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.

Issue Section:
Technical Brief
Keywords:
heat-momentum transfer analogy, Lévêque analogy, viscous friction
Topics:
Catalysts, Flow (Dynamics), Friction, Heat, Laminar flow, Momentum, Wire

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
.
Google Scholar
Crossref
Search ADS
 
11.
Schlünder
,
E. U.
,
1998
, “
Analogy Between Heat and Momentum Transfer
,”
Chem. Eng. Process.
,
37
(
1
), pp.
103
–
107
.
Google Scholar
Crossref
Search ADS
 
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
.
Google Scholar
Crossref
Search ADS
 
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
.
Google Scholar
Crossref
Search ADS
 
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
.
Google Scholar
Crossref
Search ADS
 
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
.
Google Scholar
Crossref
Search ADS
 
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
.
Google Scholar
Crossref
Search ADS
 
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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