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Research Papers: Natural and Mixed Convection

Correlating Equations for Laminar Free Convection From Misaligned Horizontal Cylinders in Interacting Flow Fields

[+] Author and Article Information
Massimo Corcione1

Dipartimento di Fisica Tecnica, University of Rome “La Sapienza,” via Eudossiana 18, Rome I 00184, Italymassimo.corcione@uniroma1.it

Claudio Cianfrini, Emanuele Habib, Gino Moncada Lo Giudice

Dipartimento di Fisica Tecnica, University of Rome “La Sapienza,” via Eudossiana 18, Rome I 00184, Italy

1

Corresponding author.

J. Heat Transfer 130(5), 052501 (Mar 27, 2008) (11 pages) doi:10.1115/1.2780183 History: Received March 08, 2007; Revised May 10, 2007; Published March 27, 2008

Abstract

Steady laminar free convection in air from a pair of misaligned, parallel horizontal cylinders, i.e., a pair of parallel cylinders with their axes set in a plane inclined with respect to the gravity vector, is studied numerically. A specifically developed computer code based on the SIMPLE-C algorithm is used for the solution of the dimensionless mass, momentum, and energy transfer governing equations. Results are presented for different values of the center-to-center cylinder spacing from 1.4 up to 10 diameters, the tilting angle of the two-cylinder array from $0degto90deg$, and the Rayleigh number based on the cylinder diameter in the range between $103$ and $107$. It is found that the heat transfer rates at both cylinder surfaces may in principle be traced back to the combined contributions of the so-called plume effect and chimney effect, which are the mutual interactions occurring in the vertical and horizontal alignments, respectively. In addition, at any misalignment angle, an optimum spacing between the cylinders for the maximum heat transfer rate, which decreases with increasing the Rayleigh number, does exist. Heat transfer dimensionless correlating equations are proposed for any individual cylinder and for the pair of cylinders as a whole.

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Figures

Figure 11

Distributions of the ratio Nu2∕Nu0 versus S∕D for the top cylinder of a two-cylinder inclined array at Ra=105 and different tilting angles in the range 0deg<φ⩽15deg

Figure 12

Distributions of the ratio Nu2∕Nu0 versus S∕D for the top cylinder of a two-cylinder inclined array at Ra=105 and different tilting angles in the range 15deg<φ<90deg

Figure 13

Distributions of (S∕D)opt versus φ for Ra=104 and 106

Figure 14

Distribution of the discontinuity angle φ* (in degrees) versus Ra

Figure 15

Distributions of the ratio Nu∕Nu0 versus φ for Ra=105 and S∕D=1.6 and 6

Figure 16

Distributions of the ratio Nu∕Nu0 versus S∕D at Ra=103, 105, and 107 and different tilting angles

Figure 17

Isotherm contour plots for a two-cylinder inclined array at Ra=105, S∕D=3, and different tilting angles

Figure 8

Distributions of the ratio Nu∕Nu0 versus S∕D for a two-cylinder horizontal array at different Rayleigh numbers

Figure 9

Isotherm contour plots for a two-cylinder horizontal array at Ra=105 and S∕D=1.4, 2, and 5

Figure 10

Distributions of the ratio Nu1∕Nu0 versus S∕D for the bottom cylinder of a two-cylinder inclined array at Ra=105 and different tilting angles in the range 0deg<φ<90deg

Figure 1

Sketch of the geometry, coordinate systems, and integration domain (out of scale)

Figure 2

Sketch of the interface between polar and Cartesian discretization grids

Figure 3

Distribution of the average Nusselt number Nu0 versus the Rayleigh number Ra for the single cylinder

Figure 4

Distributions of the ratio Nu1∕Nu0 versus S∕D for the bottom cylinder of a two-cylinder vertical array at different Rayleigh numbers

Figure 5

Close-up of the distributions of Nu1∕Nu0 versus S∕D for the bottom cylinder of a two-cylinder vertical array at different Rayleigh numbers

Figure 6

Distributions of the ratio Nu2∕Nu0 versus S∕D for the top cylinder of a two-cylinder vertical array at different Rayleigh numbers

Figure 7

Isotherm contour plots for a two-cylinder vertical array at Ra=105 and S∕D=1.6 and 3

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