0
Technical Brief

Heat and Momentum Transfer Analogies in Laminar Flow

[+] Author and Article Information
Anna Gancarczyk

Institute of Chemical Engineering,
Polish Academy of Sciences,
Bałtycka 5, Gliwice 44-100, Poland
e-mail: anna.g@iich.gliwice.pl

Marzena Iwaniszyn

Institute of Chemical Engineering,
Polish Academy of Sciences,
Bałtycka 5, Gliwice 44-100, Poland
e-mail: miwaniszyn@iich.gliwice.pl

Przemysław J. Jodłowski

Faculty of Chemical Engineering and Technology,
Cracow University of Technology,
Warszawska 24,
Kraków 31-155, Poland
e-mail: pjodlowski@pk.edu.pl

Marcin Piątek

Institute of Chemical Engineering,
Polish Academy of Sciences,
Bałtycka 5,
Gliwice 44-100, Poland
e-mail: mpiatek@iich.gliwice.pl

Mateusz Korpyś

Institute of Chemical Engineering,
Polish Academy of Sciences,
Bałtycka 5,
Gliwice 44-100, Poland
e-mail: matkor@iich.gliwice.pl

Katarzyna Sindera

Institute of Chemical Engineering,
Polish Academy of Sciences,
Bałtycka 5,
Gliwice 44-100, Poland
e-mail: katarzyna.sindera@iich.gliwice.pl

Andrzej Kołodziej

Institute of Chemical Engineering,
Polish Academy of Sciences,
Bałtycka 5,
Gliwice 44-100, Poland;
Faculty of Civil Engineering and Architecture,
Opole University of Technology,
Katowicka 48,
Opole 45-061, Poland
e-mail: ask@iich.gliwice.pl

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received February 13, 2018; final manuscript received September 25, 2018; published online November 22, 2018. Assoc. Editor: Sara Rainieri.

J. Heat Transfer 141(2), 024502 (Nov 22, 2018) (5 pages) Paper No: HT-18-1086; doi: 10.1115/1.4041799 History: Received February 13, 2018; Revised September 25, 2018

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.

FIGURES IN THIS ARTICLE
<>
Copyright © 2019 by ASME
Your Session has timed out. Please sign back in to continue.

References

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
Prandtl, L. , 1910, “ Eine Beziehung Zwischen Warmeaustauch Und Stromungswiderstand Der Flussigkeiten,” Phys. Z., 11, pp. 1072–1078.
Hagen, G. , 1839, “ Über Die Bewegung Des Wassers in Engen Zylindrischen Röhren,” Pogg. Ann., 46(3), pp. 423–442.
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.
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.
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.
Graetz, L. , 1882, "Ueber die Wärmeleitungsfähigkeit von Flüssigkeiten," Annalen der Physik, 254(1), pp. 79–94.
Lévêque, A. , 1928, “ Les Lois de la Transmission de Chaleur Par Convection,” Ann. Mines, 13, pp. 201–415.
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.
Schlünder, E. U. , 1970, “ Die Wissenschaftliche Theorie Der Wärmeübertragung. Geschichtliche Entwicklung Und Heutiger Stand,” Chem. Ing. Tech., 42(14), pp. 905–910. [CrossRef]
Schlünder, E. U. , 1998, “ Analogy Between Heat and Momentum Transfer,” Chem. Eng. Process., 37(1), pp. 103–107. [CrossRef]
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.
Ergun, S. , 1952, “ Fluid Flow Through Packed Columns,” Chem. Eng. Prog., 48, pp. 89–94. https://www.industrydocumentslibrary.ucsf.edu/tobacco/docs/#id=nnhp0209
Wakao, N. , and Kaguei, S. , 1982, Heat and Mass Transfer in Packed Beds, Gordon and Breach Science Publisher, New York.
Kolodziej, A. , and Lojewska, J. , 2009, “ Mass Transfer for Woven and Knitted Wire Gauze Substrates: Experiments and Modelling,” Catal. Today, 147, pp. S120–S124. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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.
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.

Figures

Grahic Jump Location
Fig. 1

Flow through packed bed of spherical grains: Nusselt number calculated using Wakao and Kaguei [14], Eq. (10), and due to the Lévêque analogy (Eq. (7)) with the Fanning friction factor calculated by the Ergun [13] (Eq. (9)).

Grahic Jump Location
Fig. 2

Structures studied: (a) knitted wire gauze, (b) triangular, (c) sinusoidal short-channel structure, and (d) structured carrier No. 7B

Grahic Jump Location
Fig. 3

Comparison of experimentally derived Nusselt numbers with those calculated using the Lévêque analogy (Eq. (7)), for the structures considered: (a) knitted wire gauze, (b) triangular (L = 5mm), (c) sinusoidal (L = 10 mm), and (d) triangular (L = 15mm). The Fanning friction factor is calculated from Eq. (11).

Grahic Jump Location
Fig. 4

Comparison of experimentally derived Nusselt numbers with those calculated using the Lévêque analogy (Eq. (7)) for the structured catalyst carrier (a) No. 6 and (b) No. 7B. The Fanning friction factor is calculated from Eq. (11).

Tables

Errata

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In