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Wärme - und Stoffübertragung

, Volume 26, Issue 3, pp 129–135 | Cite as

Heat transfer in an inner loop reactor

  • S. W. Tsai
Article
  • 48 Downloads

Abstract

General expressions for evaluating heat transfer in reactors with a draft tube have been derived. Theoretical results show that heat transfer can be enhanced for flow pattern (A) compared with that in an open duct whenK1 is not departed from 0.5. The competition of the residence time and the volumetric flow rate of the fluids in the annulus and in the draft tube may be used to explain the fluid behaviors. For flow patterns (B) and (C) as in a loop reactor, introduce of recycling can augment the heat transfer rate for large Graetz number, especially whenK1,K2 orR increases. The competition between the premixing and the residence time effects of the fluid may be used to describe the fluid behaviors. Moreover, asymptotic solutions for all flow patterns were also derived.

Keywords

Heat Transfer Flow Pattern Transfer Rate Apply Physic Time Effect 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Nomenclature

D

hydraulic diameter defined as four times of the ratio of the cross section area to the wetted perimeter

Gz

Graetz number defined asRe Pr D/L

H

total head loss due to friction for each flow pattern

H0

total head loss due to friction for the open duct, Eq. (3)

hm

logarithmic average heat transfer coefficient

K1

ratio of the outer radius of the draft tube to the inner radius of the open duct, Fig. 1

K2

ratio of the inner radius of the draft tube to that of the open duct, Fig. 1

k

thermal conductivity

L

total length of the duct

M

ratio of heat transfer rate for each flow pattern to that of an open duct, Eq. (30)

Num

logarithmic average Nusselt number for each flow pattern,h m D/k

Num,0

logarithmic average Nusselt number for the open duct

Pr

Prandtl number,ν/k

R

recycled ratio defined as the ratio of the recycled volumetric flow rate to the volumetric flow rate of feed stream

Re

Reynolds number,v D/ν

r

inner radius of an open duct

S

ratio of the total head loss due to friction to that of an open duct, Eq.(31)

Tw

wall temperature

T0

temperature of feed stream

T1

bulk temperature of the fluid at top of the annulus

T2

bulk temperature of the fluid at top of the draft tube

T3

temperature of outlet stream

T4

bulk temperature of the fluid at bottom of the draft tube

T5

bulk temperature of the fluid at bottom of the annulus

t

mean residence time of the fluid in an open duct

V

volumetric flow rate of feed stream

V1

volumetric flow rate of the fluid in the annulus

V2

volumetric flow rate of the fluid in the draft tube

v

bulk velocity of the fluid in an open duct

v1

bulk velocity of the fluid in the annulus

v2

bulk velocity of the fluid in the draft tube

α

thermal diffusivity

ΔP

Pressure drop between top and bottom of the duct

ξ

parameter defined in Eq. (9)

ϑ1

dimensionless temperature, Eq. (6)

ϑ2

dimensionless temperature, Eq. (7)

ϑ3

dimensionless temperature, Eq. (8)

λ0

the first eigenvalue in the annulus

ν

kinematic viscosity

Subscripts

a

for the asymptotic solution

1

for the annulus

2

for the draft tube

Wärmeübertragung im Innern eines Loop-Reaktors

Zusammenfassung

Hier werden allgemeine Ausdrücke für die Auswertung der Wärmeübertragung in Reaktoren mit einer Luftströmungsröhre beschrieben. Die theoretischen Ergebnisse zeigen, daß sich die Wärmeübertragung des Strömungsbildes (A) erhöhen kann, wennK1 nicht von 0.5 abweicht und wenn man es mit einem offenen Rohr vergleicht. Der Vergleich zwischen Verweilzeit und Volumendurchfluß der Fluide im Ringraum und in der Luftströmungsröhre kann für die Erklärung des Fluidverhaltens benützt werden. Für die Strömungsbilder (B) und (C) in einem Loop-Reaktor, unter Berücksichtigung der Rücklaufströmung, kann die Wärmeübertragungsrate für große Graetzzahlen gesteigert werden. Dies gilt besonders wennK1,K2 undR ansteigen. Der Vergleich zwischen Vormixung und Verweilzeiteinwirkung des Fluids kann möglicherweise zur Beschreibung des Fluidverhaltens genutzt werden. Zu dem sind asymptotische Lösungen für alle Strömungsbilder abgeleitet worden.

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Copyright information

© Springer-Verlag 1991

Authors and Affiliations

  • S. W. Tsai
    • 1
  1. 1.Department of Chemical EngineeringNational Cheng Kung University TainanTaiwan-R.O.C.

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