Research Papers

The Role of Entropy Generation in Momentum and Heat Transfer

[+] Author and Article Information
Heinz Herwig

Institute of Thermo-Fluid Dynamics,  Hamburg University of Technology, Hamburg, 21073 Germanyh.herwig@tuhh.de

J. Heat Transfer 134(3), 031003 (Jan 10, 2012) (11 pages) doi:10.1115/1.4005128 History: Received July 09, 2010; Revised November 08, 2010; Published January 10, 2012; Online January 10, 2012

Entropy generation in a velocity and temperature field is shown to be very significant in momentum and heat transfer problems. After the determination of this postprocessing quantity, many details about the physics of a problem are available. This second law analysis (SLA) is a tool for conceptual considerations, for the determination of losses, both in the velocity and the temperature field, and it helps to assess complex convective heat transfer processes. These three aspects in conjunction with entropy generation are discussed in detail and illustrated by several examples.

Copyright © 2012 by American Society of Mechanical Engineers
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Figure 1

Heat transfer at a system boundary (q·w=const)

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Figure 2

Quadratic shaped grooves as wall roughness in a pipe and the numerical solution domain

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Figure 3

Details of the numerical solution; pipe flow at Re = 145 (a) streamlines and (b) distribution of S·D‴. (Dark: weak, light: strong entropy generation)

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Figure 4

Poiseuille number for laminar flow in a pipe with rough walls

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Figure 5

Experimental setup for a radial channel flow with variable relative roughness k/H

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Figure 6

Pressure drop ratio versus increasing relative roughness for laminar flow in a radial channel with one rough wall

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Figure 7

Moody chart (full lines) and special results for a Loewenherz thread roughness (broken lines: second law analysis, symbols: experiment)

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Figure 8

Impact of the turbulent flow field on the temperature distribution between the hot and the cold wall in a channel. Q· and Twh are the same in both cases.

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Figure 9

Nusselt numbers according to the temperature wall gradients for channel flow with constant wall temperatures

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Figure 10

Occurrence of constant values S·C‴ in the turbulent flow field of a channel flow at ReDH  = 32,000; DNS results, see Ref. [41]

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Figure 11

Entropy generation rates S·irr'D, S·irr'C and overall entropy generation S·'irr in a smooth pipe with heat transfer; here: q·'w=2093W/m, m·=0.05kg/s (water); all values referred to S·'irr,o (at Reopt,s )

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Figure 12

Influence of wall roughness Ks  ≤ 0.5% on the entropy generation rates; extension of Fig. 1, now with Ks  ≥ 0; all values referred to S·'irr,o (at Reopt,s )

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Figure 13

Optimum Reynolds numbers

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Figure 14

Overall entropy generation as a function of the relative wall roughness Ks

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Figure 15

Influence of wall roughness Ks  ≤ 0.5% on the thermohydraulic performance parameter according to Eq. 26; ⊙: presumed optimum Re

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Figure 16

Overall entropy generation as a function of the relative wall roughness Ks for a fixed diameter Dopt,s and a diameter that is optimal for each Ks -value (Dopt,r ); all values referred to S·'irr,o (at Reopt,s ); minimum entropy generation approach




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