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G6 Heat Transfer in Cross-flow Around Single Tubes, Wires, and Profiled Cylinders

Abstract

According to Krischer and Kast [1] the equations for determining the average Nusselt number in cross-flow over tubes, wires, and profiled cylinders are the same as those over a flat plate ( Chap. G4 ) if the characteristic length used in the calculation of the Reynolds and Nusselt numbers is the “streamed length.” This streamed length is the length of the entire path traversed by a particle in flowing over the surface presented to it by the body concerned. It is defined by Pasternak and Gauvin [2] as the total surface area A of the body divided by the maximum perimeter l c perpendicular to the flow: (1) $$ l = {A \over {l_{\rm{c}} }} $$ The streamed length is shown in Fig. 1. For a long tube of the diameter d and the length L according to Eq. (1), we get (2) $$ l = {{\pi {\kern 1pt} d{\kern 1pt}L} \over {2L{\kern 1pt} }} = {{\rm{\pi }} \over {\rm{2}}}d $$ The equation suggested by Gnielinski [3] for the average Nusselt number in cross-flow over tubes, wires, and profiled cylinders arranged as in standard engineering practice is (3) $$ {\rm{Nu}}_{l,0} = 0.3 + \sqrt {{\rm{Nu}}^2 _{l,{\rm{lam}}} + {\rm Nu}^2 _{l,{\rm{turb}}} } $$ where (4) $$ {\rm{Nu}}_{l,{\rm{lam}}} = 0.664\sqrt {{\mathop{\rm Re}\nolimits} _l } {\kern 1pt} \,\root 3 \of {\Pr } $$ and (5) $$ {\rm{Nu}}_{l,{\rm{turb}}} = {{0.037\,{\kern 1pt} {\mathop{\rm Re}\nolimits} ^{0.8} \Pr } \over {1 + 2.443{\mathop{\rm Re}\nolimits} _l ^{ - 0.1} (\Pr ^{2/3} - 1)}} $$ The minimum value of Nu l,0 in Eq. (3) results from the fact that, in practice, the length of a cylinder in cross-flow is always finite. Consequently, if the surrounding is at rest, the heat flux attains a minimum. The average Nusselt number for a cylinder thus asymptotically approaches a minimum, which is assumed to be $$ {\rm{Nu}}_{\min } \approx 0.3 $$ [3].

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Title
G6 Heat Transfer in Cross-flow Around Single Tubes, Wires, and Profiled Cylinders
Book Title
VDI Heat Atlas
Book DOI
10.1007/978-3-540-77877-6
Chapter DOI
10.1007/978-3-540-77877-6_39
Part of
VDI-Buch
Volume
Editors
Authors
  • Volker Gnielinski Send Email (1_39)
  • Author Affiliation
  • 1_39 Karlsruher Institut für Technologie (KIT), Karlsruhe, Germany
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