0
Research Papers: Natural and Mixed Convection

# Numerical and Analytical Study of Reversed Flow and Heat Transfer in a Heated Vertical Duct

[+] Author and Article Information
C. S. Yang

Department of Computer Science and Information Engineering, Far East University, Hsin-Shih, Tainan County 744, Taiwan

D. Z. Jeng

Aeronautics Research Laboratory, Chung-Shan Institute of Science and Technology, Taichung, Taiwan

K. A. Yih, Win Aung

Institute of Aeronautics and Astronautics and Center for Micro/Nano Science and Technology, National Cheng Kung University, Tainan 70101, Taiwan

C. Gau1

Institute of Aeronautics and Astronautics and Center for Micro/Nano Science and Technology, National Cheng Kung University, Tainan 70101, Taiwangauc@mail.ncku.edu.tw

1

Corresponding author.

J. Heat Transfer 131(7), 072501 (May 05, 2009) (9 pages) doi:10.1115/1.3109998 History: Received June 21, 2008; Revised February 03, 2009; Published May 05, 2009

## Abstract

Both analytical and numerical calculations are performed to study the buoyancy effect on the reversed flow structure and heat transfer processes in a finite vertical duct with a height to spacing ratio of 12. One of the walls is heated uniformly and the opposite wall is adiabatic. Uniform air flow is assumed to enter the duct. In the ranges of the buoyancy parameter of interest here for both assisted and opposed convection, a reversed flow, which can be observed to initiate in the downstream close to the exit, propagates upstream as $Gr/Re2$ increases. The increase in the Reynolds number has the effect of pushing the reversed flow downstream. Simple analytical models are developed to predict the penetration depth of the reversed flow for both assisted and opposed convection. The models can accurately predict the penetration depth when the transport process inside the channel is dominated by natural convection. Local and average Nusselt numbers at different buoyancy parameters are presented. Comparison with the experimental data published previously was also made and discussed. Good agreement confirms many of the numerical predictions despite simplifications of the numerical process made, such as two-dimensional and laminar flow assumptions.

<>

## Figures

Figure 1

Streamline plots for assisted convection with (a) Re=200, Gr/Re2=100, (b) Re=200, Gr/Re2=400, (c) Re=400, Gr/Re2=100, and (d) Re=400, Gr/Re2=400

Figure 2

Isotherms for assisted convection with (a) Re=200, Gr/Re2=100, (b) Re=200, Gr/Re2=400, (c) Re=400, Gr/Re2=100, and (d) Re=400, Gr/Re2=400

Figure 3

Streamline plots for opposed convection with (a) Re=600, Gr/Re2=−2, (b) Re=600, Gr/Re2=−3, (c) Re=200, Gr/Re2=−3, and (d) Re=200, Gr/Re2=−8

Figure 4

Isotherms for opposed convection with (a) Re=600, Gr/Re2=−2, (b) Re=600, Gr/Re2=−3, (c) Re=200, Gr/Re2=−3, and (d) Re=200, Gr/Re2=−8

Figure 5

(a) Onset of flow reversal for assisted convection and (b) onset of flow reversal for opposed convection

Figure 6

(a) Comparison of the penetration depths calculated using analytical model and the numerical results for assisted convection with Re=200 and (b) comparison of the penetration depths calculated using analytical model and the numerical results for assisted convection with Gr/Re2=500

Figure 7

Comparison of the penetration depths given by the analytical model, the numerical results, and the experimental data for assisted convection

Figure 8

Comparison of the penetration depths given by the analytical model, the numerical results, and the experimental data for opposed convection

Figure 9

(a) Effect of Gr/Re2 on the local Nusselt number distribution on the heated wall at Re=600 for both assisted and opposed convection and (b) effect of Gr/Re2 on the local Nusselt number distribution on the heated wall at Re=200 for both assisted and opposed convection

Figure 10

Effect of Gr/Re2 on the average Nusselt number for both assisted and opposed convection

## Errata

Some tools below are only available to our subscribers or users with an online account.

### Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related Proceedings Articles
Related eBook Content
Topic Collections