Research Papers: Natural and Mixed Convection

Optimizing Laminar Natural Convection for a Heat Generating Cylinder in a Channel

[+] Author and Article Information
Corey E. Clifford

Department of Mechanical Engineering
and Materials Science,
University of Pittsburgh,
636 Benedum Hall,
3700 O’ Hara Street,
Pittsburgh, PA 15261

Mark L. Kimber

Department of Mechanical Engineering
and Materials Science,
University of Pittsburgh,
636 Benedum Hall,
3700 O’ Hara Street,
Pittsburgh, PA 15261
e-mail: mlk53@pitt.edu

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received May 20, 2014; final manuscript received August 29, 2014; published online October 3, 2014. Assoc. Editor: Zhixiong Guo.

J. Heat Transfer 136(11), 112502 (Oct 03, 2014) (11 pages) Paper No: HT-14-1328; doi: 10.1115/1.4028492 History: Received May 20, 2014; Revised August 29, 2014

Natural convection heat transfer from a horizontal cylinder is of importance in a large number of applications. Although the topic has a rich history for unconfined cylinders, maximizing the free convective cooling through the introduction of sidewalls and creation of a chimney effect is considerably less studied. In this investigation, a numerical model of a heated horizontal cylinder confined between two vertical adiabatic walls is employed to evaluate the natural convective heat transfer. Two different treatments of the cylinder surface are investigated: constant temperature (isothermal) and constant surface heat flux (isoflux). To quantify the effect of wall distance on the effective heat transfer from the cylinder surface, 18 different confinement ratios are selected in varying increments from 1.125 to 18.0. All of these geometrical configurations are evaluated at seven distinct Rayleigh numbers ranging from 102 to 105. Maximum values of the surface-averaged Nusselt number are observed at an optimum confinement ratio for each analyzed Rayleigh number. Relative to the “pseudo-unconfined” cylinder at the largest confinement ratio, a 74.2% improvement in the heat transfer from an isothermal cylinder surface is observed at the optimum wall spacing for the highest analyzed Rayleigh number. An analogous improvement of 60.9% is determined for the same conditions with a constant heat flux surface. Several correlations are proposed to evaluate the optimal confinement ratio and the effective rate of heat transfer at that optimal confinement level for both thermal boundary conditions. One of the main application targets for this work is spent nuclear fuel, which after removal from the reactor core is placed in wet storage and then later transferred to cylindrical dry storage canisters. In light of enhanced safety, many are proposing to decrease the amount of time the fuel spends in wet storage conditions. The current study helps to establish a fundamental understanding of the buoyancy-induced flows around these dry cask storage canisters to address the anticipated needs from an accelerated fuel transfer program.

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Fig. 1

Schematic of problem geometry and pertinent definitions

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Fig. 2

Boundary conditions for simplified computational geometry

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Fig. 3

Mesh layout for low (left) and high (right) density computational grids (C = 2.00)

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Fig. 4

Relative error (%) between medium and high-density grids for temperature (top) and velocity magnitude (bottom) (C = 18.0 and RaD = 105)

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Fig. 5

Isothermal (top) and isoflux (bottom) cylinder localized Nusselt numbers (C = 18.0)

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Fig. 6

Average Nusselt number versus Fand-Brucker correlation (11): isothermal cylinder (C = 18.0)

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Fig. 7

Dimensionless temperature (φ) distributions: isothermal cylinder (C = 18.0 and RaD = 105)

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Fig. 8

Dimensionless radial velocity (vr') distributions: isothermal cylinder (C = 18.0 and RaD = 105)

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Fig. 9

Contour plots for dimensionless temperature (φ, top) and normalized radial velocity (vr', bottom) (C = 18.0 and RaD = 105)

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Fig. 10

Average Nusselt number confinement effect for isothermal (top) and isoflux (bottom) cylinder

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Fig. 11

Effect of confinement on local Nusselt numbers (Nuθ) for Rayleigh number of 105: isothermal (top) and isoflux (bottom) at C = 1.125, 1.250, 1.375, and 18.0

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Fig. 12

Dimensionless temperature (φ) contours for isothermal (top) and isoflux (bottom) cylinders; (C = 1.125—left; C = 1.250—left-center; C = 1.375—right-center; C = 18.0—right; and Ra = 105)

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Fig. 13

Numerical optimum average Nusselt number values with proposed correlation (top: Eq. (15) and bottom: Eq. (16))




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