An effectiveness number of transfer units (ε–NTU) model is developed for use in evaporators where the evaporating stream: (1) comprises a volatile solvent and nonvolatile solute(s) and (2) undergoes a significant, but linear change in boiling point elevation (BPE) with increasing solute molality. The model is applicable to evaporators driven by an isothermal stream (e.g., steam-driven or refrigerant-driven) in parallel flow, counterflow, and crossflow configurations where the evaporating stream is mixed. The model is of use in a variety of process engineering applications as well as the sizing and rating of evaporators in high-salinity desalination systems.

References

1.
Standiford
,
F. C.
,
2000
, “
Evaporation
,”
Kirk–Othmer Encyclopedia of Chemical Technology
,
Wiley
,
New York.
2.
Glover
,
W. B.
,
2004
, “
Selecting Evaporators for Process Applications
,”
Chem. Eng. Prog.
,
100
(
12
), pp.
26
33
.
3.
Nusselt
,
W.
,
1916
, “
Die Oberflächenkondensation des Wasserdampfes
,”
Z. Ver. Dtsch. Ing.
,
60
(27), pp.
541
546
.
4.
Chen
,
M. M.
,
1961
, “
An Analytical Study of Laminar Film Condensation: Part 1—Flat Plates
,”
ASME J. Heat Transfer
,
83
(
1
), pp.
48
54
.
5.
Chun
,
K. R.
, and
Seban
,
R. A.
,
1971
, “
Heat Transfer to Evaporating Liquid Films
,”
ASME J. Heat Transfer
,
93
(
4
), pp.
391
396
.
6.
Brumfield
,
L. K.
, and
Theofanous
,
T. G.
,
1976
, “
On the Prediction of Heat Transfer Across Turbulent Liquid Films
,”
ASME J. Heat Transfer
,
98
(
3
), pp.
496
502
.
7.
Mudawwar
,
I. A.
, and
El-Masri
,
M. A.
,
1986
, “
Momentum and Heat Transfer Across Freely-Falling Turbulent Liquid Films
,”
Int. J. Multiphase Flow
,
12
(
5
), pp.
771
790
.
8.
Shmerler
,
J. A.
, and
Mudawwar
,
I.
,
1988
, “
Local Evaporative Heat Transfer Coefficient in Turbulent Free-Falling Liquid Films
,”
Int. J. Heat Mass Transfer
,
31
(
4
), pp.
731
742
.
9.
Marsh
,
W. J.
, and
Mudawar
,
I.
,
1989
, “
Predicting the Onset of Nucleate Boiling in Wavy Free-Falling Turbulent Liquid Films
,”
Int. J. Heat Mass Transfer
,
32
(
2
), pp.
361
378
.
10.
Parken
,
W. H.
,
Fletcher
,
L. S.
,
Sernas
,
V.
, and
Han
,
J. C.
,
1990
, “
Heat Transfer Through Falling Film Evaporation and Boiling on Horizontal Tubes
,”
ASME J. Heat Transfer
,
112
(
3
), pp.
744
750
.
11.
Ueda
,
T.
,
Inoue
,
M.
, and
Nagatome
,
S.
,
1981
, “
Critical Heat Flux and Droplet Entrainment Rate in Boiling of Falling Liquid Films
,”
Int. J. Heat Mass Transfer
,
24
(
7
), pp.
1257
1266
.
12.
Fletcher
,
L. S.
,
Sernas
,
V.
, and
Galowin
,
L. S.
,
1974
, “
Evaporation From Thin Water Films on Horizontal Tubes
,”
Ind. Eng. Chem. Process Des. Dev.
,
13
(
3
), pp.
265
269
.
13.
Yung
,
D.
,
Lorenz
,
J. J.
, and
Ganic
,
E. N.
,
1980
, “
Vapor/Liquid Interaction and Entrainment in Falling Film Evaporators
,”
ASME J. Heat Transfer
,
102
(
1
), pp.
20
25
.
14.
Chyu
,
M. C.
, and
Bergles
,
A. E.
,
1987
, “
An Analytical and Experimental Study of Falling-Film Evaporation on a Horizontal Tube
,”
ASME J. Heat Transfer
,
109
(
4
), pp.
983
990
.
15.
Kocamustafaogullari
,
G.
, and
Chen
,
I. Y.
,
1988
, “
Falling Film Heat Transfer Analysis on a Bank of Horizontal Tube Evaporator
,”
AIChE J.
,
34
(
9
), pp.
1539
1549
.
16.
Han
,
J.-C.
, and
Fletcher
,
L. S.
,
1985
, “
Falling Film Evaporation and Boiling in Circumferential and Axial Grooves on Horizontal Tubes
,”
Ind. Eng. Chem. Process Des. Dev.
,
24
(
3
), pp.
570
575
.
17.
Roques
,
J. F.
,
Dupont
,
V.
, and
Thome
,
J. R.
,
2002
, “
Falling Film Transitions on Plain and Enhanced Tubes
,”
ASME J. Heat Transfer
,
124
(
3
), pp.
491
499
.
18.
Li
,
W.
,
Wu
,
X.-Y.
,
Luo
,
Z.
, and
Webb
,
R. L.
,
2011
, “
Falling Water Film Evaporation on Newly-Designed Enhanced Tube Bundles
,”
Int. J. Heat Mass Transfer
,
54
(
13–14
), pp.
2990
2997
.
19.
Rose
,
J. W.
,
1998
, “
Condensation Heat Transfer Fundamentals
,”
Chem. Eng. Res. Des.
,
76
(
2
), pp.
143
152
.
20.
Thome
,
J. R.
,
1999
, “
Falling Film Evaporation: State-of-the-Art Review of Recent Work
,”
J. Enhanced Heat Transfer
,
6
(2–4), pp.
263
278
.
21.
Ribatski
,
G.
, and
Jacobi
,
A. M.
,
2005
, “
Falling-Film Evaporation on Horizontal Tubes—A Critical Review
,”
Int. J. Refrig.
,
28
(
5
), pp.
635
653
.
22.
Mistry
,
K.
,
Antar
,
M. A.
, and
Lienhard
,
V. J. H.
,
2013
, “
An Improved Model for Multiple Effect Distillation
,”
Desalin. Water Treat.
,
51
(
4–6
), pp.
807
821
.
23.
Thiel
,
G. P.
,
Tow
,
E. W.
,
Banchik
,
L. D.
,
Chung
,
H.
, and
Lienhard
,
J. H.
, V
,
2015
, “
Energy Consumption in Desalinating Produced Water From Shale Oil and Gas Extraction
,”
Desalination
,
366
, pp.
94
112
.
24.
Kays
,
W. M.
, and
London
,
A. L.
,
1998
,
Compact Heat Exchangers
, 3rd ed.,
Krieger
,
Malabar, FL
.
25.
Mills
,
A. F.
,
1998
,
Heat Transfer
, 2nd ed.,
Prentice-Hall
,
Englewood Cliffs, NJ.
26.
Lienhard
,
J. H.
, IV
, and
Lienhard
,
J. H.
, V
,
2011
,
A Heat Transfer Textbook
, 4th ed.,
Phlogiston Press
,
Cambridge, MA
.
27.
Chun
,
K. R.
, and
Seban
,
R. A.
,
1972
, “
Performance Prediction of Falling-Film Evaporators
,”
ASME J. Heat Transfer
,
94
(
4
), pp.
432
436
.
28.
Fletcher
,
L. S.
,
Sernas
,
V.
, and
Parken
,
W. H.
,
1975
, “
Evaporation Heat Transfer Coefficients for Thin Sea Water Films on Horizontal Tubes
,”
Ind. Eng. Chem. Process Des. Dev.
,
14
(
4
), pp.
411
416
.
29.
Glasstone
,
S.
,
1947
,
Thermodynamics for Chemists
, D. Van Nostrand,
New York
.
30.
Saxton
,
B.
,
Austin
,
J. B.
,
Dietrich
,
H. G.
,
Fenwick
,
F.
,
Fleischer
,
A.
,
Frear
,
G. L.
,
Roberts
,
E. J.
,
Smith
,
R. P.
,
Solomon
,
M.
, and
Spurlin
,
H. M.
,
1928
, “
Boiling-Point Elevations, Non-Volatile Solutes
,”
International Critical Tables of Numerical Data, Physics, Chemistry and Technology
, Vol.
III
,
E. W.
Washburn
, ed.,
McGraw-Hill
,
New York
, pp.
324
350
.
31.
Scatchard
,
G.
,
Hamer
,
W. J.
, and
Wood
,
S. E.
,
1938
, “
Isotonic Solutions—I: The Chemical Potential of Water in Aqueous Solutions of Sodium Chloride, Potassium Chloride, Sulfuric Acid, Sucrose, Urea and Glycerol at 25 deg
,”
Isotonic Solutions
,
60
(
12
), pp.
3061
3070
.
32.
Brown
,
E. H.
, and
Whitt
,
C. D.
,
1952
, “
Vapor Pressure of Phosphoric Acids
,”
Ind. Eng. Chem.
,
44
(
3
), pp.
615
618
.
33.
Messikomer
,
E. E.
, and
Wood
,
R. H.
,
1975
, “
The Enthalpy of Dilution of Aqueous Sodium Chloride at 298.15 to 373.15 K, Measured With a Flow Calorimeter
,”
J. Chem. Thermodyn.
,
7
(
2
), pp.
119
130
.
You do not currently have access to this content.