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Mixture Boiling

Reference work entry

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.

Nomenclature

a

surface area (m2)

Ac

cross-sectional flow area inside tube (m2)

An

coefficients given in Eq. (26)

Ai

actual inner surface area of tube (m2)

As

heat transfer surface area (m)

b

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

Bn

coefficients given in Eq. (26)

Bo

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

cp

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)

De

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

Dh

hydraulic diameter of microfin tube (m)

Dnp

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)

hfg

latent heat of vaporization (kJ·kg−1)

hi

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

hm

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

h2 ϕ

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

im

mass transfer coefficient (m·s−1)

k

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

K

mixture correction factor Eq. (15)

le

thickness of excess layer (m)

la

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)

Mw

molecular weight (g·mole−1)

na

bubble site density (s−1)

Nu

local Nusselt number based on Dh

Nf

number of fins

Nnp

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)

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

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

rc

critical site radius for bubble nucleation (m)

rb

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)

Sp

perimeter of one fin and channel (m)

tb

thickness of the fin at its base (m)

tw

thickness of the tube wall (m)

T

temperature (K)

Tb

bubble point temperature of mixture (K)

Tc

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

Td

dew point temperature of mixture (K)

Te

temperature at excess layer/bulk fluid interface (K)

Tib

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

Tit

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

Tw

temperature at roughened surface (K)

w

bulk lubricant mass fraction

x

mass fraction

xi

mass fraction or mole fraction of ith component

xm

mole fraction

xq

thermodynamic mass quality

z

axial distance (m)

Greek Symbols

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: TwTs (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

χtt

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

Ψ

sphericity

Subscripts

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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Copyright information

© This is a U.S. Government work and not under copyright protection in the US; foreign copyright protection may apply 2018

Authors and Affiliations

  1. 1.National Institute of Standards and TechnologyGaithersburgUSA

Section editors and affiliations

  • Vijay K. Dhir
    • 1
  1. 1.Mechanical and Aerospace EngineeringUniversity of California Los AngelesLos AngelesUSA

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