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Research Papers: Natural and Mixed Convection

# Characteristics of Rayleigh–Bénard Convection in a Rectangular Channel With an Inner Hot Circular Cylinder

[+] Author and Article Information
Changyoung Choi

School of Mechanical Engineering,
Pusan National University,
Busandaehak-ro 63beon-gil, Geumjeong-gu,
Busan 609-735, Korea

Man Yeong Ha

School of Mechanical Engineering,
Pusan National University,
Busandaehak-ro 63beon-gil, Geumjeong-gu,
Busan 609-735, Korea
e-mail: myha@pusan.ac.kr

Hyun Sik Yoon

Global Core Research Center for Ships
and Offshore Plants,
Pusan National University,
Busandaehak-ro 63beon-gil,
Geumjeong-gu, Busan 609-735, Korea

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received July 15, 2014; final manuscript received May 5, 2015; published online June 9, 2015. Assoc. Editor: Oronzio Manca.

J. Heat Transfer 137(11), 112501 (Jun 09, 2015) (11 pages) Paper No: HT-14-1467; doi: 10.1115/1.4030632 History: Received July 15, 2014

## Abstract

The immersed boundary method (IBM) was used for three-dimensional numerical simulations, and the results for natural convection in a rectangular channel with an inner hot circular cylinder are presented. This simulation used Rayleigh numbers spanning 3 orders of magnitude, from $1×103$ to $1×106$. The Prandtl number considered in this study was 0.7. We investigated the effects of the inner cylinder's radius on the thermal convection and heat transfer in the space between the cylinder and rectangular channel. A map of the thermal and flow regimes is presented as a function of the cylinder's radius and the Rayleigh number.

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## Figures

Fig. 1

Schematic of a rectangular channel with an inner hot circular cylinder (a) and the grid distribution for the representative case R=0.2L(b)

Fig. 2

Schematics of the computational domains for validation test: (a) step I and (b) step II

Fig. 3

Results of validation test with respect to the Rayleigh number: (a) step I and (b)–(d) step II

Fig. 4

Images of three instantaneous isotherms with |θ|≤0.25 (a) and vertical structures with λ2=-0.01 (b) for the rectangular channel without the cylinder. Thermal and flow regimes are denoted under the Rayleigh number.

Fig. 5

Typical results for SS2C regime for Ra=103 and R=0.1L: (a) isotherms with contour values of -0.25, 0, and 0.25; (b) vortical structure with λ2=-0.01

Fig. 6

Typical results for SA2C regime for Ra=104 and R=0.1L: (a) isotherms with contour values of -0.25, 0, and 0.25; (b) vortical structure with λ2=-0.01

Fig. 7

Typical results for SS3C regime for Ra=105 and R=0.3L: (a) isotherms with contour values of -0.25, 0, and 0.25; (b) vortical structure with λ2=-0.01

Fig. 8

Typical results for SA3C regime for Ra=105 and R=0.1L: (a) isotherms with contour values of -0.25, 0, and 0.25; (b) vortical structure with λ2=-0.01

Fig. 9

(a) Time series of instantaneous isotherms with contour values of -0.25, 0, and 0.25; (b) vortical structure with λ2=-0.01 for AC regime for Ra=106 and R=0.1L

Fig. 11

Map of thermal and flow regimes as function of radius of inner circular cylinder R and Rayleigh number Ra (▪: SS2C, □: SA2C, ▴: SS3C, △: SA3C, ○: AC)

Fig. 12

Thermal and viscous boundary layer thicknesses for rectangular channel with inner circular cylinder as function of Rayleigh number Ra

Fig. 10

Typical time-averaged results for AC regime for Ra=106 and R=0.1L: (a) isotherms with contour values of -0.25, 0, and 0.25; (b) vortical structure with λ2=-0.01

Fig. 13

Surface-averaged Nusselt numbers of bottom wall of rectangular channel Nub¯ as function of Rayleigh number Ra: (a) three-dimensional calculation and (b) two-dimensional calculation

Fig. 14

Surface-averaged Nusselt numbers of top wall of rectangular channel Nut¯ as a function of Rayleigh number Ra: (a) three-dimensional calculation and (b) two-dimensional calculation

Fig. 15

Surface-averaged Nusselt numbers of hot circular cylinder Nucyl¯ as a function of Rayleigh number Ra: (a) three-dimensional calculation and (b) two-dimensional calculation

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