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Technical Brief

Mixed H1 and H2 Forced Convection in a Rectangular Duct

[+] 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 July 27, 2016; final manuscript received July 28, 2017; published online October 17, 2017. Assoc. Editor: Antonio Barletta.

J. Heat Transfer 140(3), 034502 (Oct 17, 2017) (4 pages) Paper No: HT-16-1477; doi: 10.1115/1.4038001 History: Received July 27, 2016; Revised July 28, 2017

The constant flux forced convection in a rectangular duct with two highly conductive (H1) walls and two poorly conductive (H2) walls is studied for the first time. This mixed problem is solved analytically using a modified single series method. The Nusselt number is determined for various duct aspect ratios. Depending on the aspect ratio, hot spots and cold spots may occur either on the H1 walls or on the H2 walls.

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Figures

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Fig. 1

Cross section of the duct. Top and bottom are heated by H1 flux, while the sides are heated by H2 flux.

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Fig. 2

Comparison of Nusselt numbers. Top curve: H1 flux on all walls, middle curve: the present mixed H1 and H2 heating, and bottom curve: H2 flux on all walls.

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Fig. 3

Nusselt numbers for each individual wall as defined by Eq. (23)

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Fig. 4

Typical isotherms. Temperatures are lower at the center. Top: b = 5, lower left: b = 1, and lower right: b = 0.1.

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Fig. 5

Temperature deviations τc at the center, τ0 at the top and bottom walls, maximum temperature τm on the side walls (only the upper right location is shown), and τs at the middle of the sides. Maximum or minimum temperatures occur at these locations.

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