·s−1)

ν :

kinematic viscosity (m2·s−1)

ρ :

mass density of liquid (kg·m)−3

σ :

liquid–vapor surface tension (kg·s−2)

ρ :

density (kg·m−3)

ϕ :

nanoparticle volume fraction

χ tt :

Lockhart–Martinelli parameter ((1 − xq)/xq)0.9(ρv/ρl)0.5(μl/μv)0.1

Ψ :

sphericity

1:

system 1

2:

system 2

A :

additive

b :

bulk condition, fin base

c :

critical condition

f :

water

G :

surface geometry dependent

i :

inner

l :

liquid, local

L :

pure lubricant without nanoparticles

LV:

least volatile component

m :

mixture

mb:

mixture boiling

MV:

more volatile component

nL:

nanolubricant

np:

refrigerant/nanolubricant

p :

plain or smooth tube, predicted

pL:

refrigerant/nanolubricant

r :

refrigerant

s :

saturated state

v :

vapor

w :

heat transfer surface

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Authors and Affiliations

  1. National Institute of Standards and Technology, Gaithersburg, MD, USA

    Mark A. Kedzierski

Authors
  1. Mark A. Kedzierski
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Corresponding author

Correspondence to Mark A. Kedzierski .

Section Editor information

  1. Armour College of Engineering, Department of Mechanical, Materials and Aerospace Engineering, Illinois Institute of Technology, Chicago, Illinois, USA

    Sumanta Acharya

  2. Gas Technology Institute, Des Plaines, Illinois, USA

    Yaroslav Chudnovsky

  3. Universidade Federal do Rio de Janeiro - UFRJ, Rio de Janeiro, Rio de Janeiro, Brazil

    Renato Machado Cotta

  4. Department of Mechanical Engineering, Louisiana State University, Baton Rouge, Louisiana, USA

    Ram Devireddy

  5. Mechanical and Aerospace Engineering, University of California Los Angeles, Los Angeles, California, USA

    Vijay K. Dhir

  6. Cekmeköy Campus, Özyegin University, Çekmeköy - Istanbul, Turkey

    M. Pinar Mengüç

  7. Department of Mechanical and Industrial Engineering, Faculty of Applied Science + Engineering, University of Toronto, Centre for Advanced Coating Technologies, Toronto, Ontario, Canada

    Javad Mostaghimi

  8. Department of Mechanical Engineering, University of California, Riverside, California, USA

    Kambiz Vafai

  9. Mechanical and Aerospace Engineering, University of California Los Angeles, Los Angeles, California, USA

    Vijay K. Dhir

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Kedzierski, M.A. (2018). Mixture Boiling. In: Handbook of Thermal Science and Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-26695-4_44

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