Technical Brief

On the Nusselt Number for H2 Heat Transfer in Rectangular Ducts of Large Aspect Ratios

[+] Author and Article Information
C. Y. Wang

Departments of Mathematics and Mechanical Engineering,
Michigan State University,
East Lansing, MI 48824
e-mail: cywang@mth.msu.edu

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received April 22, 2013; final manuscript received November 15, 2013; published online April 8, 2014. Assoc. Editor: Sujoy Kumar Saha.

J. Heat Transfer 136(7), 074501 (Apr 08, 2014) (4 pages) Paper No: HT-13-1209; doi: 10.1115/1.4026091 History: Received April 22, 2013; Revised November 15, 2013

The H1 and H2 forced convection heat transfer in rectangular ducts are studied using an accurate, analytic method. It is confirmed that, as the aspect ratio tends to infinity, the Nusselt number for the H2 case approaches 2.9162, much lower than the parallel plate value of 8.2353 attained by the H1 case. The controversy about the H2 limit is thus settled. An explanation of the behavior is suggested.

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Grahic Jump Location
Fig. 1

Cross section of the rectangular duct

Grahic Jump Location
Fig. 2

(a) Constant velocity lines, b = 5. From inside: w = 0.499, 0.4, 0.3, 0.2, 0.1, 0. (b) Constant temperature lines for H1 heat transfer, b = 5. From inside: τ = −0.2, −0.15, −0.1, −0.05, 0. (c) Constant temperature lines for H2 heat transfer, b = 5. From inside: τ = −0.6, −0.4, −0.2, 0, 0.2, 0.4.

Grahic Jump Location
Fig. 3

The H2 Nusselt number as function of aspect ratio b. C, S are defined in Eqs. ((31) and (15)). Dashed line is the limit Nu = 2.9162.



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