In this paper, we briefly present the heat/momentum transfer analogies of Reynolds and the followers for turbulent flow. Next, we discuss differences between turbulent and laminar flow and turn to the Lévêque analogy for laminar flow. This enables heat transfer coefficients (Nusselt numbers) to be derived, based on the flow friction results that include only viscous friction. Some examples of Lévêque analogy applications, such as flow through packed beds, wire gauzes, short-channel structures (short monoliths), and structured catalyst carriers (tube inserts), are given. The Lévêque analogy gave satisfactory accuracy when compared to experiments with flow friction derived on the theoretical basis.

References

References
1.
Reynolds
,
O.
,
1874
, “
On the Extent and Action to the Heating Surface of Steam Boilers
,”
Proc. Lit. Philos. Soc. Manchester
,
14
, pp. 7–12.http://www.biodiversitylibrary.org/item/210078#page/12/mode/1up
2.
Prandtl
,
L.
,
1910
, “
Eine Beziehung Zwischen Warmeaustauch Und Stromungswiderstand Der Flussigkeiten
,”
Phys. Z.
,
11
, pp.
1072
1078
.
3.
Hagen
,
G.
,
1839
, “
Über Die Bewegung Des Wassers in Engen Zylindrischen Röhren
,”
Pogg. Ann.
,
46
(
3
), pp.
423
442
.
4.
Poiseuille
,
J.
,
1840
, “
Recherche Experimentelles Sur le Mouvement Des Liquides Dans Les Tubes de Tres Petits Diametres—I: Influence de la Pression Sur la Quantite de Iiquide Qui Traverse Les Tubes de Tres Petits Diametres
,”
Compte Rendue
,
11
, pp.
961
967
.
5.
Poiseuille
,
J.
,
1840
, “
Recherche Experimentelles Sur le Mouvement Des Liquides Dans Les Tubes de Tres Petits Diametres—II: Influence de la Longueur Sur la Quantite de Liquide Qui Traverse Les Tubes de Tres Petits Diametres; III: Influence du Diametre Sur la Quantite de Liquide Qui Traverse Les Tubes de Tres Petits Diametres
,”
Compte Rendue
,
11
, pp.
1041
1048
.
6.
Poiseuille
,
J.
,
1841
, “
Recherche Experimentelles Sur le Mouvement Des Liquides Dans Les Tubes de Tres Petits Diametres—IV: Influence de la Temperature Sur la Quantite de Liquide Qui Traverse Les Tubes de Tres Petits Diametres
,”
Compte Rendue
,
12
, pp.
112
115
.
7.
Graetz, L.
, 1882, "Ueber die Wärmeleitungsfähigkeit von Flüssigkeiten," Annalen der Physik, 254(1), pp. 79–94.
8.
Lévêque
,
A.
,
1928
, “
Les Lois de la Transmission de Chaleur Par Convection
,”
Ann. Mines
,
13
, pp. 201–415.
9.
Welty
,
J. R.
,
Wicks
,
C. E.
,
Rorrer
,
G.
, and
Wilson
,
R. E.
,
2001
,
Fundamentals of Momentum, Heat, and Mass Transfer
,
4th ed.
,
Wiley
,
New York
.
10.
Schlünder
,
E. U.
,
1970
, “
Die Wissenschaftliche Theorie Der Wärmeübertragung. Geschichtliche Entwicklung Und Heutiger Stand
,”
Chem. Ing. Tech.
,
42
(
14
), pp.
905
910
.
11.
Schlünder
,
E. U.
,
1998
, “
Analogy Between Heat and Momentum Transfer
,”
Chem. Eng. Process.
,
37
(
1
), pp.
103
107
.
12.
Martin
,
H.
,
2005
, “
The Lévêque-Analogy or How to Predict Heat and Mass Transfer From Fluid Friction
,”
Fourth International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics (HEFAT2005), Cairo
, Egypt, Sept. 19–22, Paper No. K2.
13.
Ergun
,
S.
,
1952
, “
Fluid Flow Through Packed Columns
,”
Chem. Eng. Prog.
,
48
, pp.
89
94
.https://www.industrydocumentslibrary.ucsf.edu/tobacco/docs/#id=nnhp0209
14.
Wakao
,
N.
, and
Kaguei
,
S.
,
1982
,
Heat and Mass Transfer in Packed Beds
,
Gordon and Breach Science Publisher
,
New York
.
15.
Kolodziej
,
A.
, and
Lojewska
,
J.
,
2009
, “
Mass Transfer for Woven and Knitted Wire Gauze Substrates: Experiments and Modelling
,”
Catal. Today
,
147
, pp.
S120
S124
.
16.
Kolodziej
,
A.
,
Lojewska
,
J.
,
Jaroszynski
,
M.
,
Gancarczyk
,
A.
, and
Jodlowski
,
P.
,
2012
, “
Heat Transfer and Flow Resistance for Stacked Wire Gauzes: Experiments and Modelling
,”
Int. J. Heat Fluid Flow
,
33
(
1
), pp.
101
108
.
17.
Iwaniszyn
,
M.
,
Ochonska
,
J.
,
Gancarczyk
,
A.
,
Jodlowski
,
P.
,
Knapik
,
A.
,
Lojewska
,
J.
,
Janowska-Renkas
,
E.
, and
Kolodziej
,
A.
,
2013
, “
Short-Channel Structured Reactor as a Catalytic Afterburner
,”
Top. Catal.
,
56
(
1–8
), pp.
273
278
.
18.
Iwaniszyn
,
M.
,
Piątek
,
M.
,
Gancarczyk
,
A.
,
Jodłowski
,
P. J.
,
Łojewska
,
J.
, and
Kołodziej
,
A.
,
2017
, “
Flow Resistance and Heat Transfer in Short Channels of Metallic Monoliths: Experiments Versus CFD
,”
Int. J. Heat Mass Transfer
,
109
, pp.
778
785
.
19.
Kolodziej
,
A.
,
Krajewski
,
W.
, and
Dubis
,
A.
,
2001
, “
Alternative Solution for Strongly Exothermal Catalytic Reactions: A New Metal-Structured Catalyst Carrier
,”
Catal. Today
,
69
(
1–4
), pp.
115
120
.
20.
Hawthorne
,
R. D.
,
1974
, “
Afterburner Catalysis—Effects of Heat and Mass Transfer Between Gas and Catalyst Surface
,”
AlChE Symp. Ser.
,
70
(137), pp.
428
438
.
21.
Shah
,
R. K.
, and
London
,
A. L.
,
1978
,
Laminar Flow Forced Convection in Ducts: A Source Book for Compact Heat Exchanger Analytical Data
,
Academic Press
,
New York
.
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