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Natural convection of two staggered cylinders for various prandtl numbers and vertical and horizontal pitches

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Abstract

Natural convection heat transfer phenomena of two staggered cylinders were investigated for laminar flows. Numerical simulations were carried out to examine the effect of varying the Prandtl number and the vertical and horizontal pitch-to-diameter ratios for a Rayleigh number of 1.5 × 108 using FLUENT. This study focused on phenomena related to very small vertical pitch. The heat transfer rates of the upper cylinders were influenced by plumes from the lower cylinders, exhibiting preheating, velocity, sweep, and side flow effects. The heat transfer rates of the lower cylinders were not affected by the upper cylinders at moderate vertical pitches. However, when the vertical pitch was very small, they were affected by stagnant flow, sweep, and side flow effects.

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Abbreviations

C p :

Specific heat (J/kgK)

D :

Diameter of cylinder (m)

g :

Gravitational acceleration, 9.8 (m/s2)

h :

Heat transfer coefficient (W/m2K)

k :

Thermal conductivity (W/mK)

Nu D :

Nusselt number (hD/k)

Nu L D :

Nusselt number (hD/k) of the lower cylinder

Nu U D :

Nusselt number (hD/k) of the upper cylinder

Nu S D :

Nusselt number (hD/k) of a single cylinder

P :

Pressure (Pa)

P h :

Horizontal pitch (m)

P v :

Vertical pitch (m)

Pr :

Prandtl number (ν/α)

Ra D :

Rayleigh number (gβΔTD 3/αν)

T :

Temperature (K)

T 0 :

Outer surface temperature of cylinder (K)

T ∞ :

Ambient temperature of fluid (K)

u :

Velocity components in the x-axes

v :

Velocity components in the y-axes

x :

Horizontal direction on Cartesian coordinates

y :

Vertical direction on Cartesian coordinates

α :

Thermal diffusivity (m2/s)

β :

Thermal expansion coefficient (K−1)

θ :

Angular position of cylinder (°)

μ :

Viscosity (kg/ms)

ν :

Kinematic viscosity (m2/s)

ρ :

Density (kg/m3)

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Acknowledgments

This study was sponsored by the Ministry of Science, ICT and Future Planning (MSIP) and was supported by Nuclear Research and Development program grant funded by the National Research Foundation (NRF) (Grant code: 2013M2A8A2025997).

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Authors and Affiliations

  1. Department of Nuclear and Energy Engineering, Institute for Nuclear Science and Technology, Jeju National University, #102 Jejudaehakno, Jeju, 690-756, Korea

    Jeong-Hwan Heo

  2. Department of Nuclear Engineering, Kyung Hee University, #1732 Deogyeong-daero, Giheung-gu, Yongin-si, Gyeonggi-do, 446-701, Korea

    Bum-Jin Chung

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  1. Jeong-Hwan Heo
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  2. Bum-Jin Chung
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Correspondence to Bum-Jin Chung.

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Heo, JH., Chung, BJ. Natural convection of two staggered cylinders for various prandtl numbers and vertical and horizontal pitches. Heat Mass Transfer 50, 769–777 (2014). https://doi.org/10.1007/s00231-013-1285-x

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  • DOI: https://doi.org/10.1007/s00231-013-1285-x

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